Daisy received a tape recorder as a birthday gift and is not able to return it.Her utility function is U(x, y, z) = x + z 1/2 f(y) , where z is the number of tapes she buys, y is the number of tape recorders she has, and x is the amount of money she has left to spend.f(y) = 0 if y

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Daisy received a tape recorder as a birthday gift and is not able to return it.Her utility function is U(x, y, z) = x + z^1/2 f(y) , where z is the number of tapes she buys, y is the number of tape recorders she has, and x is the amount of money she has left to spend.f(y) = 0 if y < 1 and f(y) = 24 if y is 1 or greater.The price of tapes is $4 and she can easily afford to buy dozens of tapes.How many tapes will she buy?

A) 9
B) 11
C) 7
D) 13
E) We need to know the price of tape recorders to solve this problem.

kirat singh · Accepted Answer

Final Answer : A, Explanation :  Daisy has one tape recorder, so f(y) = 24. Her utility function is U(x, y, z) = x + z 1/2  * 24. The price of tapes is $4, so she can buy z tapes with x/4 dollars. Her goal is to maximize her utility function, which is equivalent to maximizing U(x, y, z) = x + 6z 1/2 . Since she can afford to buy dozens of tapes, she will buy as many tapes as possible until her marginal utility from buying another tape is zero. The marginal utility from buying another tape is dU/dz = 6z -1/2 . Setting this equal to zero and solving for z, we get z = 36. Therefore, she will buy 36 tapes.

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