Question

. Suppose you receive ?1 of your income this period and ?2 of your income in the next period. If you can either borrow or lend at an interest rate ?, what is the most you can consume in the next period? Explain.

Answer 1

Answer

Lets first form Intertemporal budget constraint.

Let Consumption in period 1 be C1, Counsumption in period 2 be C2, Income in period 1 be Y1, Income in period 2 be Y2 and interest rate be r

PERIOD 1 :

C1 + S = Y1 where S = saving and if S is negative this means that he borrows and if S is positive this means that he lends

=> S = Y1 - C1 -------------------------------(1)

PERIOD 2 :

C2 = Y2 + rS (If he lends then he will earn interest and if he borrows then he will have to pay interest)

Using (1) we get :

=> C2 = Y2 + r(Y1 - C1)

=> rC1 + C2 = Y2 + r(Y1) ------------------------Intertemporal budget constant

From above constraint we have :

C2 = Y2 + r(Y1) - rC1

This means that more C1 means lesser will be C2. Hence we want C1 to be as least as possible and as C1 cannot be negative implies minimum C1 possible be 0. So we have C1 = 0 in order to have maximum C2

=> C2 = Y2 + r(Y1) - r*0 = Y2 + r(Y1)

Hence, Most you can consume in next period(i.e. period 2) is r(Y1) + Y2

(Note You will consume most in next period when you save all you income in period 1 and lend all that income.)