Economics W3213. Intermediate Macroeconomics

Problem Set 6 - Solutions

PROBLEM 1. CONSUMPTION: CLASSICAL AND KEYNESIAN

1. In the Life Cycle Hypothesis, we consider that people do not care about future generations. Hence, they will leave0 assets.

2. As we derived in class, it will be

Y1 +Y2

(1 + r)+ ...+

Y70

(1 + r)69= C1 +

C2

(1 + r)+ ...+

C70

(1 + r)69

3. The marginal propensity to consume will be smaller than 1, since we are considering a temporary increase inincome. People want to smooth the extra income that they get over the rest of their life. Thus, the actual amountof extra consumption will depend on the age of the agent. If he receives the extra income when she is close to die,then the MPC will be bigger than if she receives the temporary increase when she is younger.

4. A permanent increase in income will lead to a MPC = 1 no matter the age of the consumer.

5. In the case of the Permanent Income Hypothesis, people do care about future generations. In this case, the amountof bonds might be positive, negative, or zero.

6. In this case, the Marginal Propensity to Consume is close to 0. A temporary increase in income will be smoothedover infinite periods, since people care about their children, grandchildren, and so on. Then, age does not matterin this scenario.

7. Again, a permanent increase in income will be associated with a MPC = 1, no matter what.

8. If we consider a Keynesian world, we need to think of the following consumption function, Ct = A + ↵Yt, whichwas derived in class. A temporary increase in income will leave A more or less unchanged, and then, the change inconsumption will be given by ↵. Then, MPC = ↵.

9. A permanent increase in income will be again associated with a MPC = 1. In this case, A will also react to theincrease in permanent income. Remember that A was related to the fraction of people that act as a PermanentIncome Hypothesis consumer.

PROBLEM 2. DIFFERENT RATES FOR BORROWING AND LENDING

(please, see next page)

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want or choose to save. Since this fraction will try to smooth consumption, their MPC outof temporary income is close to zero. If income goes up by one dollar, the constrained willincrease their consumption by one dollar, while the rest will hardly change at all. Hence,MPC out of temporary income for the economy as a whole is approximately the fraction of constrained individuals.

iv. If income goes up by the same amount each period, the individual will consume all of theincrease each period. MPC out of permanent income is always one, whether for theconstrained individuals, unconstrained individuals, savers, and the economy as a whole.

v. The PIH and the LCC models reach different conclusions because they start from differentassumptions. Under the PIH, consumers have full access to financial markets. They canborrow or led as much as they desire and hence are able to smooth consumption. Under theLCC model, at least a fraction of consumers are constrained, meaning that they wish toborrow but cannot. Hence, they are forced to consume their current income each period.Their consumption becomes very sensitive to changes in income, even if these changes aretemporary.

4. Sebastian

i. The budget constraint is still linear and passes through the income point (y1, y2) because it is always possible to consume income without borrowing or lending. The slope is still -(1 + r). However, r = rs for saving (to the left of y1) and r = rb for borrowing (to the right of y1), where rb > rs. Hence, the budget constraint has a kink at the income point and is steeper tothe right (Diagram 7).

ii. Depending on preferences, the consumer can save (point A in Diagram 7), borrow (point B), or consume his income each period (point D).

iii. An increase in rb makes the right portion of the budget constraint steeper. When theconsumer saves (point A), it has no effect on him.

When rs increases, the left portion of the budget constraint becomes steeper. Thesubstitution effect induces the saver to decrease c1 and increase c2 because saving has become more attractive and consumption today has become relatively more expensive. Thewealth effect induces the saver to increase both c1 and c2 because he is made richer. Hence, the total effect is an increase in c2 and ambiguous for c1.

iv. An increase in rs makes the left portion of the budget constraint steeper. When theconsumer borrows (point B), it has no effect on him.

When rb increases, the right portion of the budget constraint becomes steeper. Thesubstitution effect induces the borrower to decrease c1 and increase c2 because borrowing has become less attractive and consumption today has become relatively more expensive.The wealth effect induces the borrower to reduce both c1 and c2 because he is made poorer. Hence, the total effect is a decrease in c1 and ambiguous for c2.

v. An increase in rb makes the right portion of the budget constraint steeper. When theconsumer neither borrows nor saves (point D), it has no effect on him.

When rs increases, the left portion of the budget constraint becomes steeper. Depending onpreferences and the size of the increase, it may either have no effect or induce the consumerto decrease c1, save some amount, and increase c2 due to the substitution effect (point E in Diagram 8).

PROBLEM 3. EQUILIBRIUM IN THE COOKIES MARKET

The solutions come just from the notes for the class. Then,

Temporary increase in productivity today

Shock: A1 "

Direct effects:

• Since the production function is Y s1 = A1F (L(...)), as A1 goes up, aggregate supply shifts directly to the right

(Change to the dotted green supply)

Indirect effects:

• As discussed before, the increase in productivity today will change the ratio of wages, and then, the aggregatesupply will shift to the right again (solid green supply)

• Since we have more income, this is a temporary increase in income from the perspective of the consumer. Aggregatedemand will shift to the right, but by a smaller amount than the increase in supply, since this is a temporary shock!

We move from the red equilibrium to the green one, with lower interest rates and higher GDP and consumption.

Permanent increase in productivity

Shock: A1 ", A2 "

Direct effects:

• As before, since A1 is higher, the aggregate supply will shift to the right (solid green supply). NOTICE THAT INTHE GRAPH WE ARE PLOTTING WHAT HAPPENS TODAY!!!!!!!

Indirect effects:

• No change in relative wages!!!

• Permanent increase in income, so, consumption will shift by the same amount, since the MPC = 1 in this case

In the new equilibrium we have more GDP, more consumption and the same interest rate.

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Anticipated temporary increase in productivity tomorrow

Shock: A2 "

Direct effects:

• A1 does not change, so nothing happens

Indirect effects:

• The ratio of wages will decrease, then, people will work less today and more tomorrow. Aggregate supply willshift to the left.

• This is an anticipated increase in income for the consumer. Then, the aggregate demand will shift a bit to the right.

As a result, in the new equilibrium we transition from the red to the green point where ouput decreases and the equilib-rium interest rate is higher in the first figure. But, the effect in output and consumption is ambiguous. The reason isthat the increment in the demand for consumption is related to the increase in income tomorrow. Therefore, we cannotcompare the increase in the demand for consumption with the decrease in output supply today. It might be the case thatthe demand for consumption increases more than the decrease in the output supply if labor supply is close to be inelastic.In the last figure, I show that it can be possible that GDP increases. But the interest rate will unambiguously be higher.

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