Suppose that Molly had an income of $500 in period 1 and an income of $250 in period 2.Suppose that her utility function were c^a₁c¹^-^a₂, where a = 0.60 and the interest rate were 25%.If her income in period 1 doubled and her income in period 2 stayed the same, her consumption in period 1 would A)double. B)increase by $300. C)increase by $150. D)stay constant. E)increase by $500.

Question

Quizplus · Accepted Answer

Molly's utility function can be rewritten as:
U = cS1 + aS1S1P0(S1U1B1-S1U1B0) + aF1(S1U1P1 - S1S1P0F1) + aF0(S1U1P0 - S1S1P0F1)
Taking the derivative of U with respect to cS1, we get:
dU/dcS1 = 1 + aS1S1P0/(1+r)[(S1U1B1-S1U1B0)-(S1U1P1-S1S1P0F1)]
Since r = 0.25, and aS1S1P0 = 0.60, we get:
dU/dcS1 = 1 + 0.60/1.25[(S1U1B1-S1U1B0)-(S1U1P1-S1S1P0F1)]
The terms in the bracket represent the income and substitution effect of a change in cS1. Since a rise in income in period 1 should lead to an increase in consumption in period 1, the substitution effect should dominate, which implies that the bracketed term is positive. Hence, dU/dcS1 is positive, and an increase in cS1 would lead to an increase in utility. Therefore, if her income in period 1 doubles and her income in period 2 stays the same, her consumption in period 1 would increase by $300 (option B).

Suppose That Molly Had an Income of $500 in Period