Question

Jason is currently spending all of his income on apples and pretzels. In each of the following cases, Jason’s current consumption basket is listed as (xA, xP ). The marginal utility at this basket for each good is listed as MUA and MUP and the price of each basket is listed as pA and pP . In each case, determine if Jason is maximizing his utility, and if not, how he should reallocate his spending in order to increase his utility. (a) xA = 17, xP = 11, MUA = 18, MUP = 12, pA = 6, pP = 4 (b) xA = 4, xP = 6, MUA = 15, MUP = 14, pA = 8, pP = 19 (c) xA = 15, xP = 4, MUA = 7, MUP = 13, pA = 9, pP = 6 (d) xA = 4, xP = 15, MUA = 6, MUP = 18, pA = 3, pP = 9

Answer 1

Utility is maximized if MUA/pA = MUP/pP

(a) MUA/pA = 18/6 = 3
MUP/pP = 12/4 = 3
So, MUA/pA = MUP/pP
So, Jason is maximizing his utility.

(b) MUA/pA = 15/8 = 1.875
MUP/pP = 14/19 = 0.74
So, MUA/pA > MUP/pP
So, Jason is not maximizing his utility. To increase his utility, he should increase his spending on xA.

(c) MUA/pA = 7/9 = 0.78
MUP/pP = 13/6 = 2.17
So, MUA/pA < MUP/pP
So, Jason is not maximizing his utility. To increase his utility, he should increase his spending on xP.

(d) MUA/pA = 6/3 = 2
MUP/pP = 18/9 = 2
So, MUA/pA = MUP/pP
So, Jason is maximizing his utility.