Mike's income is $450 per month.He spends all of it on books (B)and CDs (C).Books cost $10 and CD's cost $15.His preferences correspond to the utility function U(B,C)= BxC.For that utility function,the marginal benefit of books is C and the marginal benefit of CDs is B. How many books and how many CDs will he purchase in a month?
A) 10 CDs and 30 Books
B) 30 CDs and 10 Books
C) 20 CDs and 15 Books
D) 15 CDs and 30 Books

Question

Quizplus · Accepted Answer

To maximize utility given the budget constraint, Mike will allocate his income to equalize the marginal utility per dollar spent on books and CDs. The prices of books and CDs are $10 and $15, respectively. The utility function is U(B,C) = BxC, with marginal benefits of C for books and B for CDs. Setting the marginal benefit per dollar equal for both goods, we get C/10 = B/15. To spend all $450, we solve 10B + 15C = 450. Solving these equations simultaneously, we find that Mike buys 30 books and 10 CDs.

Mike's Income Is $450 Per Month