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.

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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