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.