Question

Suppose that Jessica has the following utility, U = C1^1/2 C2^1/2 and that she earns $400 in the first period and $700 in the second period. Her budget constraint is given by C1 + C2/1+r = Y1 + Y2/1+r . The interest rate is 0.25 (i.e., 25%). She wants to maximize her utility.

(a) What are her optimal values of C1 and C2?

(b) Is Jessica a borrower or a saver in period 1?

(c) Suppose the real interest rate rises from 0.25 to 0.4, what are her new optimal values of C1 and C2?

Answer 1

Utility function is U = C1^1/2 C2^1/2

Here Y1 = $400 and Y2 = $700.

Budget constraint is given by C1 + C2/1+r = Y1 + Y2/1+r

Use r = 0.25 so that budget constraint is C1 + C2/1.25 = 400 + 700/1.25

1.25C1 + C2 = 1200

This indicates that the slope of the budget constraint is -1.25.

From utility function the slope of the indifference curve is -MUC1/MUC2 = -C2/C1

At the optimum choice, slope of the indifference curve = slope of the budget constraint

-C2/C1 = -1.25 so C2 = 1.25C1

Use this in the budget constraint 1.25C1 + 1.25C1 = 1200

This gives C1 = 480 and C2 = 600

(a) C1 = 480 and C2 = 600

(b) Y1 is 400 and C1 is 480 so Jessica is a borrower in period 1.

(c) Suppose the real interest rate rises from 0.25 to 0.4.

Use r = 0.25 so that budget constraint is C1 + C2/1.40 = 400 + 700/1.40

1.4C1 + C2 = 1260

This indicates that the slope of the budget constraint is -1.40

From utility function the slope of the indifference curve is -MUC1/MUC2 = -C2/C1

At the optimum choice, slope of the indifference curve = slope of the budget constraint

-C2/C1 = -1.40 so C2 = 1.40C1

Use this in the budget constraint 1.40C1 + 1.40C1 = 1260

This gives C1 = 450 and C2 = 630