Question

Vesta will live only for two periods. In period 0 she will earn $50,000. In period 1 she will retire on Latmos Hill and live on her savings. Her utility function is U(C0,C1) = C0C1, where C0 is consumption in period 0 ,and C1 is consumption in period 1 .She can borrow and lend at the interest rate i= 0.10. a) Write an expression for her consumption in period 0 as a function of the parameters specified. b) Having solved her utility maximization problem, suppose the interest rate rises .Will her period 0 consumption increase, decrease, or stay the same? Explain.

Answer 1

a)

Period 0 income (M0)= $50,000

Consumption in period 0 (C0)

Consumption in period 1 (C1) = Savings in period 0 + Interest earned on savings(i)

= M - C + i (M - C)

C1 = 1 + i (M - C)

Slope of Budget Line = dC1/dC = -(1+i)

Divide C1 by (1+r) gives   

The above equation is budget line in present value terms.

U = C0C1  

Interest rate i = 0.10, M0 = $50,000

To maximise utility set MRS = - slope of budget line

      

= C1/C0

Expression for her consumption in period 0 as a function of the parameters specified -

C1 = (1+ i) C0 = 1.1C0

Plug this into budget constraint

C0 = $25,000

C1 = 1.1 (25,000) = $27,500

b) When the interest rate rises suppose from 10% to 20% her period 0 consumption stays the same.

C1 = (1+ i) C0 = 1.2C0  

C0 = $25,000