Harmon's utility function is U(x 1 , x 2 ) = x 1 x 2 .His income is $100.The price of good 2 is p 2 = 4.Good 1 is priced as follows.The first 15 units cost $4 per unit and any additional units cost $2 per unit.What consumption bundle does Harmon choose?A) (12.5, 12.5)B) (25, 12.5)C) (12.5, 25)D) (15, 10)E) None of the above.

Question

Harmon's utility function is U(x 1 , x 2 ) = x 1 x 2 .His income is $100.The price of good 2 is p 2  = 4.Good 1 is priced as follows.The first 15 units cost $4 per unit and any additional units cost $2 per unit.What consumption bundle does Harmon choose?A) (12.5, 12.5)B) (25, 12.5)C) (12.5, 25)D) (15, 10)E) None of the above.

Brianna Tedesco · Accepted Answer

Final Answer : A, Explanation :  Harmon's budget constraint is 100 = 4x 1  + 4(15) + 2(x 1  - 15) = 6x 1  + 20. Solving for x 1 , we get x 1  = 12.5. Substituting this into the utility function, we get U(12.5, x 2 ) = 12.5x 2 . To maximize utility, Harmon should choose x 2  = 12.5.

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