Question

Assume the representative consumer lives in two periods and his preferences can be described by the utility function U(c,c′)=c1/3 +β(c′)1/3, where c is the current consumption, c′ is next period consumption, and β = 0.95. Let’s assume that the consumer can borrow or lend at the interest rate r = 10%. The consumer receives an income y = 100 in the current period and y′ = 110 in the next period. The government wants to spend G = 30 in the current period and G′ = 35 in the future period. The consumer pays a lump sum tax t in period 0 and t′ in period 0.

1. Write down the consumer’s intertemporal budget constraint. [03 points]

2. If the government sets t = 50, what will be the consumer’s estimate of the value of t′? [04 points] 1

3. Is it optimal for the consumer to consume his disposable income in each period? [10 points]

4. Solve the consumer’s problem by finding the optimal allocations c⋆ and c′⋆. [10 points]

5. Is the consumer a lender or a borrower? [03 points]

6. Assume the consumer has to choose between two different jobs. Job 1 offers him the in- come bundle (y1, y1′ )=(100, 110) while job 2 offers (y2, y2′ )=(110, 100). Which job will you recommend to the consumer? [10 points]

Answer 1