What determines the amount of goods and services...

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1Macroeconomics I (IG). Topic 2. Javier AndrésMacroeconomics I (IG). Topic 2. Javier Andrés

Macroeconomics I International Group

Course 2006-2007

Topic 2: THE DETERMINANTS OF NATIONAL INCOME.

THE LONG RUN


• What determines the amount of goods and services produced in an economy in a period of time?

• How are incomes generated in the production process distributed among the owners of productive factors?

• Consumption, saving and investment decisions.

• What can the public authorities do to increase output?

Learning objectives

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Topic Outline

Income receivers spend part of their income: Income receivers spend part of their income: consumptionconsumptionFirms and Governments spend but they do not earn Firms and Governments spend but they do not earn incomes.incomes.Governments have the legal backing to raise revenues Governments have the legal backing to raise revenues out of household incomes: from taxes to public out of household incomes: from taxes to public spending.spending.Firms may obtain funds to spend the part of income Firms may obtain funds to spend the part of income not spent by households, but they must pay a return for not spent by households, but they must pay a return for it: from savings to investment. it: from savings to investment.

From income to From income to spendingspending

SpendingSpending (Demand) = Y(Demand) = YDD

How are incomes generated.How are incomes generated.How is total income distributed.How is total income distributed.How are total incomes used.How are total incomes used.

From From production to production to incomeincome

IncomeIncome (remuneration for (remuneration for the use of productive the use of productive factors)factors)

What is behind Y: Technology and factor marketsWhat is behind Y: Technology and factor marketsRelationship Relationship between P and between P and Y Y

ProductionProduction or Output or Output (Supply) = Y(Supply) = YSS

Y: Y: the long runthe long run


• In this Topic we take a long-run perspective. In doing so we may answer these questions by looking at the demand and the supply sides of the economy independently from each other.

• This is not what we shall usually find in macroeconomics, which is about how aggregate markets interact. As we know from microeconomics it takes both the demand and the supply side of one particular market to determine the equilibrium prices and quantity traded.

• NOTE: With flexible prices the aggregate supply curve is vertical; output is determined by the supply side alone, and equilibrium prices for that level of output are determined by the demand side. This makes it possible to conduct an independent analysis of aggregate supply and demand.

Learning objectives

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Aggregate markets in the long run

Supply and demand determine P and Y

Y is determined on the demand

side of the market

Y is determined on the supply

side of the market


Aggregate markets in the long run

Aggregate (long-run) demand and supply

Supply and demand in a single market

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• Since marginal costs rise with ouput, the supply curve of a firm is upward sloping. Recall that the supply curve reflects how the firm’s production reacts to changes on its relative price: P(j)/P

• If each single firm increases output as prices rise, why does the aggregate curve reflect that aggregate output does not change when the aggregate price rises?

From microeconomics to macroeconomics


• Notice that when the aggregate price rises, we are assuming thatall individual prices rise in a similar proportion. Thus relative prices do not change and individual firms do not find it optimalto change production.

• When the relative price rises, a firm finds that its revenue rises faster than its costs. Thus it is optimal to increase output. If all prices rise in a similar proportion the firm knows that its costs will rise as much as its revenues, thus there is no incentive tochange production.

• This is why in an economy with flexible prices, a change in aggregate demand leads to a change in all prices with no reaction of aggregate output: the aggregate supply curve is vertical under flexible prices.

From microeconomics to macroeconomics

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• Under flexible prices (the long run) real variables are determined on the supply side of the economy (nominal variables are determined by the amount of money in the economy).

The ‘classical dichotomy’



The ‘classical dichotomy’Real variables are determined independently of the amount of money in

circulationThis is what we learned in microeconomics. If all prices change in the same proportion, so does nominal income, and individual households and firm’s decisions are left unaffected.

Nominal variables (P, W, R) are determined by the amount of moneyThe CPI is the inverse of the price of money. Thus as the amount of money in circulation

grows, its price falls and the CPI rises

Real wages, the rental cost of capital, employment, capital and output are determined by the conditions of the supply side

The real interest rate r is determined by the (real) decisions of saving and investment

This the decision of how much to spend today and how much to leave for tomorrow (saving)

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Inflation and growth in the OECD

TUR

ICE

J APSWI

NZE

FRA FINDEN

GER NETBEL

AUL

LUX

GRE

SP AITA

NORIRE

P OR

CAN AUT

UK

SWEUSA

0

5

10

15

20

25

30

35

40

1 2 3 4 5 6

Per capita income rate of growth

Infla

tion


How we organize the study of the long run

• In this Topic we study:– The determination of real variables: output,

employment, factors income, etc. We focus here on the supply side of the economy.

– The determination of the real interest rate: the market for ‘loanable’ funds (the saving-investment decision).

• We leave aside until Topic 3 the study of the interaction between the amount of money and prices in the money market.

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The aggregate supply• The aggregate supply is the relationship between the price level

and the amount of goods and services that the firms in an economy are willing to produce in a given period.

• To establish this relationship we consider the following elements:– Output depends on the amount of inputs (factors of

production) available as well as technology. We summarize this relationship in the PRODUCTION FUNCTION

– Technology depends on the general knowledge accumulated by the society. Its evolution (rate of change) is called TECHNOLOGICAL PROGRESS

– The amount of inputs used in production depends on their availability as well as on the decisions of the firm: (SUPPLY AND DEMAND) FACTORS MARKETS


• The production function relates output with inputs. It shows how much output (Y ) the economy can produce using K units of capital and L units of labor. It is a technological relationship not an economic one, and can be represented as:

( , , )Y F A K L=

The aggregate supply: The production function

• K, L: represent the amount of capital and labor used.Why we do not include intermediate inputs in the production function?A: reflects the ‘state of the art’ of technological knowledge. Is technological knowledge a productive factor? Why is it different from K and L?

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The production function

( , , )zY F A zK zL=

( ,0, ) ( , ,0) 0F A L F A K= =

( , , ) 0

( , , ) 0

F A K LL

F A K LK

∂>

∂∂

>∂

2

2

2

2

( , , ) 0

( , , ) 0

F A K LL

F A K LK

∂<

∂∂

<∂

• Constant returns to scale

• Both factors of production are necessary

• Marginal products are positive and decreasing:


The production function for a given level of capital

1) Y rises with L. L rises with Kand A.

2) The ratio (∆Y/∆L) is positive

3) The ratio (∆Y/∆L) is decreasing in L

The production function

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The long run• As we discussed in the previous Topic, the long run

has two dimensions: – A notional one: all prices and wages are fully flexible and all

markets clear.– A time dimension: as time goes by the capital stock,

population growth and technological knowledge improves. • We shall concentrate on the first dimension, and thus

we shall assume that:– A is constant (normalized to A=1)– Capital supply is given– Labor supply is given

• Thus, the key decision is how much of the available capital and labor to use.


The labor market: labor demand

• The MPL is decreasing in L

• The firm demands L* that satisfies MPL (L*)=(W/P)– L(-): MPL (L(-))>(W/P)– L*: MPL (L*)=(W/P)– L(+): MPL(L(+))<(W/P)

• Increases in K and A shift the marginal product of labor rightwards so that the firm is willing to demand more labor: L(+)

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• If the labor demand falls from L1 to L2, the use of labor input does not fall if the real wage adjusts downwards from (W/P)1to (W/P)2.

• If the real wage adjusts: there is NO UNEMPLOYMENT

• Autonomous changes in the price level do not affect the real wage if the nominal wage adjusts in the same proportion.

1

1

10 15 552 3 1

10 14 425 7 2

WPWP

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞= = = =⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞= = = =⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

The labor market: equilibrium


• If the labor demand falls from L1 to L2, the use of labor input falls even if the real wage adjusts downwards from (W/P)1to (W/P)2.

• If the real wage adjusts: there is NO UNEMPLOYMENT

• Autonomous changes in the price level do not affect the real wage if the nominal wage adjusts in the same proportion.

1

1

10 15 552 3 1

10 14 425 7 2

WPWP

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞= = = =⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞= = = =⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

The labor market: equilibrium

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The capital market: capital demand

• The MPK is decreasing in K

• The firm demands K* that satisfies MPK (K*)=(R/P)– K(-): MPK (K(-))>(R/P)– K*: MPK (K*)=(R/P)– K(+): MPK(K(+))<(R/P)

• Increases in L and A shift the marginal product of capital rightwards so that the firm is willing to demand more capital: K(+)


• If capital demand falls from K1 to K2, the use of labor input does not fall if the rental cost adjusts downwards from (R/P)1 to (R/P)2.

• If the rental cost adjusts there is full CAPITAL UTILIZATION.

• Autonomous changes in the price level do not affect the real rental cost if the nominal rental cost adjusts in the same proportion.

The capital market: equilibrium

1

1

20 30 10102 3 1

18 36 663 6 1

RPRP

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞= = = =⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞= = = =⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

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• If capital demand falls from K1 to K2, the use of labor input falls even if the rental cost adjusts downwards from (R/P)1 to (R/P)2.

• If the rental cost adjusts there is full CAPITAL UTILIZATION.

• Autonomous changes in the price level do not affect the real rental cost if the nominal rental cost adjusts in the same proportion.

The capital market: equilibrium

1

1

20 30 10102 3 1

18 36 663 6 1

RPRP

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞= = = =⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞= = = =⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠


Under flexible prices and wages a rise in P does not change the use of labor

• If P rises for some reason (because nominal aggregate demand rises for instance), this tends to reduce the real wage (W/P) thus increasing labor demand.

• At this new real wage, labor demand is higher than labor supply.

• This induces a rise in the nominal wage until the labor market clears at the same real wage as before (but with higher P and W).

• Thus the use of labor is not altered.

The aggregate supply curve is vertical

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Under flexible prices and wages a rise in P does not change the use of capital

• If P rises for some reason (because nominal aggregate demand rises for instance), this tends to reduce the real rental cost of capital (R/P) thus increasing capital demand.

• At this new real rental cost of capital, capital demand is higher than capital supply.

• This induces a rise in the nominal rental cost of capital R until the capital market clears at the same real rental cost as before(but with higher P and R).

• Thus the use of capital is not altered.



• If P rises, the amount of output that firms are willing to produce does not change.

• Their marginal revenue and marginal cost rise by the same amount in nominal terms.

• They find it optimal to produce the same amount of output as they did before the price rise.

• Aggregate output does not change if all prices (P, W, R) are fully flexible and adjust.


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( )

( )

,

,

( , )

d d WP

sd

d d RP

sd

s

L L K

L L L

K K L

K K K

Y F K L Y

⎫=⎪⎪= = ⎪⎪= ⎬⎪⎪= =⎪

= = ⎪⎭

Changes in P have no real effect on L, K, Y, W/P, R/P:formal analysis


From production to income: Income distribution• The total value generated in the production process minus the

payment to productive factors are the aggregate profits:

PY profits WL RK− = +

( ) ( )L LPY profits P MP L P MP K− = +

,L KW RMP MPP P

⎛ ⎞ ⎛ ⎞= =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

• But we know that factors are paid according to their marginal product:

• Thus:

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Income distribution

• But recall that CRS functions have the following property

( , ) L KY F K L MP L MP K= = +

• Thus, combining all previous results we have that:

0L KW Rprofits Y L K Y MP L MP KP P

⎛ ⎞ ⎛ ⎞= − − = − − =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

• Check this property for the following function:(1 )( , )Y F K L K Lα α−= =


• Thus,

W RY L KP P

⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

Income distribution

• Under constant returns to scale the payment to productive factors exhausts total output. There are not extraordinary profits (over and above the remuneration for the service of capital).

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• Households are the owners of the factors of production (K, L) and perceive income (Y).

• They use their income: – To pay taxes (T). After tax income (Y-T) is called

disposable income and may be used:– To purchase goods and services today: Consumption

(C).– To accumulate for the future: Saving (S).

From income to spending: the uses of income

Y C S T= + +


• Aggregate output produced by firms becomes aggregate income earned by households.

• Income in turn becomes spending which constitutes aggregate demand.

• In equilibrium aggregate supply and aggregate demand are equal. Thus we shall close the circle: income equals spending, which equals output, which equals income ....

• But there is something missing in this chain. Households only spend a fraction of their income: consumption. Neither taxes nor saving involve the purchase of goods and services.

• Thus, where does the rest of spending come from, so that all output produced (Y) is demanded?

From income to spending: aggregate demand

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• Consumption (C): Purchases of goods (durable and non-durable) and services by households.

• Investment (I): Purchases of equipment and buildings by firms.

• Public spending (G): Purchases of goods and services by the public sector (this does not include transfers).

From income to spending: aggregate demand

The components of aggregate demand: total spending

Y C I G= + +


Consumption depends mainly on disposable income

Aggregate demand: consumption

( )C C Y T= −

The marginal propensity to consume (MPC) reflects by how much consumption increases with each new euro earned:

CPMCY

∆=∆

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Private investment depends mainly on the real interest rate: r

Aggregate demand: investment

1) The real interest rate approximates the user cost of capital and represents the opportunity cost of those funds spent on investment goods.

2) Investment also increases if the prospects of future profits improve.

( )I I r=


1e

t t

t

P Pr iP

+⎛ ⎞−≈ − ⎜ ⎟

⎝ ⎠

• Let us assume that I borrow 100€ in 2005 to be repaid in 2006. The nominal interest rate (i) is 5%. The 2005 CPI is 40 and is expected to be 41 in 2006

• The true cost of the loan is given by the ratio:

How much do I have to pay in 2006/How much have I borrowed in 2005

• The real interest rate (r) is approximated as the difference between the nominal rate (i) and expected inflation (πe).


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• Gross nominal interest rate

1 0 0 (1 0 .0 5) 11 0 0

i+⎛ ⎞ = +⎜ ⎟⎝ ⎠

• Gross real interest rate

1 0 0 (1 0 . 0 5 )1 . 0 54 1 1 . 0 2 51 0 0 1 . 0 2 5

4 0

+⎛ ⎞⎜ ⎟ ⎛ ⎞= ≈⎜ ⎟ ⎜ ⎟

⎝ ⎠⎜ ⎟⎝ ⎠


• Net real interest rate er i π= −

2 0 0 6

2 0 0 5

(1 ) 1 1 ( )1

ee

i i iPP

ππ

⎛ ⎞⎜ ⎟+ +⎛ ⎞= ≈ + −⎜ ⎟ ⎜ ⎟+⎝ ⎠⎜ ⎟⎜ ⎟⎝ ⎠


• Public spending: purchases of goods and services (consumption goods or equipment) made by the public sector.

• Public transfers are not public spending. They are considered as‘negative taxes’. As far as aggregate demand or total spending is concerned, public spending and transfers are very different: – An increase in public spending increases total spending– An increase in public transfers may or may not increase public spending,

depending on the use that the recipients of such transfers make of them.

• For most of this course we shall assume that public spending is exogenously given and any changes are considered as policy decisions. The implications of alternative ways of public spending financing (taxes, public debt) shall be analyzed in Macro II.

Aggregate demand: public spending

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• Aggregate demand may be expressed as:

Aggregate demand and supply equilibrium

( ) ( )DY C Y T I r G= − + +

( ) ( )Y C Y T I r G= − + +

• Aggregate demand equals aggregate supply in equilibrium. We shall assume that the goods and services market clears. Thus,


Note

• Notice that, because of the equilibrium condition, Y represents not only output and income but also spending. Thus we shall refer toany of these indistinctively. We shall also use Y to refer to aggregate demand and aggregate supply. This is not a lack of imagination. We do it on purpose to remind ourselves that we areanalyzing the joint determination of variables, which interact in different markets.

• Although they are equal in equilibrium, they are not conceptually the same. Output (Y) is what the firms in the economy produce, income (Y, also) is what the owners of the factors of production (labor and capital) are paid for the use of these, and spending (Y, again) is the total amount spent, by households, firms and the government, in purchases of goods and services.

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( ) ( )Y C Y T I r G r= − + + ⇒

• As much as we had to study the labor and capital market to understand how production is carried out and incomes earned, we must also study the goods market.

• In a decentralized economy demand and supply decisions are made by different agents independently of each other. Equilibrium in factor markets is achieved because factor prices are flexible and move to eliminate any excess demand or supply.

• Equilibrium in the goods market. Notice that output is given by the supply side, taxes and public spending are exogenous. Thus the only remaining (endogenous) variable that may adjust to bring the goods market equilibrium about is the real interest rate (r).


( )

( ) ( )

( ) ( )

Y C I r G

Y C Y T S Y T T

S Y T T G I r

= + +

= − + − +

− + − =

How do we explain that the real interest rate adjustment ensures the goods market equilibrium? The market for ‘loanable’ funds


( )S T G I r r+ − = ⇒

Savings (private, S, plus public, T-G) equals investment (I)

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• The goods market equilibrium can also be viewed as the total saving-investment equilibrium. Movements in the interest rate ensure that part of the income that households withdraw from spending (S+T) is transferred to other agents with no income, who spend it in goods and services (G+I).

• Aggregate supply and demand equilibrium is the same as the saving-investment equilibrium. Total savings constitutes the supply of ‘loanablefunds’, whereas investment is also the demand for ‘loanable funds’. Supply does not depend on the interest rate (although it might, as we shall see later) but demand always does. The real interest rate moves to clear this market, thus ensuring aggregate demand and supply equilibrium of goods and services as well.

• NOTE. This argument should make it clear that the interest rate is not the price of money (as it is commonly named) but the price of loans. Most people get confused since loans are usually made in money. You may borrow 100 tons of wheat today and promise to return 105 tons of wheat tomorrow. No money would be involved in the transaction but the interest rate would still be 5%.



(( ), ) ( )S Y T r T G I r− + − =

So far we have assumed that consumption only depends on income. However the real interest rate may also affect the consumption/saving decision. In such a case, the equilibrium can be represented as:


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The determinants of the real interest rate

Oferta y demanda agregadaImprovement

in expectations:Both I and r rise

Reduction in public savings(G rise or T cut):r rises and I falls


Deficit and real interest rates in EMU

-0.04

-0.02

0

0.02

0.04

0.06

0.08

70 74 78 82 86 90 94 98

T

Tipo

de

inte

rés

real

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

Supe

rávi

t /PI

B

T ipo de interés real Superávit /PIB

Rea

l int

eres

t rat

e

Surp

lus/

GD

P

Real interest rate Surplus/GDP

24


0.02

0.03

0.04

0.05

0.06

0.07

0.08

tipo

de in

teré

s re

al

-0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01

superávit(+)/déficit(-) (sobre PIB)

70

71

7273

74

75

76

77

78

79

80

8182

83

84

85

86

8788

89

90

9192

9394

95

96

97

Rea

l int

eres

t rat

e

Deficit (-) Surplus (+)/GDP

Deficit and real interest rates in Spain


( )

( ) }{

,

, , , , ,

( , )

d d WP

sd

d d WR RP P P

sd

s

L L K

L L L

K K L K Y L

K K K

Y F K L Y

⎫=⎪⎪= = ⎪⎪= ⇒⎬⎪⎪= =⎪

= = ⎪⎭

}{( )d

d s

Y C I r Gr

Y Y Y

⎫= + + ⎪⇒⎬= = ⎪⎭

Nominal variables (P, W, R) are determined by the amount of money circulating

The real interest rate r is determined by the decisions

of saving and investment


Real variables are determined independently of the amount of

money in circulation

W/P, R/P, L, K Y are determined by the conditions

of the supply side

25


• We now start the study of the open economy. This brings into theanalysis of how an economic system works some additional markets and relative prices. In particular, the domestic economycan trade in goods and financial assets with the rest of the world and the decisions about where to buy or where to invest depend mostly on two relative prices: the interest rate differential and the real exchange rate.

• To facilitate the exposition, we proceed along the same steps as in the closed economy: We consider an open economy in the long run, i.e. all prices are flexible (the supply curve is vertical). Thus changes in aggregate demand do not have any effect on output, we look mainly at the determination of savings and investment.

Investment and savings in the open economy


• The supply side of the economy is affected by openness:– The rate of technological progress (A) is stimulated by transfers of know-how

and ideas across countries.– Productive capital (K) is also reallocated across countries. Firms move in

search of a better economic environment and higher profits. – Migrations alter the amount of labor available in an economy (L) and the

labor market at large.

• However, we shall leave these supply side effects aside and focus primarily on the effects that openness has on the demand side of the economy. These effects are: – There is a new component of aggregate demand: net exports (exports minus

imports).– Investment can be financed by domestic or foreign saving.– Households and firms may now hold their wealth both in domestic and in

foreign assets.

Investment and savings in the open economy

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Aggregate spending in the open economy

• Total expenditure in the open economy is given by:

d d dY C I G EX= + + +

• Cd: spending by domestic households on goods and services produced at home.

• Id: spending by domestic firms on new capital goods produced at home.

• Gd: public spending on goods and services produced at home. • EX: total exports of goods and services produced at home.


• We can rewrite this expression in a way that resembles what we had in the closed economy.

• Let us define:– Cm: spending by domestic households on goods and services produced

abroad.– Im: spending by domestic firms on new capital goods produced abroad.– Gm: public spending on goods and services produced abroad.

• Total consumption, investment and public spending are defined as: – Consumption: C= Cd +Cm

– Investment: I= Id +Im

– Public spending: G= Gd +Gm


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Rearranging terms,

( ) ( ) ( )m m mY C C I I G G EX= − + − + − +

( )m m mY C I G EX C I G= + + + − + +

Y C I G EX IM= + + + −

Y C I G XN= + + +

Aggregate demand equals total domestic spending(in goods and services produced at home and abroad)

plus net exports (exports minus imports)



Savings, investment and the trade balance

• As we know, there is a close link between goods markets and financial markets.

• Total income in the domestic country has three uses:

Y C I G XN= + + +

Y C S T= + +

• While, total expenditure is given by:

• Then, in equilibrium, the following condition must hold:

I G XN S T+ + = +

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• As such, equilibrium implies:

• Domestic investment (I) can be financed by raising funds from public domestic savings (T-G), private savings (S) as well as from foreign savings (-XN).

• A VERY IMPORTANT REMARK: The amount of savings that an economy is able to attract in the foreign financial markets equals minus net exports. If a country is running a trade deficit (XN<0) it is being financed by foreign funds, while an economy with a trade surplus is financing the rest of the world.

I S T G XN= + − −



• To see this, let us write:

• The difference between total domestic savings (private plus public: S+(T-G)) and domestic investment (I) is the amount of funds the country’s residents can lend abroad. This amount equals net exports (XN).

• If the excess of domestic savings is positive it means that we are providing funds to the rest of the world. The rest of the world is using our funds to buy our goods in excess of what they sell to us, thus the country with excess savings is running a trade deficit.

• If we have a trade balance surplus (XN>0), we are lending abroad (S+(T-G)-I>0) and we shall get the returns from our lending in the future. If our trade balance is negative (XN<0), then we are borrowing from abroad because we have a shortage of savings (S+(T-G)-I<0), and we shall have to pay the interest on our borrowing in the future.

( )S T G I XN+ − − =


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In the open economy the model is slightly different:

• 1) the interest rate does not depend on the domestic economic conditions. Since all agents, domestic and foreign, can lend andborrow anywhere in the world, the interest rates cannot permanently differ across countries.

• 2) net exports are a component of aggregate demand. Thus aggregate demand will respond to whatever variables affect imports and exports.

• Let us discuss these new features in turn.

The macroeconomics of the open economy


• We shall assume further that the domestic economy is small enough that it does not influence the world interest rate. Thus r* is exogenous.

Perfect capital mobility and interest rates

* .r r dep risk= + +

• Let us assume that international investors can trade assets in any market without restrictions (‘perfect capital mobility’). Then anybody investing in, say, European bonds will have to get a return that is at least equal to what she can obtain elsewhere (the international interest rate, r*) plus a premium to compensate for realignments in the nominal exchange rate (she will have to buy euros today to buy European bonds and then change the return in euros back into dollars to consume abroad) plus an additional premium associated to the specific risk of investing in Europe, as compared with investing elsewhere.

*r r=

• To simplify matters we shall assume throughout that both the exchange rate and the risk premia are zero. Then the following ‘arbitrage condition’ must hold:

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How big is a small open economy?

• Not all economies in the world fit well the description of a small open economy. Japan, the U.S. and the E.M.U. are big enough that their economic policies and domestic shocks can have an influence on the world interest rate.

• The macroeconomics of a large open economy differs from that of a small open one in one single feature: if the economy is large enough the relevant interest rate is no longer exogenous. Domestic investment and financial decisions taken in the large economy depend on the real interest rate, but this is not independent of developments in this economy. – In a way, the study of the large open economy is very similar to that of the

closed economy.– After all, the largest open economy is the world as a whole, which is itself

a closed economy .

• Thus, the study of the small open economy is most interesting because it takes us beyond the closed economy case. In this and in the next topics we shall concentrate on this case.


• We call the difference between exports and imports net exports. What we export will increase with income abroad (Y*) and fall with the relative price of our goods, while domestic imports will rise with our income (Y) as well as with the relative prices of the domestic goods.

• The relative price of our domestic goods is called the real exchange rate (ε).

The trade balance (net exports)

*( , , )XN XN Y Y ε=

• In the long-run neither Y nor Y* are affected by developments in the demand side. Thus we shall assume them to be exogenous and we shall focus on the determination of the real exchange rate. Thus. We may write:

*( , , ) ( )XN XN Y Y XNε ε= =

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• When a US resident is considering buying a European car she must take into account two relative prices: – The price of the European car in euros (P) with the price of a comparable

American car in dollars (P*)– How many dollars she has to pay to purchase the amount of euros needed to

buy the car.• The appropriate comparison has to be made in the same currency, thus we must

consider the price in euros of the American car (eP*) relative to the price in euros of the European car (P). This is what we call the real exchange rate, which is the product of two relative prices: the nominal exchange rate and the relative price of domestic goods.

( ) ( )

( )

$€ €

*$

e PPε =

The real exchange rate


• The nominal exchange rate (e) is the relative price of the currency in two countries. For instance, the euro/dollar nominal exchange rate tells us how many (e) dollars we must pay to buy one euro or how many euros (1/e) we are given for one dollar.

• Variations in the nominal rate: – e rises: the euro appreciates vis-a-vis the dollar (the dollar depreciates

vis-a-vis the euro) if the amount of dollars I have to pay to buy a euro rises (the amount of euros I am given for one dollar falls).

– e falls: the euro depreciates vis-a-vis the dollar (the dollar appreciates vis-a-vis the euro), if the amount of dollars I have to pay to buy a eurofalls (the amount of euros I am given for one dollar rises).

($)1(€)ee =

The nominal exchange rate

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Next exports and the real exchange rate• A high real exchange rate means that domestic goods are expensive relative

to foreign goods. This may be due either to:– High domestic prices in euros (P).– Low foreign prices in dollars (P*).– Euros are expensive relative to dollars (e).

Net exports fallas the

real exchange rate rises

( )XN XN ε−

=


Full open economy model

( , )Y Y F K L= =

( )C C Y T= −

( )I I r=

*r r=

( )XN S T G Iε = + − −

( *)XN S T G I r= + − −

Equilibrium in the open economy

( )XN S T G Iε = + − −

For a given domestic output(Y) and world interest rate (r*),

the equilibrium betweenexcess domestic savings

and net exports determines the equilibrium real interest rate (ε)

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Equilibrium real interest rate

Excess domestic savings do not depend on the real exchange rate.

S+(T-G)-I may be considered as the net supply of domestic funds

(and currency)in the international financial market.

Net exports depend on the real exchange rate.

XN may be considered as the ‘net demand’ of domestic currency

in the international financial market.

ε* represents the equilibrium real exchange rate


Domestic fiscal policy. Increase in public spending (G2>G1) (or tax cut (T2<T1))

An increase of G reduces national savings and the

supply of domestic currency in foreign markets.

The domestic currency becomesmore expensive.

Both the nominal and the real exchange rate

appreciate. Net exports fall.


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• NOTE: Unlike what happens in the closed economy, now the reduction in public savings does not imply a reduction in domestic investment, since the country can always borrow in the international capital market.

• But to be able to do so, it must be prepared to run a trade deficit (or to reduce the trade surplus). Net exports must worsen and the economy loses competitiveness in the goods markets.

• Thus fiscal deficits undermine the countries position either by reducing investment and installed capacity (in the closed economy) or by worsening the competitive position of domestic firms selling abroad (in the open economy case).

Public deficits and trade deficits


The twin deficits in the U.S.

-4

-3

-2

-1

0

1

2

3

4

1950 1960 1970 1980 1990 2000

Percentof GDP

-8

-6

-4

-2

0

2

4

6

8 Percentof GDP

Public deficit (d)

Net Exports (NE)

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Improvements in domestic expectations that raise investment (I2> I1)

Domestic demand rises,excess savings fall.The foreign supply

of domestic currency falls.

The domestic currency becomes

more expensive.The exchange rate

appreciates. Net exports fall.



• The level of output (aggregate supply) is determined by the amount of capital and labor and by the level of technological knowledge available in the economy. Aggregate supply is independent of the price level.

• Factors of production are paid according to their marginal product. Labor income plus capital income exhaust the value of output.

• Part of the income is used to pay taxes. The remaining amount of income (disposable income) is used for consumption or is saved.

• Total spending (aggregate demand) is made by households (consumption) firms (investment) and the public sector (government spending).

What have we learned?

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What have we learned?• The goods and services market clears: aggregate demand equals

aggregate supply.

• The mechanism that ensures that aggregate demand equals aggregate supply is the adjustment in the real interest rate. Adjustments in the interest rate ensure that total savings (private saving plus the public surplus) equal investment.

• The real interest rate depends on saving and investment decisions. A fall in either private or public saving raises the real interest rate and reduces investment.

• An improvement in firms’ expectations raises the real interest rate and investment.


• In the open economy domestic investment can be financed by raising funds from public domestic savings, private savings as well as from foreign savings.

• The real exchange rate depends only on real factors, over the long run. For a given domestic output and world interest rate, the equilibrium between excess domestic savings and net exports determines the equilibrium real exchange rate.

What have we learned?

What determines the amount of goods and services...

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