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?

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28 June, 09:36

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?

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Answers (1)

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Valentina Howard · Answer 1

The answer is 9 tapes

Explanation:

U (x, y, z) = x+z^1/2*f (y)

Since Daisy has one tape recorder, f (y) = 24. Utility function becomes

U (x, y, z) = x+24*z^1/2=x+24z^1/2

Marginal utility from x=MUX=dU/dx=1

Marginal utility from z=MUY=dU/dz=12/z^1/2

Utility maximization requires that

MUX/MUY=PX/PY

1/[12/z^1/2]=1/4

z^1/2=3

Taking square at both sides

(z^1/2) ² = (3) ²

z=9 (answer)