# Finance assignment question 8

## HOMEWORK 3

1) Consider a consumer living for 2 periods. Her income is *Y*_{1 }=200 and *Y*_{2 }=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*, where

_{t}*C*is consumption in each period

_{t }*t*=1

*;*2.

- What is the consumption in each period? What is the marginal propensity to consume?
- 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 = C_{1}^{1/2} C_{2}^{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).

- Derive the intertemporal budget constraint of this consumer and draw it with
*C*_{1 }on the horizontal axis and*C*_{2 }on the vertical axis. - 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
*C*_{1 }and*C*_{2 }exactly but be as precise as you can and provide intuition. - Now, assume that the interest rate is zero. What does the consumer consume in each period?
- 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)?
- (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
*Y*_{1 }=50 and*Y*_{2 }=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
*Y*_{1 }=200 and*Y*_{2 }=50. If the interest rate is 10% and the consumer aims for her consumption to decline by 10 (that is*C*_{1 }=*C*_{2}+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%.

- Find the optimal stock of capital. Show graphically.
- 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?
- 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.

- Find the velocity of money in this economy.
- 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%.
- What is the nominal interest rate?
- If inflation is 6% instead, what is the real interest rate (given the nominal interest rate you found in part a)?