Assume the representative consumer lives in two periods and his preferences can be described by the utility function

U(c,c)=c1/3 +(c)1/3,

where c is the current consumption, c is next period consumption, and = 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.
2. If the government sets t = 50, what will be the consumer's estimate of the value of t?
3. Is it optimal for the consumer to consume his disposable income in each period?
4. Solve the consumer's problem by finding the optimal allocations c* and c'* .
5. Is the consumer a lender or a borrower?
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?