Suppose a consumer live two periods, in the first have an income m1 = 30 and in the second an income of m2 = 20. Suppose the interest rate is 10% and can borrow and lend at that interest rate.

(a) What is the maximum quantity he can consume in the first period?

(b) What is the maximum quantity he can consume in the second period?

(c) Draw the budget line clearly stating the intercepts and the slope. Suppose that the preferences for consumption in periods 1 and 2 of this individual can be represented by the utility function U(C1, C2) = (C2^2/3)*(C2^1/3) .

(d) Calculate the MRS at the endowment point (m1, m2) and tell if the consumer is patient or impatient.

(e) Find the optimum of the consumer. Suppose that the interest rate increases to 20%:

(f) Draw the new budget line clearly stating the intercepts and the slope.

(g) Explain what will happen with the optimal amounts of consumption in period 1 and period 2 with the new interest rate