Jane spends $210 per month on wine and beer.Her utility function is given by TU = 100WB,where W represents the number of bottles of wine that she buys and B represents the number of cases of beer that she buys.If wine costs $10 per bottle and beer costs $15 per case,she will maximize utility by buying:
A) 10.5 bottles of wine and 7 cases of beer.
B) 2 bottles of wine and 3 cases of beer.
C) equal amounts of wine and beer.
D) 10 bottles of wine and 13.33 cases of beer.
E) none of the above.

Question

Quizplus · Accepted Answer

To maximize utility, Jane should spend her budget such that the marginal utility per dollar spent on wine equals the marginal utility per dollar spent on beer. Given the utility function TU = 100WB, the marginal utility of wine is 100B and for beer is 100W. Setting the marginal utility per dollar equal gives 100B/10 = 100W/15, simplifying to B = 1.5W. Solving the budget constraint 10W + 15B = 210 with B = 1.5W gives W = 10.5 and B = 7.

Jane Spends $210 Per Month on Wine and Beer