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8 July, 15:50

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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  1. 8 July, 16:14
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    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)
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