Lecture Note No - University of Western...

Macroeconomics 41 Chapter III. Keynesian Cross Diagram

III. Keynesian Cross Diagram 1. IntroductionWhat determines GDP in an economy? Keynes says that the actual or equilibrium national income is not necessarily equal to the maximum potential output (full employment income). The question is what prevents us from enjoying the full employment income?

This is a simple Keynesian Model of Income Determination. It is ‘simple’ in the sense that it does not have the money market, and all the consequent implications and complications: For instance, there is no Crowding Out of government expenditure policy. We will introduce the money market in the next chapter.

Within this chapter, depending on the specifications of components of aggregate expenditures, there are three different cases; Case 1 has just lump-sum taxes; Case 2 has proportional as well as lump-sum taxes; Case 3 has imports and exports as well as proportional taxes.

2. Basic Principle (Strategy for Solving for Y*)

Always go through the following steps to solve for Y*:

Step 1. Spell out the Aggregate Supply side income; YS (=W+R+I+P+D) = Y (=C+S+T).

Step 2. Spell out Aggregate Expenditure side income; AE = C + I + G + X-M.

And, then Substitute the functional specifications given by the question for the variables C,I,G, X-M, and rewrite it in the form of AE = A + B Y, where A and B are specific (constant) numbers.

Step 3. At the equilibrium, we know S=D and that here YS = AE.Y = C + I + G + X-M, or Y = A + B Y.Therefore

where B is the slope of Aggregate Expenditure curve, and A is a set of Autonomous Aggregate Expenditures.

Note that B has the terms that are associated with Y and A has a set of variables independent of Y.

Step 4. From the above equation, get the first derivatives of various components of A;

3. Case 1: T = T0

Basic Assumptions

i) No money market; No inflation (price level is fixed);ii) All taxes are lump-sum or of a fixed amount.iii) There are no exports or imports (closed economy).

P (the price level) is assumed to be fixed because

a) we are dealing with short-run, where prices are inflexible;

b) we have unemployment situation. So an increase in demand would lead to the increase in production/output, not inflation;

Producers would not have any difficulties in increasing output fairly quickly without raising the costs or prices; there are idle capacities of capital and equipment. It is almost costless to bring them into production. And unemployed labour forces are standing by and are willing to be hired for pittance.

c) Y (= y) adjusts rather than P with the change of Demand.

d) All variables, such as consumption, investment, and government expenditure, are expressed in real terms. There is no distinction between real and nominal magnitude as the price level is fixed. The interest rate here is the real interest rate.

1) Supply Side

YS (=W+R+I+P+D) = Y(=C+S+T)

(Interpretation) The value of supply of final goods and services (=YS) will be paid out to households (in the forms of W, R, I, P, D) to become national income (=Y). It will be disposed of by the households either in consumption, savings, or taxes.

Graphically, in a quadrangle with YS on the vertical axis and Y on the horizontal axis, the 45 degree line from the origin represents the supply side of national income.

The horizontal distance from the origin to point A is equal to the vertical distance from the origin to point B on the 45 % line. It has a degree of 1. YS = Y. The line can be nothing but a 45 degree one as the firms pay out to households all of what they earn from production.

2) Demand Side: Aggregate Expenditure

(1) Consumption Function

Keynesian Consumption function:

C = C0 + c1 Yd, where Yd is disposable income, or Yd = Y-T.

For simplicity, let us assume that T = T0 independent of income level, or that all taxes are lump-sum.

What is the constraint on the value for C0 and c1 respectively?

C0 is a basic consumption regardless of income level;

Macroeconomics 41 Chapter III. Keynesian Cross Diagram c1 is the Marginal Propensity to Consume.

0< c1<1; MPC measures how much of an increase in income will be consumed. The consumption increases as income increases (>0), but is not increasing as fast as income is (<1).

Graphically, c1 or MPC is the slope of the consumption curve drawn with C on the vertical axis and Y on the horizontal axis;

C = C0 + c1 (Y-T)

= {C0 – c1T} + c1 Y

Average and Marginal Propensity to Consume;

(Definitions)

Let's quote Keynes' explanation of MPC;

"The fundamental psychological law is that men are disposed, as a rule and on average, to increase their consumption as their income increases but not by as much as the increase in income."

(Questions)

What is MPC at y1 and y2 respectively?What is APC at y1 and y2 respectively?

Graphically, the MPC is the slope of the consumption curve, and is constant everywhere on the straight line of the consumption curve regardless of the level of income.

The APC is the slope of the line linking the origin and the point of interest on the consumption curve (= tangent of the angle Theta). APC at y1 is given by the slope of a hypothetical line linking the origin and point A. APC at y2 is equal to the slope of the imaginary line liking the origin and point B. The flatter is a curve, the smaller its slope will be. So APC at y2 is smaller than APC at y1; the APC decreases as the national income level increases.

Also, naturally APC > MPC holds at all income level.

(2) Investment

Demand for addition to fixed capital formation and a voluntary addition to inventory.

I is for now assumed to be exogenous, such as

I = I0;

What it means is that we are assuming that investment is geared to long run; entrepreneurs make investment decision based on expected future income which is independent of current income.

Macroeconomics 41 Chapter III. Keynesian Cross Diagram Even if the current income is very low, when there is a prospect that the demand for their goods will increase in the future, they will be engaged in the expansion of production facilities.

Naturally, the dependence of investment on expectations makes investment very volatile. What will be the impact on the output or income? As the expectations or business outlook changes, investment decision will vary. The expectations and business outlook are very much affected by rumours, fear, etc aroused by unexpected events. Would such variations in investment lead to smaller or larger changes in output than the changes in investment itself?

(3) Government Expenditures

G = G0.

Numerical Example: G= 150

(4) Foreign Sector

Let us assume that X-M = 0 for simplicity.

(5) Aggregate Expenditures

Macroeconomics 41 Chapter III. Keynesian Cross Diagram AE = C + I + G + (X-M);

Suppose that specifications of each variable are given as follows;

C = C0 + c1 (Y-T)

= C0 - c1 T + c1 Y;

I = I;

G = G;

X-M = 0 for simplicity.

Substituting the above specifications for the variables in the equation, we get

AE = C + I + G + X-M

Note that I,G,C in the first equation are variables, and I,G in the second ones are numbers or specific values

AE = C0 – c1 T0 + I0 + G0 + c1 Y intercept slope

AE consists of two parts; one is independent of Y or national income, and the other dependent on Y. The first is called `Autonomous Aggregate Expenditures, and the latter `Induced Aggregate Expenditure.'

AE = Autonomous AE + induced AE

= A + B Y,

where A = C0 – c1 T0 + I0 + G0, and B = c1.

Note that the slope of the Aggregate Expenditure curve is equal to that of the consumption curve and the MPC = c1.

3) Equilibrium Y*

(1) Graphic Solution

(2) Algebraic Solution

Step 1: YS = Y; Supply side.

Step 2: AE = C+I+G+X-M; Demand side.

By substituting the functional forms, given by the question, for C,I,G,X-M, and rewriting it, we get

AE = {C0 – c1 T0 + I0 + G0} + c1 Y, or (X – M = 0)

= A + B Y, where A and B are numbers.

Step 3: YS = AE at equilibrium, so

Y* = {C0 – c1 T0+ I0 + G0} + c1 Y* Solving for Y*, we get

The above is the equilibrium national income equation. If we know the values for C0, c1, T0, I0, and G0, we can get the numerical value for Ye.

(3) The Equilibrium Condition

YS = Y = C + T + S

AE = C + I + G + X-M

Equilibrium Condition S + T = I + G + X-M ; .Without government and foreign sector, S = I.

S = I + (G-T) + X-M suggests that the private sector has three ways of disposing its savings; by lending to the business sector which uses the funds for investment. By lending to the government which uses the funds for financing the government deficits. By lending to foreigners who would buy more goods and services from us than we are buying from them.

4) Comparative Statics

No change in the supply side or YS can alter the equilibrium national income.

Only change in the demand side or AE can do so. (Keynesian Idea)

AE = C0 – c1 T0 + I0 + G0 + c1Y = A+BY = Autonomous AE + Induced AE

Alternatively, when we draw the above AE curve with Y on the horizontal axis, we get

(1) Increases in Autonomous AE; changes in the intercept of the AE curve.

The vertical shift of the AE curve brings about the horizontal changes in Y*. The ratio of the (horizontal) change in Y* to the (vertical) change in the AE is given by a `(generic) multiplier', and is equal to one over one minus the slope of the AE curve. The slope of the AE curve is equal to that of the consumption curve in this particular case;

If all taxes are lump-sum, the slope of the consumption curve is equal to MPC or c1. So the multiplier is 1/(1-c1).

If there is a tax proportional to income, then the slope of the consumption curve is equal to c1 (1-t1) where t denotes the tax rate. The multiplier is equal to 1/{1-c1(1-t1)}.

Slope (B) : c1

Intercept (A): C0 – c1 T0 + I0 + G0;

(2) Individual Multipliers

What constitutes the intercept? - The components of the intercept {C0 – c1T0 + I0 + G0 + X0-M0}, that is, C0, T0, I0, G0, and X0-M0, are the components of `Autonomous Aggregate Expenditures'. Changes in autonomous expenditures are illustrated by changes in the intercept of the AE curve. These changes in the intercept shift up or down the AE curve in a parallel way. Then there will be resultant changes in Y* (given by the intersection of AE and YS=Y curves. The resultant

Graphic Proof of Multiplier: We are interested in getting the ratio of ΔY* to ΔAE. First, along the YS=Y curve, the slope is a unit. So ΔY = A = B. The AE and AE' are parallel. Let us called B minus ΔAE `C'; C = B-ΔAE. The slope of the AE curve is C over A by definition. This is equal to c1.

Macroeconomics 41 Chapter III. Keynesian Cross Diagram changes in Y* is usually larger than the initial changes in AE. Therefore any change in the intercept will bring about the multiplier effect on national income.

C0: determined by consumers. I0: determined by firms.

G0 and T0: determined by government. A set of rules determining the level and changes in G0 or T0 is called fiscal policy.

X-M: determined by foreign sector.

The multiplier for each component can be obtained by differentiating the equilibrium national income equation with respect to the variable of Autonomous Aggregate Expenditure: A multiplier of a variable should be equal to the coefficient of the variable in the equilibrium national income equation.

Note that all multipliers but the tax multiplier one is equal to 1/1-c1.

Macroeconomics 41 Chapter III. Keynesian Cross Diagram a) Changes in C0, I0, and/or X0-M0 can cause a change in national income. C0 varies over time; I0 is even more volatile. These changes are beyond control by government; they constitute shocks to aggregate expenditures. Changes in I0 are magnified into larger changes in Y through the multiplier. If the changes are cyclical, there occurs a business cycle.

Government may try to counter the changes in the AE due to changes in C0, I0 or X0-M0 by adjusting T 0and G0 in the opposite direction by the same amount. If the changes in AE are successfully ironed out in this manner, there would not be any change in Y*; when I is decreasing, government increases G and thus AE is held constant and so is the national income. This kind of government policy is called `Counter-Cyclical Fiscal Policy.' Can government actually fine-tune the economy in this fashion? The answer is rather negative mainly because of Time-lags.

b) An increase in G0 ( Δ G 0):

ΔY* = 1/(1-c1) ΔG0

ΔG0= k ΔY* = 1/(1-c1) ΔY*

Example) c1 = 0.75, and all taxes are lump-sum. Government is increasing its expenditure on final goods and services by $ 5 billion. What is the resultant increase in the national income?

The government expenditure multiplier is 1 over 1 minus 0.75, that is, 4. So ΔG will be multiplied into ΔY* by the factor of 4; k = 4. Therefore, ΔY* = 4 ΔG= 4 times $ 5 billion = $ 20 billion.

c) An increase in T ( Δ T 0) leads to a decrease in Y *. ΔT = k ΔY* = - c1/(1-c1) ΔY*

An increase in T will lead to a decrease in Disposable Income by ΔT 0 (note it does not increase Y for now); in Yd = Y - T, 0 ΔT 0= - ΔYd. The decrease in disposable income by dT will decrease consumption only by c2 ΔT0 (a MPC fraction of changes in disposable income = changes in consumption). This is shown as shift up of the intercept of the consumption curve and thus AE curve;

ΔT0 -ΔYd = -ΔT0 -ΔC = c1 x (-ΔYd) = -c2 ΔT0 =ΔAE (< -ΔT0)

This change should be classified as Autonomous, so there is multiplier effect to this increase in consumption;

ΔY* = k ΔAE= (1/(1-c1)) (-c1 ΔT0) = -c1/(1-c1) ΔT0.

Note that when taxation is increased by say, $1, the AE curve does come down vertically by less than $1; In other words, one dollars increase in taxes will bring about a less-than-one-dollar -decrease in consumption or AE.

d) Balanced Budget Multiplier;

Suppose government increases G by 1 billion dollars and at the same time taxes by 1 billion dollars. What happens to the National Income?

From (1) and (2), in this case, there are two forces working in opposite directions; ΔG brings about an increase in income and ΔT a decrease in income. However, the first is larger in its impact on Y* than the second, and thus there is a net positive increase in income. The increase in Y* is equal to the magnitude of operation, that is, the increase in government expenditure or taxation. In other words, if government expenditure is increased by ΔG and at the same time

Macroeconomics 41 Chapter III. Keynesian Cross Diagram taxes are increase by ΔT where ΔT = ΔG, then ΔY= 1 ΔG= 1 ΔT. Balanced budget multiplier is 1 regardless of what the MPC is.

Proof 1 of Balanced Budget Multiplier being equal to one

Government increases G and T at the same time by the same amount, say, $1. We can think of the government operation as a sequence of two separate actions.

First, government increases its expenditure by $1. This pushes the AE curve upward by $1.

Second, government increases taxation by $1. This pushes the AE curve down by less than $1; people are taxed $1 more, and their disposable income decreases by $1. But the decrease in consumption will be less than $1; it will be a fraction of $1. They spend $ c 1 (<$1) less than before. So the decrease in AE is $ c1.

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Combining the first and second changes in AE, there occurs a positive net increase in AE by 1-c1. We know that a $1 increase in AE will lead to an increase in the equilibrium national income by the factor of a multiplier k = ΔY* /ΔAE= 1/(1-c1); the net increase in AE by 1-c2 will lead to an increase in Y* by k time 1-c1 = 1/(1-c1) x 1-c1 = 1. The increase in G accompanied with an equal amount of increase in T will lead to an equal amount of increase in Y *. If G and T are increased by say, $50 billion, then Y* will increase by $50 billion.

Proof 2 of BBM =1 in Case 1 In this case, government increases G and T at the same time and by the same amount. Therefore, the resultant Balanced Budget Multiplier is a combination of the government expenditure and tax multipliers:

ΔY/ΔG= 1/(1-c1) = government expenditure multiplier;

An increase in G by 1 billion increases income by 1/1-c1.

ΔY/ΔT = -c1/(1-c1) = tax multiplier;An increase in T by 1 billion decreases income by c1/1-c1.

Combined Effect on income = 1/(1-c1) – c1/(1-c1) = 1.

ii) Change in the slope of the AE curve, which is equal to the slope of the consumption curve and MPC.

The larger MPC, the larger Y* and the larger K will be:

AS the MPC increases not only the income level but also the multiplier will increase.

i) As c1increases, Y * increases.

The larger MPC leads to a steeper AE curve and a larger Y*.

ii) the larger MPC is, the larger the multiplier will be.

4. Generalization of Keynesian Cross-Diagram of Income Determination

Recall Case 1: We have so far examined the case where all taxes are lump-sum; T= T0

Case 2: Now there are two kinds of taxes. The one is fixed or lump-sum, and the other is proportional to the income level; T= T0 + t1 Y.

Step 1: Supply Side: YS = Y

YS = (W + R + I + P) = Y ( = C + S + T) ; Supply Side

Step 2: Demand Side: AE = C + I + G

= C0 + c1 Yd + I 0 + G 0 ; Yd is disposable income

= C0 + c1 (Y - T) + I0 + G0 ; Yd = Y - T

= C0 + c1 {Y - (T0 + t1 Y)} + I0 + G0 ; recall T = T0 + t1 Y

= Co + c1 Y - c1 T0 - c1 t1 Y + I0 + G0 ; expand the bracket

= C0 - c1 T0 + I 0 + G0 + c1 Y - c1 t1 Y ; separate Y terms

= C0 - c1 T0 + I0 + G0 + (c1 - c1 t1) Y ; factor Y out

= C0 - c1 T0 + I 0 + G0 + c1 (1 - t1) Y ; factor c out

Step 3. At equilibrium, Y = AE and thus

Y* = C0 - c1 T0 + I0 + G0 + c1 (1 - t1 ) Y*

{1 - c1(1 - t1 )} Y* = C0 - c1T0 + I0 + G0 ; transpose Y to the left

Step 3: Equation

Step 4: Multipliers

The multiplier of a particular variable is obtained by differentiating the above equilibrium national income equation with respect to that variable.

What are the multipliers for the autonomous consumption and the autonomous investment?

The slope of the consumption curve is smaller in this case with proportional taxes than the case without them; c2 (1-t) < c2. The consumption curve is flatter.

We know that the slope of the AE curve is the same as the consumption curve. Thus, we can predict that the multiplier will be smaller in this case than in the case without proportional tax.

What are the multipliers for government expenditures and lump-sum taxes? (Fiscal Policy)

What is the multipliers for a balanced budget multiplier for the case where an increase in government expenditures is financed by an increase in lump=sum taxes?

Is this equal to one?

What if the government does not increase T0 not by the full amount of ∆G0 in the first round but makes the overall increase in T equal to ∆G0?

Eventually the proportional tax revenues for the government will rise as the new equilibrium national income rise over time: In T = T0 + t1 Y, overall T increases as Y rises.

Thus in this case, the increases in proportional taxes resulting from increases in Y supplement the initial increase in lump-sum taxes. BBM is equal to one in this case. The result is the same as the previous Keynesian balanced budget multiplier as long as the change in the tax revenue is made by lump-sum taxes.

Proof:

Suppose that G0 = T = 1. We know that T = t1 Y; T t1 Y = 1 t1 Y

Remarks: Here again, we may note that the government expenditure multiplier is smaller

with proportional taxes than otherwise; For a given vertical shift-up of the AE curve (due to an increase in G), the resultant ∆Y* will be smaller with a flatter AE curve than a steeper AE curve. When the income tax rate increases, the national income will be smaller, and the impact of an increase in G will be smaller, too.

I0 and C0 exhibit cyclical movement over time, depending on, for instance, investors’ assessment of business outlook and consumer confidence. They are not directly controllable by the policy-makers. Their multipliers are the factor by which cyclical changes in basic consumption C0 and autonomous investment I0 are magnified into larger fluctuations in the equilibrium national income. Therefore, the multipliers associated with the above two variables have something to do with business cycles.

We also have noted that these multipliers are smaller for the case with proportional taxes than for the cases without proportional taxes (thus with only lump-sum taxes). With the presence of proportional taxes such as income taxes, the impact of cyclical changes in C0 and I0 on national income will be smaller than in the case with only lump-sum taxes. Therefore the proportional tax system is called an ‘Automatic or Built-In Stabilizer’.

When national income increases in a booming stage, the proportional taxes increases too. This will in turn decrease the disposable income and the aggregate expenditures to a certain extent. And thus the overall increase in national income will be moderated. When income decreases in recession, the proportional taxes will also decrease. Thus there will be a boost to disposable income and consumption. It will offset the initial decrease in Y*. The overall decrease in national income will be moderated. All in all, business cycles will be smaller with the proportional taxes.

Case 3: There are imports proportional to national income:

Case 3 is built upon Case 2. There are two kinds of taxes. The one is fixed or lump-sum, and the other is proportional to the income level; T = T0 + t1 Y

T =T0 + t1 Y; and

AE = C + I + G + X – M.

The Aggregate Expenditures will have one additional element such as

NX = X – M;Net exports = Exports – Imports.

X = X0 …………(1)Exports are the demand for our domestic products by foreign countries. The exports are given and thus exogenous from the viewpoint of our economy: The domestic country has no control over the exports. The national income of the foreign countries is the major determinant of our exports to them.

M = M0 + m1 Y, …………(2)where M0 is the basic import, and m1 is the Marginal Propensity to Import (MPI).

Solution for Y*:

Step 1. YS = (W + R + I + P) = Y ( = C + S + T)

he import demand for foreign goods is the function of the entire national income, not just the disposable income portion of it. This contrasts with the consumption function where the consumption is a function of the disposable income. In the case of imports, there are two agents of imports: The one is the private sector whose imports are based on the disposable income. The other is the government whose imports are based on tax revenues. Thus, the total imports are a function of disposable income plus taxes, the sum of which is the national income itself.

Step 2. AE = C + I + G + X - M

= C0 + c1 {Y - (T0 + t1 Y)} + I0 + G0 + X0 - (M0 + m1 Y)

= C0 + c1 Y - c1 T0 - c1 t1 Y + I0 + G0 + X0 - M0 - m1 Y

= C0 - c1 T0 + I0 + G0 + X0 - M0 + c1 Y - c1 t1 Y - m1 Y

= C0 - c1 T0 + I0 + G0 + X0 - M0 + (c1 - c1 t1 - m1) Y

= C0 - c1 T0 + I0 + G0 + X0 - M0 + {c1 (1 - t1) - m1} Y

Step 3. At equilibrium, Y = AE and thus

Y* = C0 – c1 T0 + I0 + G0 + X0 - M0 + {c1 (1 - t1) - m1} Y*

{1 - c1 (1- t1) + m1} Y* = C0 - c1 T 0+ I0 + G0 + X0 - M0

Step 4. Multipliers – Comparative Static

The multipliers for autonomous expenditures can be obtained by differentiating the above equation with respect to C0, T0, I0, G0, X0, and M0 respectively.

Remarks:

The multipliers are still smaller in this case than in all the previous cases; the existence of m1 further reduces the magnitude of the multiplier. The open economy (with international trade) has a smaller multiplier than the closed economy. The more open the economy, the smaller the multiplier.

The smaller magnitude of the multipliers are "mixed blessings", being good and bad.

A small open economy has a larger value for m1 than a large country or a closed economy.

Show the impact of a $1 increase in government expenditures on the equilibrium national income and on the import, when (1) c1 = 0.8; t1 = 0.5; m1=0.3, which may be the case for a small open economy, and when (2) c1 = 0.8; t1 = 0.5; m1=0.1, which may be the case for a large and less-open country, respectively. Prove numerically that in a small open economy, compared to a large less-open economy, an increase in government expenditures has smaller impact on the national income but a larger impact on the import thus on the trade balance.

We also know that the balanced budget multiplier is the sum of the government expenditure multiplier and the tax multiplier. Specifically, what will be the balanced budget multiplier if initially an increase in government expenditures is financed only by an increase in lump-sum taxes or ∆ T0

, if ↑ => total value of ↓, if m = 0,

=> very large multiplier => larger business cycle.

Macroeconomics 64 Chapter III. Apendix

Appendix for Chapter III.

1. Numerical Examples:

A question will specify the functional forms for consumption, investment, government expenditure, and net exports.

What you should do is

Step 1: Write down YS [=(W+R+I+P+D)+IT] = YStep 2: Write down AE = C + I + G + X-MStep 3: Invoke the equilibrium condition,

YS = AE or Y = C + I + G + X-M

Step 4: Substitute the given functional forms for the variables C,I,G, and X-M in the above equilibrium equation.

Step 5: Solve for Y* by rearranging and rewriting the equation.

(Question 1) In a simple economy without government or foreign sector, the consumption and investment functions are given as follows. Get the equilibrium national income.

C = 40 + 0.8 YI = 60

(Solution)As there are no government or foreign sector, there is no G, T, or X-M.

Step 1: YS = YStep 2: AE = C + I Step 3: At Equilibrium, Y = C + I (Note there is no G or X-M)Step 4: Substitute C = 40 + 0.8 Y (Note that YD = Y as T = 0), and I = 60 for C and I in the

equilibrium equation, and thus get Y = 40 + 0.8 Y + 60

Step 5: Sending all the terms involving Y to the left hand side of the equality, we get

Y - 0.8 Y = 40 + 60 0.2 Y = 100

Therefore, Y = 100/0.2 = 500.

(Question 2) Now in a little more complex economy with government and foreign sector, the consumption, investment, government expenditure, taxation, and net exports function are given as follows. Get the equilibrium national income.

C = 50 + 0.75 Yd; Yd = Y - TI = 70G = 120T = 100; all taxes are lump-sum.X-M = 0

Step 1: YS = YStep 2: AE = C + I +G + X-MStep 3: At Equilibrium, Y = C + I + G + X-MStep 4: Substitute C = 50 + 0.75 (Y-T) = 50 + 0.75 (Y-100),

I = 70, G = 120, and X-M = 0 for C, I , G , X-M in the above equation, and get

Y = 50 + 0.75 (Y-100) + 70 + 120

Step 5: Sending all the terms involving Y to the left hand side of the equality, we getY - 0.75 Y = 50 - 75 + 70 + 120 0.25 Y = 165

Therefore, Y = 165/0.25 = 660//.

(Question 3) If taxes are proportional to income and thus T = 0.6 Y instead of T = 100, and all other things are identical to the above economy, what is the equilibrium national income?

Step 1: YS = YStep 2: AE = C + I +G + X-MStep 3: At Equilibrium, Y = C + I + G + X-MStep 4: Substitute C = 50 + 0.75 (Y-T) = 50 + 0.75 (Y-0.6Y) = 50 + 0.75 (1-0.6) Y, I = 70,

G = 120, and X-M = 0 for C, I , G , X-M in the above equation, and get

Y = 50 + 0.75 x 0.4 Y + 70 + 120

Step 5: Sending all the terms involving Y to the left hand side of the equality, we getY - 0.75 x 0.4 Y = 50 = 70 + 120 0.7 Y = 240

Therefore,Y = 240/0.7 = approx. 343//.

(Question 4)

C = C + c2 (PDI) = 50 + 2/3 PDII = 70G = 120T = 100

(1) What is the equilibrium level of national income (Y*)?(2) What is the consumption at the equilibrium?(3) What is the Saving at the equilibrium?(4) What is the APC ?

(Solution)

First, it is important to figure out what to invoke to get the equilibrium, which is not given in the question.

Step 1. YS = Y = C + S + T

Step 2. AE = C + I + G= C0 + c1 (Yd) + I + G= (C0 + c1 Y - T) + I + G= 50 + 2/3 (Y - 100) + 70 + 120

Step 3. At equilibrium YS = AE, thereforeY* = 50 + 2/3 (Y*- 100) + 70 + 120 (Y becomes Y* now)

Putting all the terms involving Y on the left-hand side of the equation, we getY* - 2/3 Y* = 50 - 2/3 x 100 + 70 + 120.1/3 Y* = -2/3 x 100 + 240Y* = $ 520 billion.

C = 50 + 2/3 (Y - T) = 50 + 2/3 (520 - 100)= 330.

APC = C/PDI = 330/(520-100) = 33/42

S = Y - T - C = 520 - 100 - 330 = 90.

We can double-check the equilibrium; At equilibrium, S + T = I + G; the left hand side in this case is 90 + 100 =190, and the right hand side in this case is 70 + 120 = 190. Here the left hand side = the right hand side. So we can be reassured that this is an equilibrium.

(5) What will happen to Y* when the government simultaneously increases government expenditure and tax by an equal amount, 60 billion dollars? Now T = 160, and G = 180 billion dollars.

Solution:

YS = YAE= C + I + G

At the equilibrium, Y* = C + I + G;We substitute the above given functions of C, I, and G for the variables of C, I, and G.

Y* = 50 + 2/3 (Y* - 160) + 70 + 180

Y* = 580 (billion dollars)

Alternatively, we can answer the above question as follows;this is a case for the balanced budget multiplier where the increase in government expenditure (G) is accompanied by the equal amount of increase in tax (T), and thus the balance of the government budget does not change; ΔG= ΔT. The balanced budget multiplier dictates that an increase in G accompanied by an equal amount of increase in T will add itself, nothing more or nothing less, to national income. In other words, the balanced budget multiplier is one. So ΔY= 1 x ΔG. With a $1 billion of increase in G accompanied by an $1 billion of increase in T will lead to an $ 1 billion of increase in Y*. ΔG= $ 60 billion, so Y* will increase by $ 60 billion from $ 520 billion to $ 580 billion.

2. Criticism against Balanced Budget Multiplier (A Monetarists' view of government fiscal policy)

1) Nonsensical Implication of the Keynesian Balanced Budget multiplier.

When government takes away $100 billion from the private sector in the form of taxation and puts it back to the economy through its expenditure, there should be an increase in income by $100 billion.

Ow! Thus it seems that you are pulling yourself up by your own bootstraps; you are increasing Y by 1 at no real cost by simply shifting resources from consumer to government.

In a hidden way, the MPC associated with government expenditure is regarded as 1, while the MPC associated with consumption expenditure is regarded as less than one. It is related to the way G is evaluated, i.e. on the cost (expenditure) basis; whenever there is an increase in G, it will be counted in national income to the full (all of government expenditure is regarded as the production of final goods).

2) Basic Tenet:"There is no such a thing as free lunch."It seems strange that an increase in G should have a multiplier effect on income.

Contention: To the extent that government expenditures are on intermediate goods, the balanced budget multiplier is less than one.

Indeed, in a special case, the Balanced Budget Multiplier may be zero.

3) Review of Multipliers

(we have already seen the illustration, which is also in the textbook in a great detail)

Remember the illustration of multiplier.Increase in Autonomous Expenditure/Aggregate Demand______________________________________________________Period Increase in Increase in Increase in

Demand Production Income______________________________________________________1 ΔAE ΔAE ΔAE

2 c1 ΔAE = c1 ΔAE = c1 ΔAE

3 c12 ΔAE c1

2 ΔAE c12ΔAE

4 c13 ΔAE c1

3 ΔAE c13 ΔAE

___________________________________________________. .. .

. . . .

The cumulative sum of the increases in income is

ΔY = ΔAE+ c1ΔAE+ c12 ΔAE+ c1

3 ΔAE.........

= ΔAE (1 + c1 + c12 + c1

3 ...........)

= 1 ---- ΔAE

= multiplier x ΔAE

Note: If there is no net increase in AE in the first round (ΔAE= 0), there would not be anything which can bring about the multiplier effect; ΔY= k x 0 = 0.

Balanced Budget Financing Re-examined;

Government increases government expenditure (G) and at the same time increases tax (T) by an equal amount; ΔG = ΔT > 0.

If there is $ 1 billion of increases in G (Δ G = $ 1 billion), now it is assumed that there is $ 1 billion of increases in aggregate expenditures in the first round. On the other hand $ 1 billion increase in tax leads to a decrease in consumption by "c1 (MPC)" fraction of $ 1 billion because $ 1 billion increase in tax decreases personal disposable income by $ 1 billion, and the resultant consumption would decrease by c2 x $ 1 billion. In the equation of AE for the first round, in AE + Δ AE = C + ΔC + I + G + ΔG, ΔG= $ 1 billion, and Δ C = c1 x $1 billion, and thus net change in ΔAE = $ (1 – c1) billion. This is a net increase in AE, the parallel shift-up (an increase in the intercept) of aggregate expenditure curve. This parallel shift-up of $(1-c1) billion brings with it the multiplier effect (by k times ΔAE) as going through the second, third...... rounds. The resulting total cumulative increase in national income will be ΔY* = ΔAE x k = (1-c1) x 1/(1-c1) = 1.

4) A Correct National Income Accounting Identity without Double Counting

We should note the present inappropriate Definition of National Income;In the conventional national income accounting system,

AE = C + I + G + X-M;

However, erroneously, we regard all government expenditure as increasing aggregate expenditure or national income. But parts of government expenditures are on intermediate goods (eg. J. Carr's example of a shoe factory's road).

But only part of ΔG, the portion of government expenditure on final goods should be included in the 'correct' national income; In Canada 77% of ΔG are on final goods.

The correct national income account should be

AE = C + I + 0.77 G in Canada.

5) A Correct Balanced Budget Multiplier

When government increases its expenditure and taxation by the equal amount; ΔG= ΔT. Then, on the one hand, ΔG increases AE on final goods and services by 0.77 ΔG. On the other hand, ΔT decreases the disposable income by ΔT (ΔYd = -ΔT) and consumption by MPC times the decrease in the disposable income or -ΔT; ΔAE = -c1 ΔT;

AE = C + I + 0.77 G + X-M, and thus AE + ΔAE= C - ΔC + I + G + 0.77 (ΔG); ΔG ΔAE= 0.77 ΔG

ΔT ΔAE= -ΔC = MPC x – ΔYd = -c1 ΔT......(2)

The net change in AE is (1) + (2);Net ΔAE= 0.77 ΔG- ΔC = 0.77 ΔG- c1 ΔT.

As ΔT = ΔG with balanced budget fiscal policy, Net ΔAE= (0.77 – c1) ΔG.

The resultant change in the equilibrium national income is

ΔY= k (multiplier) x ΔAE= (0.77-c1)/(1-c1) ΔG.

The Balanced Budget Multiplier is (0.77-c1)/(1-c1) and smaller than the conventional Balanced Budget Multiplier which is equal to 1 = (1-c1)/(1-c1).

In a very special case where MPC happens to be 0.77, then the BBM = 0.

Balanced Budget Multiplier works through redistribution of income;

Income is redistributed from people whose MPC <1 to government whose MPC is assumed to be 1.

But real MPC of the government on final goods is not one.

You can have a non-zero balanced budget multiplier where expenditures by government are not a take over of private services (i.e., not an intermediate goods, eg. military expenditure)The above case, the only case you can get something for nothing is in the world of rigid prices and unemployed resources.

If national income were to be Y = C + I + G - T, the balanced budget multiplier would be equal to zero. Here all taxes would be regarded as taxes on intermediate goods, thus C > C + cY.

3. Criticism against a Naive View of the role of government

It seems strange that an increase in G should have a multiplier effect on income.

Why can't government expenditure simply be consolidated into the rest of the economy?

-i.e. we cannot view government as a giant corporation which produces goods and services and sells (or gives) them to consumers and is owned by the citizens as shareholders of the country. The corporation (is assumed to) acts in the interests of its shareholders.

It is true and to some extent it is recognized by people making consumption decisions that government expenditures of a consumption nature are of value only the extent that they have a consumption value to individual households and that under full employment the making of either type of expenditure (C or I) reduces the total real resources currently available to households for private consumption and addition to wealth.

If these facts were recognized and given exactly accurate weight by households in every relevant respect, then the government can, without error, be consolidated into the private sector.

From the standpoint of economic analysis there would be no more reason for treating government as an entity separate from the private sector than there would be for treating a company as an entity separate from its shareholders, where the stockholders were in full and knowledgeable control of its own affairs.

The point has generally been overlooked, the government having, habitually, and without justification, been cast in a separate role in effect as if households placed no value whatsoever on the goods and services supplied by government.

The truth may be somewhere between these two extremes.

If households do, after all, value government expenditures as income, as they would (meals supplied without charge at their jobs or other such income in kind) and similarly count in their consumption the consumption component of government expenditures then the consumption function will be

C + Gc = C0 + c1 (Y - T + Gc) = C0 + c1 Y if G = T (balanced budget).

i.e. government expenditure is income in kind. So consumption depends in total income. If people decide to spend money on recreation collectively (i.e. Gc up - parks built) they will spend less in recreation privately. You don't have to go up North for vacation if government builds national park besides you.

Here the changes in (balanced change) Gc have no effect (zero multiplier); balanced budget multiplier = 0 because the decrease in private consumption in C is equal to the increase in Gc. The result for consumption happens because an increase in government consumption(expenditure) will be matched by an equal decrease in private consumption, leaving no net increase in aggregate expenditure. These are same results which would be obtained if government were consolidated in private sector.

A zero multiplier for Gc, though it may appear paradoxical, is not because it simply shifts the composition of total consumption at any given level of income.

We can view the private offset to the consumption supplied by the government as having two components.

(1) those who are taxed to finance reduce their consumption by c2 of the taxes

(2) those who are recipients reduce private consumption by the fraction 1-c2 of their consumption (= regular fraction saved out of any income).

(3) the sum of (1) and (2) is one, giving total re-caution in private consumption = increase in Gc.

To the extent that the above is correct, balanced budget multiplier and the effect of G and T on NI given originally must be modified. We can also extend the above logic to Gc financed by bonds.

Macroeconomics 74 Chapter IV

Chapter IV. The IS-LM Curve Model

We are starting a new paradigm, IS-LM analysis.

The IS-LM curve model gives the equilibrium level of national income (Y*) in a larger setting. We have obtained Y* from the Keynesian Cross Diagram. The equilibrium condition of the goods market will be condensed into a curve of IS. We will introduce the money market; the equilibrium condition of the money market will give a one-line curve of LM. The IS and LM curves are delineated with two explicit variables of national income and interest rates.

In the IS-LM Curve Model, the interactions between the goods (output) market and the financial market gives the equilibrium Y* and the equilibrium interest rate i*.

As this new Y* satisfies the equilibrium condition in the goods market as well as the money market, it is an equilibrium of a broader scope and a higher order.

We still maintain the assumption about the fixed price level: The price level P is assumed to be fixed in the IS-LM model unless it is specified otherwise. This could be reasonable assumption when the actual equilibrium national income Y* is below the full employment national income level Yf. If there is such a buffer, an increase in demand would not push up the price level in any significant way.

1. Introduction

First, we will establish an inverse relationship between interest rates and investment in the goods market. This eventually leads us to the IS curve or the various combinations of i and Y, which satisfy the equilibrium condition in the goods market or make the demand equal to the supply in the goods market.

Second, we will establish an inverse relationship between interest rates and (real) money demand in the money market. This leads us to the LM curve or the various combinations of i and Y, which satisfy the money market equilibrium or make the demand equal to the supply in the money market.

Third, we will solve for the national income Y* and the interest rates i*, which satisfy the goods and money market equilibrium conditions at the same time. Basically, they are obtained from the intersection of the IS and LM curves.

Fourth, we will examine the Crowding-Out effect. An increase in aggregate expenditures will in general be accompanied by an increase in interest rates in the money market. This in turn will have a negative spill-over or feedback to the goods market as an increase in interest rates shaves off investment to an extent. Particularly when ∆G causes an increase in i and a decrease in I, it is called ‘Crowding-Out Effect’ of government expenditures

2. Modification of Investment Function

So far the investment function has been regarded as exogenous: It is determined or given from the outside.

Now let us endogenize the investment by making it a mathematical function of interest rates. The following re-specification of the investment function leads to a new paradigm.How can I establish the inverse relationship between investment I and interest rates i?

1) Marginal Efficiency of Capital Method

Investment is the demand for resources to be used for specific physical additions to the capital stock. An increase in capital stock or investment is expected to yield ‘a stream of net income’ over time. We can find the rate of return, which equates the present price tag of investment project on the left side of the equality and the stream of the expected returns. This rate of return is called ‘Marginal Efficiency of Capital’. As we start investing in the most lucrative project and move onto less profitable projects, the Marginal Efficiency of Capital declines as the amount of capital input increases.

The cost of the fund is the cost associated with the borrowing the fund. This is the ‘Marginal Cost of Fund’. It is generally equal to the interest rate paid on the interest bearing security, such as government bonds. In other words, the marginal cost of fund is fixed, and thus can be delineated by a horizontal line in the graph.

The entrepreneurs then weigh the benefit and the cost associated with the potential investment project. They will invest up to the point where the benefit is equal to the cost at the marginal level.

Marginal Cost of Fund = Interest Rate

When the interest rate goes up, the amount of capital input or investment declines. Simply, think of the project which is exactly making both ends, revenues and costs, meet in right now. If the interest rate and borrowing costs go up, the project has loss and will be knocked off. The investment volume decreases by the amount of investment.

2) Intuitively Speaking

How does a high real interest rate dampen economic activities? Actually it works in two ways; first it reduces the investment, and thus the AE, eventually reducing Y*. It also reduces the real money demand. At this moment ignore the second impact.

The (real) interest rate constitutes a cost of obtaining (financial) capital for additions to capital stock or investment. A higher interest rate means a higher cost, a lower profitability and the lower rate of return on investment projects.

Some investment projects which used to be marginally profitable or managed to make both ends meet are no longer profitable. So the desired investment will decrease as the interest rate increases.

3) Functional Form of Investment

I = I0 – b i,I0 is the autonomous investment and b is the elasticity of investment with respect to interest rates. b > 0. Here b measures the responsiveness to changes in investment to changes in the interest rate.

The larger the value of b, the more responsive the investment with respect to changes in interest rates. In other word, the larger the value of b, the more interest-rate elastic the investment will be.

A numerical example would be I = 100 – 5i: One percentage increase in interest rates will bring about a 5% decrease in investment.

(w.r.t. = with respect to)

3. IS Curve: Goods Market Equilibrium

The IS curve shows various combinations of national income and interest rates which bring out the equilibrium, or the equality between demand and supply, in the goods market.

Let’s plug the aforementioned modified investment function into the aggregate expenditure function, and solve for Y* and i*.

1) Algebraic Derivation

Recall there are three different cases of AE.

Case 1. All taxes are lump-sum or autonomous. T = T0. (Assume NX = X- M = 0 for simplicity for now)

Suppose that we are dealing with the aggregate expenditures with only lump-sum taxes and no exports or imports (This is Case 1 in the last chapter of the Keynesian Cross Diagram).

The AE will be

AE = C0 + c1 (Y – T0) + I0 – bi + G0

= c1 Y + (C0 - c1 T0 + I0 + G0 – bi0 )

At equilibrium, YS = AE

Y = c1 Y + (C0 – c1 T0 + I0 + G0 – bi)

Y – c1 Y = C0 – c1 T0 + I0 + G0 – bi

Solve for Y* and i*: We can rewrite this equation as a functional relationship between Y*

and the interest rate i.

This is the algebraic expression of the relation between (i, Y) which represents equilibrium in the final goods market.

Note that the slope has a negative sign and thus the IS curve is downward sloping. This means that in equilibrium, of the goods market, the interest rate and income move in the opposite direction; if interest rate increases for some reason, in order to stay at the same equilibrium in the goods market, national income should decrease.

Also, we can draw the IS curve by putting i on the vertical axis and Y on the horizontal axis.

2) Intuitive Explanation of the IS curve.

We can also give the following intuitive explanation about the negative slope of the IS curve;

Let us start from one equilibrium: Y = YS = AE = C + I + G. Here let us change the interest rate and examine the responsive changes in Y. If i and Y turn out to be moving in the same direction, the slope of the IS curve will be positive, and vice versa.

Let us suppose that the interest rate decreases from i0 to i1. If investment is inversely related to the interest rate, there will be an increase in investment and thus an increase in the AE. This means that there will be an excess aggregate demand (now Y < AE’). How can we re-establish the equality between AE and Y? The answer is by increasing Y. In the equality of AE and YS, or the equilibrium of the goods market, when interest rates goes down and national income goes up. The interest rate and national income should move in the opposite direction.

We can express the above relationship with a curve in a graph with Y* on the horizontal axis, and the interest rate i* on the vertical axis. This curve is called the IS curve because, at equilibrium, AE = Y, which means C + I + G + X – M = C + S + T. As C in both side cancels out, the equilibrium condition of the goods market can be expressed as I + G +X = S + T + M. The first letter of each side of the equality read ‘I’ and ‘S’. So along the IS curve, I + G + X = S + T + M. So that is how the name, ‘IS curve’, came about.

3) Graphic Derivation of the IS curve.

Start with the Keynesian Cross- Diagram with which you are very familiar. Redefine the Investment function in the AE curve as being inversely related to the interest rate

Suppose that the initial interest rate is i0, it gives a certain investment level in AE, which in turn gives Y*. (see the initial equilibrium point at A in the graphs below)

Now change the interest rate up to i1. See the corresponding new Y*’ AE decreases: the new equilibrium point at B;

Also, change the interest rate down to i2, See the corresponding new Y*’’. AE increases, the new equilibrium at C.

These combinations of i and Y* will give an IS curve.

4) Comparative Statics of the IS Curve

What can cause a change in the IS curve?

(1) The slope of the IS curve

In summary, the following factors determine the slope of the IS curve:

i) The larger the marginal propensity to consume (c1), the flatter the IS curve.

ii) The larger the elasticity of investment demand with respect to interest rate (b), the flatter the IS.

iii) The lower the income tax rate (t1), the flatter the IS.

Let us examine the second point: The more elastic the investment demand with respect to interest rate, the flatter the IS curve. The more sensitive the investment demand is

towards the interest rate, the flatter the IS curve will be. Here the magnitude of b, or the elasticity of investment with respect to the interest rate, determines the slope of the IS curve.

Numerical Examples: Suppose that we have the following two different investment functions, which have different elasticity of investment with respect to the interest rate.

Case 1: Interest-rate Inelastic Investment eg) I = I 0 – 0.5 i

Here, the investment demand is inelastic with respect to interest rate: A 1% increase in the interest rate i will bring about a 0.5% decrease in the investment demand (Δ I0). Therefore, for a given increase in the interest rate, there occurs a relatively small decrease in AE = C + I + G , which will bring about a magnified but still small decrease in Y through a multiplier effect in the cross diagram.

Case 2: Interest-rate elastic Investment eg) I = I 0 – 10.0i

A 1% increase in interest rate will bring about a 10% decrease in investment (Δ I 0). Therefore there occurs a relatively large decrease in AE = C + I + G (Δ AE), which will bring about a correspondingly large decrease in Y through a multiplier (Δ Y) in the cross diagram.

Student Notes:________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

We can see that the first example of IS curve is much steeper than the second example of the IS curve.

2) Changes in the intercept of IS curve.

Changes in the intercept of the IS curve will bring about Parallel Shifts of the IS curve. Changes in C0, I0, T0, G0 which constitute the intercept of the IS curve, will lead to the parallel shift of the IS curve.

i) Δ G0, Δ C0, and Δ I0 shift the IS curve to the right by the actor of their (simple) multiplier 1/(1-c1) (times the changes in those variables).

For instance, Δ G0 will bring about a horizontal shift of the IS curve. The distance of the horizontal shift is given by Δ G0 times 1/(1-c1).

ii) Δ T0 will shift the IS Cure to the left by the amount of its multiplier c1/(1-c1) times Δ T0.

4. LM Curve and Money Market Equilibrium

LM curve shows the combinations of the interest rate and the income (i, Y) which satisfies the equilibrium in the money market.

1) ‘Nominal’ versus ‘Real’ Money Supply/Demand

We should make distinction between Nominal Supply or Demand and Real Supply or Demand. The first one is in monetary terms, and the second in quantity terms.

In microeconomic analysis of equilibrium, we define the demand and supply in real terms, not in monetary or nominal terms. For instance, if we say that $20,000 worth of hamburgers are demanded (or supplied), the statement is not clear enough. This $20,000 is nominal demand in monetary terms. What about the real demand or quantity? If the price is $1 per hamburger, in real terms, 20,000 units of hamburgers are demanded. If the price is $10, in real terms 2,000 hamburgers are demanded.

In the same vein, for the analysis of the money market equilibrium, the quantity of money should be also defined in real terms, not in nominal or monetary terms. The nominal quantity of money is the face value of the money, and the real quantity of money is the face value divide by the price level;

Real quantity of money = Nominal quantity of money/Price level.

m = M/ P

The real quantity of money supply m is the nominal money supply divided by the price level. For instance, nominal money supply is $2,000,000,00 dollars or $ 2 billion. The price level is measured by a price index. Suppose that the price index is 100 (or 1.00) right now. The real money supply m = 20,000,000,000/100 or 20/1.0 (units do not matter as long as there is a consistency).

2) Money Supply

The nominal quantity of the money supply is determined by the monetary authority, which usually is the central bank.

MS = M

Money supply varies depending on the scopes of money: it may include only cashes (in circulation) in a narrow scope, and may include cashes and all deposits in a broad scope such as M2. The different scopes of money supply will be discussed in full in the separate chapter.

For instance, M = $20,000,000,000 or $20 billion.

The monetary authority does not have to determine the nominal money supply on the basis of any variables in any given manner over time. Thus, we regard the nominal money supply as an exogenous variable, and regard it as arbitrarily determined by the monetary authority.

Mathematically, this means that the nominal money supply curve is vertical, being independent of interest rates. As the money supply is independent of the interest rate, when drawn in the interest rate and real quantity dimension, the money supply curve is vertical, being the same regardless of the level of the interest rate.

At one point of time it is fixed. However, of course, over time it can be changed by the monetary authority. In fact, the monetary authority sets the nominal money supply in each period.

2) Real Money Demand

(1) Uniqueness of Real Money Demand

A few important things to remember about real money demand:

First, note that the money market equilibrium should be defined in terms of real money supply and demand;

Nominal money supply is equal to nominal money demand at all times, i.e., at and out of equilibrium. The nominal quantity of money demanded by the society as a whole is

For instance, depending on circumstances, the monetary authority may increase or decrease the nominal money supply when there is an increase in the national income. If the monetary authority wants to accommodate the booming or growing economy, it would increase the nominal money supply in the face of a rising national income. The logic is that a larger economy has a larger volume of economic transactions and needs a larger amount of medium of exchanges, i.e., money. On the other hand, if the monetary authority judges that the rising national income may touch off inflation and thus decides to fight the inflation, it will decrease the money supply in the face of a rising national income. This is called ‘ leaning-against-wind’ monetary policy. All in all, the monetary authority can choose any of these policies. Mathematically, this means that there is no consistent functional relationship between the national income and the nominal money supply. In fact, nominal money supply has no consistent relationship with any economic variables.

always equal to the nominal quantity of money supplied by the government; MS = MD at all times. Suppose the government is handing out newly printed paper monies or notes on the street. IS there anyone who would refuse them? Every dollar of money supply will be gladly demanded.

Second, while an individual can control real money demand, the general public as opposed to the monetary authority cannot control real money demand;

When an individual receives some new paper monies, her/his nominal (and real) balances increase. S/he may succeed in decreasing the nominal money demanded or the real money balanced back to the initial level by spending the excess money holdings. However, because her/his expenditures will become someone else’s receipts, some other members are getting the increased money supply. So from an individual’s view point the nominal money demanded may be controllable, while it is not controllable from the entire society’s viewpoint. What is true for individuals is not necessarily true for the society as a whole. This is the ‘fallacy of composition’ commonly founded in macroeconomics.

As individuals are busy getting rid of the excess of money holding over the desired level of demand (“I would like to have $200 in my pocket, but as government gives me a new $100 bill, now I have the excess of money holding by $100. I would like to go back to the desired level of money demanded, that is $200 by spending $100 away.”) The increased money becomes a kind of ‘hot potato’. What does this mean in terms of the real money demand? The real money demand, which is the nominal money demand (= the nominal money supply) divided by the price level, is going back to the initial level. The increased speed o spending and expenditure will eventually push up the price level. The general public are collectively changing the price level and thus controlling the real money demand.

Suppose MS = M = MD = $200 billion and P = 1.00 initially in the equilibrium; the real money demand is MD/P = 200/1 = 200 and should be equal to the real money supply at the equilibrium. This real money demand is at the desired level at the equilibrium in light of all the determinants of the demand including the income level and the interest rate.Now the monetary authority increases the nominal money supply MS to $400 billion.

First, all the increased nominal money supply will be demanded. So the nominal money demanded is equal to the new nominal money supply; MD’ = MS’ = M’ = $400 billion.

In the short-run, the price does not change, and thus the actual amount of the real money holding will be m’ = m’’ = M’/P = $400/1.00 = 400. This is much larger than the desired real money demand, that is, 200. As there are no changes in the determinants of the real money demand, there should not be any change in the level of real money balances the general public wishes to hold. There is an excess of real cash balances over the desired real money demand; ‘actual’ real money balances > ‘desired’ real money balances.

As individuals with excessive money balances try to recover the desired real money balances by spending the excess money receipt, the price level is going up to P’. At this

new price level, the new ‘actual’ real money balances (M’/P’) become equal to the desired level of real money balances.

Specifically, the price level will go up to the level of 2 (or the index number 200). The actual real money demand will be 400/2 = 200, the same level as before any changes.

(2) Functional Form of Real Money Demand

The real money demand is given a functional form such as

md = L ( i, Y ).

The above equation defines the real money demand as a decreasing function of interest rates and an increasing function of national income. What determines the desired level (quantity) of real money demand? Just as the desired quantity of hamburgers is determined by the consumers’ income and the price of hamburger, the real demand for money is determined by the income level of the economy, that is the national income, and the price of the money, that is, the interest rate.

Let us examine the second point in the above statement: the price of money is the interest rate. In other words, the opportunity cost of holding money balances is the interest rate.

Money is one of many assets, which include bonds, stock, equities and real assets. Money and other assets are substitutes. The major difference between money and other assets is that money does not bring in any positive pecuniary returns. Actually it is very often subject to the erosion of real value due to inflation, and other assets do have pecuniary returns. However money, or cash balances in a precise term, renders a unique non-pecuniary service, which is known as ‘liquidity’. Money is the most generally accepted medium of exchange and most ‘liquid’. So when you decide to hold assets in the form of cash balances instead of any other, you are showing your preference for liquidity over pecuniary returns. This is the reason why the money demand is called’ liquidity preference and the money demand function ‘liquidity preference function.’

(Digression: Diversity of various interest rates) The pecuniary returns of other assets are, in fact, no uniform because the risks associated with other assets differ: risky assets have higher rates of returns an safe assets have a lower rate of return. The difference in the rate of returns is compensation for entering the risk, in buying risky assets. However, for simplicity, let us simply suppose that the rate of return on other assets than money can be represented by a certain representative ‘interest rate’.

The interest rate represents the foregone pecuniary return or the economic sacrifice you have to take when you are choosing cash balances over other assets, as your mode of holding assets; in other words, the interest rate is the opportunity cost of holding cash balances. When the interest rate goes up, the cost of holding cash balances increases and naturally you would like to hold less assets in the form of cash balances and more interest

bearing assets. This means that the demand for money is inversely related to the interest rate.

Now we have another major factor to be considered, which affect the real money demand; the income level. When real income increases, in most cases, the demand for money increases in real terms, too. To name one reason, when real income increases, there occur more transactions, and then more cash balances should be held to back up the increased transactions.

We can give the liquidity preference function the following specific functional form;

Md = kY – h i + u,

where K is the elasticity of real money demand with respect to the national income; h is the elasticity of real money demand with respect to interest rates; and u is the random component of real money demand.

The liquidity preference curve is negatively sloped when drawn with the interest rate on the vertical axis and the amount of real money on the horizontal axis. The variables Y and u are the shift parameters of the real money demand curve.

(Note: Y and u are shifting parameters)

Also, we can draw a set of liquid preference curves for different levels of income; the higher the level of national income, the larger the demand for real money balances. You may remember, from the class of introductory economics, that an increase in income shifts the demand curve to the right.

3) Money Market Equilibrium and LM Curve

As emphasized, the money market equilibrium should be defined in real terms; the money market is in equilibrium when real money supply is equal to real money demand ex-ante. If the demand is larger than the supply, the price will go up. With an increased price some people will give up their demand. The price, which adjusts to equate the supply and demand, is nothing but the interest rate. The money market interest is set at such a level as to make the supply equal to demand ex-ante.

(1) Algebraic Solution

LM Curve: Money market equilibrium condition ms = md yields the following equations. Rearranging the equation with ‘i’ on the left hand side and ‘Y’ on the right hand side, we

get a LM Curve. Real money supply = , = L(i,Y,u) = kY – hi + u

↓ ↓ intercept slope

We can draw a LM curve with the interest rate on the vertical axis and the national income on the horizontal axis. The LM curve is upward-sloping, or in other words, it as a positive slope. (Along LM )

(2) Intuitive Explanation

Why is the LM curve upward-sloping LM?

Let us start with an equilibrium, ms = md.

When the interest rate increases there will be a decrease in the real quantity of money demanded, (a new md < an old md = ms).

How can we recover the equality between the real money demand and the real money supply? The real money supply cannot change unless the government changes the nominal money supply MS or M to a higher level, or the price level changes. So the real money demand should rebound back to the initial level in order to re-establish the equality. One way of doing it is to increase Y*. When the national income increases, the real money demand will increase. This increase in real money demand offsets the previous decrease in real money demand. So we can observe that the interest rate and the national income move in the same direction.

(3) Graphic Derivation of LM curve:

The real money demand and supply mainly carve up the relationship between the interest rate and the real money balances. However, we are interested in getting the LM curve which carves up the relationship between Y and i*.

To get the relationship between the two, we have to change the value of Y and look at the responsive change in i* or the money market equilibrium interest rate;

When Y increases from Y1 to Y2 the real money demand curve shifts to the right. Here the Y variable is a shift parameter I the real money demand function.

When the real money supply remains unchanged, the increased real money demand will push up the equilibrium price of the money in the market, that is, the equilibrium interest rate I the money market. Previously Y1 corresponded to i1, and now a higher Y2 to i2.

So a higher level of income means a higher level of interest rate. Y and i are moving in the same direction. The LM curve should be upward sloping.

4) Comparative Statics of LM curve

(1) Change in the Slope of LM curve.

i) Elasticity of real money demand with respect to Income, or income elasticity of real money demand (K):

The larger the income elasticity of real demand, the steeper the LM curve.

For instance, when Δ Y = 1% for the following two cases:

Case I with K = 1 : md = Y – 20 i+ u

Case II with K = 0.5 : md = 0.5 Y – 20 i + u

ii) Elasticity of real money demand with respect to Interest rate, or Interest rate elasticity of real money demand (h): the elasticity of real money demand with respect to the interest rate, or in short interest elasticity of money demanded.

In general, the larger the value of h, or the more (interest rate) elastic the real money demand, the flatter the real money demand.

In the following two cases, assuming that K = 0.5 and u = 20 for both in the money demand function md = K Y – h i + u,

Case 1 with h=0.5; Inelastic money demand, md = 0.5 Y – 0.5i = 200

Case II with h =20; Elastic money demand, md = 0.5 Y – 20 i +200

In the above graphs, we can see that with a flat md curve with a large interest-rate elasticity, a very small drop in the interest rate will bring about a very large increase in md. We may also review some extreme cases.

When the real money demand is perfectly inelastic with respect to interest rate (the interest elasticity h = 0)

This is the case where interest rates do not enter the real money demand or liquidity preference function. In other words, real money demand is not responsive to the change in interest rate all; real money demand is completely inelastic with respect to the interest rate; real money or liquidity preference function is drawn as a vertical line, and the derived LM curve is also vertical.

Under what conditions will the elasticity of real money demand with respect to its own price, that is, the interest rate become equal to zero?

The magnitude of the (own price) elasticity is determined by the availability of alternatives or substitutes. If people regard non-money assets, such as bonds, equities, and so on, as completely useless as substitutes for money, the (own price) elasticity of real money demand should be equal to zero. As there are no substitutes for money, regardless of the cost of holding money (whether it is high or low), there would be a certain amount of real money balances that they think they must absolutely hold.

At the equilibrium in the money market, where real money supply is equal to real money demand as:

In this case, there is a strict proportionality between the National Income (Y) and the Real Money Supply (ms). Only money supply determines the equilibrium national income. The goods market is completely irrelevant in the determination of the equilibrium national income.

When the real money demand is perfectly elastic with respect to the interest rate (h is infinitely large): the Keynesian ‘Liquidity Trap’.

When a small change interest rate leads to a very large change in real money demand; real money demand is extremely responsive to a change in interest rate; real money demand is infinitely interest rate elastic. Graphically, the real money curve is horizontal. With a horizontal money demand curve, changes in money supply would not affect the interest rate at all. The interest rate will be stuck at the same level. The derived LM curve is also horizontal at that level of interest rate.

Here monetary policy is ineffective, as any increased money supply will be gobbled up as soon as it is injected into the economy. The public has a hefty appetite for liquidity, or money, and thus, it will swallow it up even with little incentive to do so, that is, a very small drop of interest rate. Therefore, the increased money supply would not have had much of a change to exert any downward pressures on interest rates. This situation is called a ‘liquidity trap’. It could have been named ‘liquidity blackhole’ if Keynes had been well versed in astronomy.

Interest Pegging Monetary Policy: When the monetary policy which involves changes in money supply is completely ineffective, the LM curve is horizontal. However, the reverse is not necessarily true. The horizontal LM curve does not necessarily mean that monetary policy is ineffective. Even if the real money demand curve is downward sloping in a normal way, when the monetary authority or the central bank is dedicated to maintaining a fixed interest rate at all cost, the LM curve will be horizontal.

Let us illustrate this point. There are a set of money demand curves which correspond to different levels of income. This gives the LM curve, linking different levels of Y and i. Let’s suppose that now changes in some factors other than Y and i cause a decrease in money demand: the money demanded decreases at a given level of interest rate and income, and thus real money demand curves with different level of national income shift all down or to the left at the same time.

In this situation, if the government is not doing anything, thus the money supply is fixed, obviously this decrease in real money demand will bring about the decrease in the money-market-equilibrium interest rate at all level of income: ms = md. Initially, and md i – md’ < m’ – i'. Therefore the LM curve shifts to the right. This will be an ordinary case.

However, if the central bank stands ready to offset any change in the interest rate, as is assumed in this question, it should decrease the money supply. If the money supply is changed exactly by the same amount as the changes in the money demand, there will be no change in the money-market equilibrium interest rate. The interest rate will be always constant at a fixed level. This implies that the LM curve is horizontal at that level of interest rate.

We can also think of the reverse case. The interest rate will be still kept at the target level. In this monetary policy regime, monetary policy is effective in pegging the interest rate. Here the policy target is the fixed interest rate, and the monetary authority changes money supply in response to the uncontrollable changes in real money demand.

(2) Shift of the LM curve.

i) Change in nominal Money Supply; Δ MS

The LM curve shifts to the right when the monetary authority increases the nominal money supply: An increase in nominal money supply leads to the increase in real money supply when the price level is fixed.

ii) Change in Real Money Demand unrelated to any changes in the interest rate or the income level: ∆ u

The LM curve shifts to the right when the real money demand decreases at the given interest rate and income level.

Under what circumstances could this happen? Think about the case where people lose their confidence in currency due to the imminent currency reform. The domestic residents will decrease the demand for money and seek safe haven for their wealth elsewhere. Also, in an open economy situation, the demand for domestic currency could decrease as the foreigners wish to convert the domestic currency that they are holding into foreign currencies.

Suppose that due to a decrease in the residual term of the money demand function, an initial money demand md = K Y – h i + u (eg: md = 0.5 Y – 20 i +200, and here u = 200) is reduced to md’ = K Y – h i + u’ (eg: md = 0.5 Y – 20 i +100, and here u’ = 100). The entire set of money demand curves for different levels of income should decrease.

Note: md (Y2, u) and md’(Y2, u’) have the same Y2; and md (Y1) and md’ (Y1) have the same Y1. Initially, Y1 corresponds to i1, and Y2 to i2. With a decrease in real money demand and consequent shift of the demand curves, Y1 corresponds to i1,and Y2 to i2. When md decreases as u decreases to u’, the LM curve shifts to the right.

5. Equilibrium National Income and Interest Rate in the IS-LM Framework

The intersection of the IS and LM Curves give the equilibrium national income and the interest rate that satisfy the market clearing condition in both goods markets and money markets; ex-ante all the goods produced are demanded, and real money supply is equal to the real money demand.

1) Graphic Solution

2) Algebraic Solution

Steps1. Get the IS and LM curve2. Equate the IS and LM curve3. Solve for Y*

4. Substitute the solution of the Y* for the variable Y and the LM equation to get the value for i*;

5. Differentiate the above equations for multipliers.

Case 1. All taxes are lump-sum or autonomous. T = T0. (Assume NX= 0 for simplicity)

Recall the IS Curve: Goods market equilibrium condition AE = Y yields

Recall the LM Curve: Money market equilibrium condition ms = md yields

(Note: = slope of LM curve, h↑ ↓, thus, LM gets flatter)

where K is the elasticity of real money demand with respect to the national income; h is the elasticity of real money demand with respect to interest rates; and u is the random component of real money demand.

Equate the above two equations for i or Y: The Simultaneous Equilibrium of Goods and Money Markets yields

{Note: (- ) = slope of IS Curve}

Multipliers:

i)Impacts on Y*

We may remember that in the simple Keynesian model of income determination (the Cross-Diagram with Y = YS and AE) the multipliers were obtained by differentiating the equilibrium national income equation.

Now, in the IS-LM curve model, another set of the multipliers can be obtained by differentiating the first equation, which describes the equilibrium national income in the goods and money market, with respect to the Autonomous components of AE ( C, T, I, G

and M). The result of differentiation is the coefficient of each variable in the above equation.

(Note: the above two are business cycles)

(Note: = “Fiscal Policy Multiplier”)

The first two multipliers have something to do with business cycles as the C0 and I0 show cyclical movements over time beyond the control by government.

The third one is called the ‘Fiscal Policy Multiplier’. It measures the ratio of the change in the goods and money market equilibrium national income to a change in government expenditure. Note that this new multiplier or the fiscal policy multiplier in the IS-LM framework is smaller than the government expenditure multiplier in the Cross-Diagram setting. Both measure ∆Y* due to ∆G. However, the fiscal policy multiplier takes account of the resultant change in interest rate and the consequent crowding out effect while the government expenditure multiplier does not; the difference between the government expenditure multiplier and the fiscal policy multiplier is the crowding-out effect which results from an increase in interest rates and its suppression of private investment. Because of the secondary feedback in the money market, the magnitude of fiscal policy multiplier is smaller and thus ∆G has a smaller impact on Y*.

The following multiplier measures the change in income to a change in a lump-sum tax responsible for it.

The following multiplier is called the ‘Monetary Policy Multiplier’. It measures the ratio of the increase in income to an increase in money supply.

“Monetary Policy Multiplier”

ii) Impacts on Interest Rates:

Remarks: Note that compared with the equilibrium national income equation without the

LM curve (in the previous handout), there is an additional term kb/h in the multiplier for the autonomous expenditures.

A $1 increase in G shifts the IS curve by $1/(1 - c1), and y* by $1/(1-c1 +kb/h). What makes the difference?

Now, let’s extend our model to more complex cases of aggregate expenditures as we have seen before.

Case 2. There are Autonomous and Proportional Taxes. T = T0 + t1Y,

IS Curve: Goods market equilibrium condition AE = Y yields

LM Curve: Money market equilibrium condition ms = md yields

Simultaneous Equilibrium of Goods and Money Markets

Note: compared with the equilibrium national income equation without the LM curve (in the previous handout), there is an additional term kb/h in the multiplier for the autonomous expenditures.

Case 3. There are proportional taxes, and Imports are proportional to national income.

NX = X - M;

M = M0 + m1 Y;

X = X0, where M0 denotes the Autonomous imports and m1 denotes the Marginal Propensity to Import.

IS Curve: Goods market equilibrium condition AE = Y yields

LM Curve: Money market equilibrium condition ms = md yields

Simultaneous Equilibrium of Goods and Money Markets

Note: compared with the equilibrium national income equation without the LM curve (in the previous handout), there is an additional term kb/h in the multiplier for the autonomous expenditures.

3) Comparative Statistics: Business Cycle, Fiscal and Monetary Policies

The above equilibrium equations for Y* and i* indicate that

(1) Business Cycles

∆I0, and ∆C0 are beyond direct control by government and cause undesirable fluctuations in Y*: The factor by which the changes in autonomous investment and consumption are multiplier into larger changes in Y* is given by the coefficient of I0 and C0 in the above equilibrium income equation.

(2) Fiscal Policy:

i) ∆G0 leads to an increase in Y* and an increase in i*

ii) ∆T0 leads to a decrease in Y* and an decrease in i*.

(3) Monetary Policy

i) An increase in money supply leads to an increase in national income:

ii) An increase in money supply leads to a decrease in the interest rate.

Let us examine the above (2) and (3) in a formal and rigorous way:

5. Fiscal and Monetary Policies in the Conventional IS-LM Curve Model

1) Fiscal Policies

Government expenditures may be financed either by taxes or by deficits. In the latter, the deficits should be made up by issuing bonds. Perversely, a bond-financed increase in government expenditures has a larger impact on national income than a tax-financed increase in government expenditures. This inequivalence in terms of financing is a main feature of the conventional IS-LM model. We will later discuss the problem of this view and present an alternative view developed by Barro-Richardo. For now, we are simply having a review of fiscal policies in the IS-LM model.

(1) A Bond-Financed Increase in Government Expenditure: ∆G = ∆B

When government increases its expenditure without increasing tax revenues, there occur deficits. The government has to make up for deficits by borrowing funds. The certificates of borrowing by the government are bonds. So deficit-financing is the same as bond-financing. There is no corresponding increase in taxes when government expenditures increase.

In the Keynsian Cross-Diagram, ∆G0 shifts the AE curve up by ∆G0 and the Y (note that there is no longer * on Y because this Y is just an equilibrium in the goods market as opposed to the Y* which is the equilibrium in the goods and money markets) increases by ∆G0 times 1/(1-c1).

Accordingly, in the IS-LM curve model, there occurs a parallel shift of the IS curve to the right by ∆G0/(1-c1). This results into the increase in Y* by ∆G0 times 1/(1-c1 + Kb/h) which is smaller than ∆G0 (1-c1).

The increase in Y*, shown as the rightward movement of Y*in the graph, is smaller than the rightward shift of the IS curve. The reason is that ∆G0 leads to ∆Y*and this increased income increases real money demand. An increase in real money demand pushes up the interest rate when real money supply is fixed. A higher interest rate decreases investment and through the multiplier, income falls. This mechanism partially offsets the initial increase in the income due to ∆G0. This is called ‘Crowding Out’. The increased government expenditure crowds out the private investment by raising the interest rate.

(2) A Tax-Financed Increase Government Expenditure: ∆G = ∆T

When government is increasing its expenditure with revenues raised through taxation, it is engaged in balanced budget operation.

A: the horizontal distance of IS curve shift

In the Cross Diagram, ∆G = ∆T leads to a rightward shift of Y or the goods market equilibrium national income by ∆G times 1.

Accordingly, in the IS-LM curve model, the IS curve shifts to the right by ∆G. This results into the rightward shift of Y*, goods and money market equilibrium national income by ∆G times (1- c1)/(1- c1 + Kb/h) which is less than ∆G. Also the interest rate goes up.

2) Issues of Monetary Policies

We will examine some relevant issues in the separate chapter.

3) Policy Mix

The crowding out effect shows that as long as the IS and LM curves are normally shaped, a change in G will bring about undesirable side effect of a higher interest rate and a smaller investment.

Now the policy mix enables a desired Y* and a desired I* to achieved simultaneously if and only if Y* is below Y1 or the full employment national income (maximum potential national income).

CASE STUDY: “ House or Gun ” for the Americans during the Vietnam war(Credited to Professor R. Gordon, Northwestern University)

The 1965-67 period, during which U.S. government spending expanded rapidly as our involvement in the Vietnam war deepened, provides an unusual case study of the consequences of fiscal expansion while the real money supply remains fixed. In the fourth quarter of 1966 (October through December), written as 1966:Q4, the real money supply was almost exactly the same as five quarters earlier, in 1965:Q3. An LM curve corresponding to this fixed level of Ms/P is drawn in the figure. During this five-quarter interval the level of real government purchases grew by 12.2 percent, represented in the figure by the rightward shift in the IS curve from IS0 to IS1.

How did real income and the interest rate behave over the five-quarter interval? Real income increased by $129.9 billion, more than the $60.2 billion increase in government spending, because of the (fiscal policy) multiplier effect. And the higher demand for money forced an increase in the interest rate from 4.7 to 6.0 percent to keep the total demand for money equal to the fixed real money supply.

The immediate victim of the higher interest rates was investment in residential housing. By 1966:Q4 this component of investment had declined 17.9 percent from

the level reached in 1965:Q3. This is the Crowding out effect. (Nonresidential investment including inventory change and expenditures on plant and equipment-continued to grow despite the increase in interest rates through 1966:Q4. The reason for this growth stems from the delay between the increase in the interest rate and the subsequent decline in nonresidential investment, a factor our IS-LM model does not take into account.)

A basic principle of economics holds that a wartime economy cannot boost military spending without decreasing civilian expenditures; that is, the economy “cannot have both guns and butter”. In this case the economy could not have both “guns and houses”.

The principle is not true in a recession or depression which has some buffer in productive capacity and has the actual national income below the full employment income level. With expansionary monetary policy which shifted the LM curve, the interest rate was brought down. This is the policy mix. In 1967 and the early 1968 the economy tried to have both “guns and butter” due to this policy mix of the simultaneous use of expansionary fiscal and monetary policies.

President Lyndon Johnston delayed proposing a tax increase, which was not finally approved by Congress until Jul 1968. Consequently, the money supply began to grow rapidly, and this allowed private spending as well as defense spending to grow.

The problem arose when the resultant Y*exceeded the full employment income Y*. The excessive spending growth of 1967 –68 in an economy that was straining at the limit of its productive capacity unleashed a serious inflation. Many analysts think that an underlying cause of the inflation suffered by the United States sine the late 1960s dates back to President Johnston’s refusal to “pay for” the Vietnam war in 1966.

The IS-LM curve model shows that there could be a number of policy mixes or the combinations of fiscal and monetary policies to achieve a certain level of national income. For instance, when the economy is stuck at the equilibrium with Y* and i*

which is below Yf or full employment equilibrium, the government can attain Yf by entirely relying on ‘expansionary fiscal policy’ (case I), by entirely relying on ‘easy money policy’ (case II), or even the combination of the two policies (case III).

Although the equilibrium income is the same for both cases, the relative composition of private and government sectors will be different. In the first case, at the given level of income, the share of private investment and consumption compared to that of the government sector is smaller than in the second case. The reason being, the increased government expenditure raises the interest rate and thus decreases private investment. In other words, the relative share of the public sector rises at the expense of the private sector.

(4) Effectiveness of Fiscal and Monetary Policies

The degree of effectiveness of fiscal and monetary policies depends upon the magnitude of the underlying parameters.

1) Effectiveness of Fiscal Policies

Depending on the magnitude of the elasticity of real money demand with respect to interest rate (=h), the LM curve could be vertical (h=0), upward sloping (0<h<infinity), and horizontal (b is infinitely large).

An expansionary fiscal policy (∆G or ∆T) shifts the IS curve to the right. The same shift of the IS curve could bring about different degrees of ∆Y* depending on the slope of the LM curve.

Cf. Now you may remember that the Interest Pegging Monetary Policy leads to a horizontal LM curve: The interest rate is constant at a fixed level. In this case of the horizontal LM curve, the fiscal policy will be very effective because there is no crowding out; the expansionary fiscal policy does not increase the interest rate and thus does not have any dampening effect on investment or partially offsetting effect on national income. However, the bad side of the horizontal LM curve (which would not have any crowding out effect) is that a decrease in consumption or investment will bring about a larger decrease in national income in this horizontal LM curve than when the LM curve is upward sloping.

2) Effectiveness of Monetary Policies

6. Controversies and Pitfalls of the IS-LM curve analysis:

1) Ricardian Equivalence

IS-LM curve model suggests, “Bond-financed government expenditures have a larger impact on the national income than the same amount of tax-financed government expenditures.”

“A tax cut without an equal decrease in government expenditures leads to an increase in government budget deficits. This switching from one method of financing government expenditures to another should alone increase the national income.”

“An increase in government deficits due to tax cuts will lead to an increase in national income.”

(1) Illustration: What does the IS-LM model imply?

This is just to paraphrase the Keynesian position that in the simplified Keynesian model the government expenditure multiplier ∆Y/∆G = 1/(1-c2) is larger than the balanced budget multiplier ∆Y/∆G + ∆Y/∆T = 1 or that in the IS-LM model the fiscal policy multiplier ∆Y*/∆G = 1/(1-c2 + Kb/h) is larger than the balanced budget multiplier (1- c2/ (1-c2 + Kb/h).

Graphically,

Keynesian school gives a very clear answer: when the bond-financed government expenditure increases, the AE increases, and thus IS curve shifts to the right which results in an increase in Y* and i*.

The upshot of the Keynesian theory is that ∆G will have different impacts on Y* depending on how ∆G is financed, or the method of financing ∆G. ∆G financed by bonds does shift the AE and the IS curves more to the right than ∆G financed by taxes.

To corollary is that the switching of revenue sources from taxation to bond-issues without any changes in G will lead to a net increase in Y*: A tax-cut increases disposable income, which in turn increases consumption by a lesser amount, AE, and finally Y*.

A gullible mind would conclude that deficit financing is more effective and thus better than tax-financing. We are now experiencing the legacy of this line of thinking by having the problem of the accumulated amount of deficits. That is a huge amount of public debts.

(2) Uncertainty from Intergenerational Transfer and Bequest

Whether the above statement is correct or not depends on (1) the degree of farsightedness of the consumers, and (2) their sense of responsibility towards the welfare of the future generation. The crucial problem is that the beneficiary of the present tax cut may be different from those who will eventually pick up the tap in the form of an increased tax in the future.

Let us examine the following concrete real world examples faced by consumers:

As soon as the NDP party came to power in the province of Ontario in 1989, it increased government expenditures drastically. Sensible and far-sighted people predicted that as the government did not hit any bonanza, it would soon have to increase taxes. In 1992, in fact, the government proposes major tax hikes. It has turned out that the government was riding a fiscal time-machine, and simply playing the game of transferring resources from 1992 to 1990. Back in 1990, what would be the impact of the increased government expenditures on those who benefited directly from it and correctly foresaw the future tax-liability attached to it?

In the year 1992, the government announces that it will decrease taxes in 1992-93, and issue bonds with a maturity of 100 years. It will raise taxes to retire the bonds in the year 2092. Let us suppose that the average life expectancy is 75 years. What will be the impact of this proposed tax-cut on Y*?

The following two scenarios are possible:

First, if the consumers are short-sighted or myopic, or have no concerns about the welfare of the future generation on whom the tax burden will be imposed after

their death: they will be just concerned about their life-time income. The tax-cut increases disposable income now, but the corresponding tax increase will come after their death in 2092. So this tax-cut is free lunch for these people. They will spend the part of increased disposable income on consumption, which increases AE, and eventually, through the multiplier effect of the A, Y*.

Alternatively, if the consumers are far-sighted and responsible for the welfare of the future generation: They foresee the price tag of an increased future tax liability attached to the goody of the present tax cut. They do not want the future generation to be affected by the tax-hike. They would not spend their increased current disposable income on consumption. They save it and leave the savings as the bequest to the future generation so that the future generation may cash the savings to pay for an increased tax liability in the future. The consumption by the current generation does not change, and thus neither the AE nor Y* change. The IS curve will not shift to the right.

(3) Ricardo-Barro Equivalance

Ricardian Equivalence states that there is equivalence between bond and tax-financed issuing bonds instead of increasing taxes, the Canadians used increases in disposable income in raising their standard of living rather than increasing savings for the future generation. The present generation cannot help feeling that they are forced to pick up the lunch bill for the past generation. To that extent, Ricardian Equivalence failed. This failure does not reduce the need to learn the theory itself, but rather strengthens it: it will help the current generation to remember that there is no such a thing as free lunch in the economy and that the tax-cut for the current generation comes at the expenses of an increased tax liability of the future generation.

2) Timing and Expectations

The IS-LM curve model simply suggests, “Investment tax cut will boost economy.”

According to the Keynesian theory, ∆Y*/∆I = 1 /(1- c1) in the simple cross diagram model without the crowding out, and ∆Y*/∆I = 1/(1- c1 + Kb/h) in the IS-LM model with the crowding out.

When we introduce the element of time and expectations, the results could be uncertain.

Example: Carefully analyze the following economic situation.

The Canadian economy is caught in a serious recession. Some measures to boost investment are needed. Now in January of year 2010, the concerned Canadian government announces that it will give an investment tax credit, which will last only for four months. But it says that it will take eight months from now to pass through the parliament.

What will be the instant impact of this supposedly ‘expansionary measure’ on the economy during January to August?

The firms will delay the preplanned and newly planned investment until the bill passes through the parliament. During January to September, there will be very little investment to be made. This decrease in investment will decrease Y* through the multiplier effect.

Would this measure more expansionary between September and December than a permanent investment-tax-break at the same rate? Why?

If the tax break is only for a limited time, then the investors would like to take advantage of it by rushing investment during the period of the tax break. They will delay and forward the investment projects. In the case of a permanent tax break, there is no reason to forward investment projects along the time scale: the tax cut will be effective forever, so why hurry to invest? There will be only delaying investment projects from the time of the announcement to the time of the tax break coming into effect. In other words, as far as investment is concerned, a temporary tax break has a larger expansionary impact on the economy than a permanent investment tax break.

3) Time-lags

It takes time for any economic problem to get recognized, for any remedial decisions to be made, and for the policies to be formulated and executed. These are Recognition Lag, Decision Lag, and Execution Lag of an economic policy. It also take time for the economy to respond to an applied policy; this is the Effectiveness Lag. The former is Inside Lag, and the latter Outside Lag.

Due to time lags, contradictory fiscal or monetary policies may come into effect at a wrong time.

4) Lucas’ Critique of Economic Policy Evaluation

Government economists use some version of the IS-LM model in order to predict and to evaluate a proposed economic policy.

The equilibrium national income equation shows the quantitative relationship between Y*

and various variables such as G, I, C and T: they are related through the coefficients, such as 1/(1- c1 + Kb/h), which in turn consist of many parameters, such as h, b, K, c1, and so on.

Econometrics enables us to estimate the magnitude of h, b, K, c1 with past data. We use these estimated values of parameters in the IS-LM model, and thus make some quantitative evaluation of newly proposed policy. For instance, if c1 is estimated from past data to be equal to 0.8, K to be equal to 0.5, b to be equal to 20, h to be equal to 20, a proposed decrease in government expenditures by $50 billion will lead to a decrease in national income by $ 75 billion, that is, 50 times the multiplier of 1.5 (1 over 1 minus c1 plus Kb/h) in case of no crowing-out.

This use of econometrics along with the IS-LM curves could lead to problems under certain circumstances.

When government changes its whole set of rules of the game, there occurs a ‘regime change’. This is different from a mere ‘policy change’, a quantitative change in government expenditures or money supply. If the general public takes a regime change as permanent and credible, they will accordingly change their behavior. This change in behavior is reflected in the parameters of behavioral equations such as consumption function. This is a ‘parameter drift’ due to regime change. The use of estimated parameters under the old regime to a new policy under the new regime would give a wrong prediction of the proposed policy. This is the core of Professor Lucas’ Critique against Econometric Policy Evaluation: when there is a regime change which causes a parameter drift, the use of estimated parameters from the past regime would give the wrong evaluation of the new proposed policy.

Case I (a mere policy change). There is no regime change. Now government is going to decrease its expenditure by $50 billion. The econometric technique gives you that the marginal propensity to consume is estimated to be 0.8 from the past 10 year data. In this case, the use of the old parameter 0.8 for a new policy is justifiable as there was no change in government’s rule of game or regime change and thus the consumers have no reason to change their behavior. The IS curve will shift to the left by ∆G times 1 over 1 minus 0.8 or $250 billion. There will be a decrease in Y*

by a less amount.

Case II. (a regime change). Government announces that it will change the rules of game entirely. It will turn away from the past ‘spending’ regime to a new ‘saving’ one. Now as part of such fundamental change, the government is decreasing its expenditure by $50 billion. What will be the change in Y*? The past behavior of the consumers under the old regime was that a $1 increase in disposable income increased consumption by $1 time the marginal propensity to consume, say, 0.8. Now as they expect leaner days ahead of them, they would like to practice thrift, too. This change in consumers’ behavior will be reflected in the change in the marginal propensity to consume or c2, say 0.6, will be smaller than the c2 before the regime change. The IS curve will move to the left by ∆G times 1 over 1 minus 0.6, that is, %50 times 4 = $200 billion, not by $50 times 1 over 1 minus 0.8 = $250 billion. Of course, the resultant decrease in the equilibrium Y* will be smaller due to the crowding out effect.

Student Notes:

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Appendix I. Review Questions

In the IS-LM curve model, the general price level is assumed to be fixed. This is a reasonable assumption if the economy is operating under the full employment income level.

The IS Curve

1. From the Keynesian cross diagram, derive the IS curve, which shows various combinations of interest rate and national income in the goods market equilibrium, 1) when the investment function is independent of interest rate, and 2) when investment is inversely related to interest rate.

The LM Curve

2. Derive the LM curve, which shows various combinations of interest rate and national income in the money market, 1) when the money demand is independent of interest rate (h = 0 in the real money demand function Md/P = KY – hi), 2) when the money demand is inversely related to interest rate, and 3) when the money demand is infinitely elastic with respect to interest rate (h is infinitely large): Draw money demand and supply curves in a graph, and the LM curve in the other.

3. Show graphically what happens to the LM curve when the central bank increases money supply.

4. The following question shows what happens to the LM curve when there occurs a decrease in money demand which is caused by other things than changes in income or interest rate:

Suppose that in a country called ‘Erehwon’ there breaks out a rumor of the currency reform which would penalize the holders of money balances. People naturally scramble to make a flight from cash balances and to buy up alternative assets. Describe the situation with the graphs of the liquidity preference function and the LM curve. What will be its impact on national income?

5. Let’s suppose that the money supply and demand curves are normally shaped, and that the Bank of Canada is committed to maintaining interest rate at a certain level. This means that the Bank of Canada stands ready to change the nominal money supply in response to changes in the real money demand which could affect interest rate. What will be the resultant shape of the LM curve in this case? Explain why, under this monetary regime, the impact of a reduction in investment on national income would be felt more painfully than under alternative monetary regime?

Equilibrium of IS-LM: Crowding-Out Taken into Account

[Cam you tell the difference between Fiscal Policy Multiplier and Government Expenditure Multiplier: the first takes Crowding-out Effects into account while the second does not. Accordingly, the first is usually smaller in magnitude than the first.)

6. Suppose that the following report was made by an economist who offers consultation to an opposition party ‘Libertarian’ in a country called ‘Erewhon’. If you ar the opposition leader who is properly trained in economics, why would you feel like switching to another consulting company? – Let’s assume that the facts used are all correct. Indicate the missing points which lead to the drawing of the underlined wrong conclusion from the correct facts.

“My econometric analysis using a very sophisticated programme and the data of the past 10 years shows that the marginal propensity to consume is 0.67 in this country (fact). Now the government treasury is cleaning its house, and ready to cut down on its expenditures by 50 billion this year (fact). Therefore, I can forecast that the accumulated total decrease in national income over time will amount to 50 billion dollar times the implied multiplier equal to 1 over 1 minus 0.67, that is, about 150 billion dollars. (opinion). Everyday the news media is pounding into the head of the citizens that the idea that the citizens should be prepared for lean days (fact). However, one social study show that the thresh-hold point is a 100-billion-dollar reduction beyond which the citizens will prefer a political regime change to the economic sacrifice however necessary it might be (fact). Therefore, it is my prediction that with the reduction of national income by 150 million dollars the present ruling party ‘Troy’ will most likely lose the next election (opinion).”

7. Answer the following questions:

1) Let’s suppose that the IS-LM curves are normally shaped: the first is downward-sloping and the second upward-sloping. Evaluate the following argument within the Keynesian framework:

“The government spending raises interest rate, which chokes off private investment. As now the Canadian economy is heading toward recession, the government spending should be reduced, thereby lowering the interest rate and preventing recession from taking its toll any further.”

2) In each possible case of the LM curves given in Question 3 on Page 3, what is the extent of Crowding-out effect when government increases its expenditures?

Policy Mix

8. Suppose that two administrations, one the Liberal and the other Socialists, all use fiscal and monetary policies to raise the national income to a target level which is still below the maximum potential national income, and that the Liberal administration relies relatively more on the expansionary policy while the Socialists relies more on fiscal policy.

1) On a single graph, show how the IS and LM curves of these two administration differ.

2) Indicate whether the following variables will be higher under the Liberal or Socialist administration: interest rate, private investment, and government spending.

Alternative Frames of Reference

9. Keynesian ‘Non-equivalence’ and Ricardian Equivalence.

At time t, the government announces that it will decrease taxes on consumers’ income, and issues bonds to make up for the decrease in government revenues. The bonds will be paid back in 90 years with an increase in taxes at that time. The average life expectancy is 75 years, which means that the current generation of consumers will not be hit with the tax-hike in their life-time.

Note that government expenditure has not changed, but some part which used to be financed by taxes is now financed by bond issues.

1) The Keynesian framework assumes that the consumers are near-sighted or selfish, and thus do not have any concern for the welfare of the future generation. What will be the impact of such a tax cut on national income? Illustrate it with the IS-LM model.

2) Now let us assume that the consumers are far-sighted and responsible for the welfare of the future generation, and thus do have bequest motive for their descendants. What will be the impact of the tax cut on the national income at time t and time t + 4?

Appendix 2: Summary of Chapter

1. Fiscal Policies: G (Case 1: all taxes are lump sum)

2. Monetary Policies: M (Case 1: all taxes are lump sum)

b=0 normal b b-> (h = 0)

IS & LM is perfectly inelastic

(Normal h)

LM is perfectly elastic

3. Effectiveness of Monetary Policies in Various Settings: How much Y results from

b = 0 normal b b - >

normal h

4 Effectiveness of Fiscal Policies in Various Settings: How much Y results from G

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