Question

Consider a consumer that lives only for two periods. He works in period 1 (and gets income Y1) and retires in period 2 (and gets income Y2 < Y1).

This consumer has the usual preferences over time: u(C1) + βu(C2)

Assume that now the consumer is allowed to save or borrow. Write down the new budget constraint. What is the consumption in period 1 and period 2? Display graphically. Could the consumer be worse of? Could the consumer be better of? Draw budget constraints such that for one of them consumer prefers to borrow and for the other - prefers to save

Answer 1

Let’s assume that the consumer is a saver implied will save for future if saving and borrowing are allowed. So, if initially saving and borrowing are not allowed the consumer consume at “W”, where he or she consume all his or her income in each respective years. Now, if saving and borrowing are allowed the consumer move to “E” where “C1* < Y1” and “C*2 > Y2”, the consumer is getting “U2 > U1” level of utility implied the consumer gets better off.

Future Consumption (C2) U2 C*1 < y1 Present Consumption (C1)

Now assumes that the consumer is a borrower implied will borrow for present if saving and borrowing are allowed. So, if initially saving and borrowing are not allowed the consumer consume at “W”, where he or she consume all his or her income in each respective years. Now, if saving and borrowing are allowed the consumer move to “E” where “C1* > Y1” and “C*2 < Y2”, the consumer is getting “U2 > U1” level of utility implied the consumer gets better off.

Future Consumption (C2) Y1_C1 A2 Present Consumption (C1)

So, in both the cases the consumer gets better off.