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29 July, 13:20

Harmonâs utility function is U (x1, x2) = x1x2. His income is 100 dollars. The price of good 2 is p2 = 4. Good 1 is priced as follows. The first 15 units cost 4 dollars per unit and any additional units cost 5 dollars per unit. What consumption bundle does Alex choose?

a. (12.5, 12.5)

b. (25,12.5)

c. (12.5, 25)

d. (15, 10)

e. None of the above.

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  1. 29 July, 13:28
    0
    Option (a) is correct.

    Explanation:

    U (x1, x2) = x1x2

    Income = 100 dollars

    Therefore,

    Alex budget constraint is $100.

    (a) (12.5, 12.5)

    Cost of this bundle = 12.5 * $4 + 12.5 * $4

    = $50 + $50

    = $100

    (b) (25, 12.5)

    Cost of this bundle = 15 * $4 + 10 * $5 + 12.5 * $4

    = $60 + $50 + $50

    = $160

    This bundle is not possible because of budget constraint.

    (c) (12.5, 25)

    Cost of this bundle = 12.5 * $4 + 25 * $4

    = $50 + $100

    = $150

    This bundle is not possible because of budget constraint.

    (d) (15, 10)

    Cost of this bundle = 15 * $4 + 10 * $4

    = $60 + $40

    = $100

    Hence, it is possible to buy bundle (a) and (d).

    Utility function for (a) and (d) bundle:

    (a) (12.5, 12.5)

    Utility = 12.5 * 12.5

    = 156.25

    (d) (15, 10)

    Utility = 15 * 10

    = 150

    Therefore,

    Alex will choose bundle (a) (12.5, 12.5) because this will give maximum utility.
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