macroeconomics

ECO 209 - Assignment 5 - Due Wednesday, April 2

1. Consider an economy where limited commitment imposes a borrowing constraint on households. That is, instead of being freely able to borrow against future income, households can only borrow up to a certain amount in the first period. The amount they can borrow depends on how much collateral, H, they have as security against the loan, and the price of that collateral, p, in the first period. Collateral is necessary because banks only have the power to repay loans through collateral - they cannot seize a person’s income directly.

Households have an income endowment of y − t in the first period and y′ − t′ in the second, and the economy has some interest rate r. Collateral can be consumed in the second period only.

(a) Write down the borrowing constraint implied by this structure and diagram the consumer’s budget constraint. Will the indifference curve here always be tangent to the budget constraint?

Now imagine that there is some uncertainty about the price of the collateral in the second period. In particular, with probability a the price remains p, but with probability 1 − a the price will be p

2 in the second period.

(b) Why does this mean the bank needs to change its lending practices? (c) How much can the bank now safely lend? (d) In a competitive banking sector, what interest rate will be charged on loans in excess

of this safe limit? (e) Write down the new borrowing constraint and diagram the new budget constraint for

the consumer in this world. (f) Briefly describe what happens when a decreases. Is there any significant difference

between a decreasing and p 2

decreasing?

2. Consider our two-market (labor and goods) two-period model of Ch. 11, where the flexible wage is clearing the labor market and the flexible interest rate is clearing the goods market. Labor supply is determined by the optimal choice of hours, and labor demand by the marginal product of labor. Output supply is determined by the production function and output demand by the demand for consumption, investment and government spending.

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(a) The government, in an effort to stimulate investment, decides to raise taxes on house- holds in order to subsidize firms. Firms will receive s1 for each unit of output they produce this period. Diagram and explain the effects of this policy.

(a) The government, in an effort to stimulate investment, decides to raise taxes on house- holds in order to subsidize firms. Firms will receive s2 for each unit of investment they undertake this period. Diagram and explain the effects of this policy.

(c) Which policy do you prefer? Explain your choice.

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