Finance assignment question 8

HOMEWORK 3

1) Consider a consumer living for 2 periods. Her income is Y₁ =200 and Y₂ =50. Assume rst that this consumer is Keynesian, in the sense that the consumption choice is tied to current income.

Moreover, assume that C_t = Y_t, where C_t is consumption in each period t =1;2.

1. What is the consumption in each period? What is the marginal propensity to consume?
2. Discuss the shortcomings of this consumption function.

Consider next a consumer who has the same income and is forward-looking (i.e. the consumer behaves according to the Permanent Income Model). Her lifetime utility function is:

U = C₁^1/2 C₂^1/2(this utility function is fully consistent with the type of utility function and

indifference curves that we studied in class)

The consumer can borrow or lend at a 15% interest rate (r =0:15).

1. Derive the intertemporal budget constraint of this consumer and draw it with C₁ on the horizontal axis and C₂ on the vertical axis.
2. Illustrate graphically the optimal choice of consumption in each period. How does the consumerbehave in each period (borrowing or lending)? Why? You do not need to nd C₁ and C₂ exactly but be as precise as you can and provide intuition.
3. Now, assume that the interest rate is zero. What does the consumer consume in each period?
4. How does the optimal consumption level change if period 1 income increases by 20? What ifincome increases permanently by 20 (i.e., in both periods)?
5. (This is just additional exercise; do not turn it in but make sure you work on it) Redo parts c,dand e assuming this time that Y₁ =50 and Y₂ =200. How do the answers di⁄er in this case and in the previous case?

• (Additional exercise; do not turn it in but make sure you work on it) Consider a consumer living for 2 periods. Her income is Y₁ =200 and Y₂ =50. If the interest rate is 10% and the consumer aims for her consumption to decline by 10 (that is C₁ = C₂+10) calculate consumption and savings in periods 1 and 2.

• suppose a rm produces according to the following production function:

Y = TFP K^0:5

where TFP =2 (for simplicity, we have abstracted from labor). The price of each unit of output is one (P =1) and the annual interest rate is 4%.

1. Find the optimal stock of capital. Show graphically.
2. Suppose there is a positive technological shock. Furthermore, there is a nancial shock and the rate of interest rises. How is the optimal stock of capital a⁄ected?
3. Does your answer to part b change if there is a fall in the interest rate (instead of a rise)?

If yes, how? Show graphically.

• Consider an economy where

the monetary base consists of 200 monetary units (H = 150); and

the reserve requirement is 15%.

Find the money multiplier and the stock of money. What if the reserve requirement is 100%? How does your answer change?

• The stock of money (M) in the economy is 200, the price level (P) is 1, and real output (Y) is 1000.

1. Find the velocity of money in this economy.
2. Country X s real GDP has grown by 3% and money supply has grown at a rate of 5%over the last year. What should the in ation rate be according to the quantity theory of money?

• In country X, the inflation rate is 4% and the real interest rate is 3.5%.
  1. What is the nominal interest rate?
  2. If inflation is 6% instead, what is the real interest rate (given the nominal interest rate you found in part a)?