Question

Fred consumes quantities of butter and margarine; his utility function is given by U = 5M + 2B. If Fred has $10 to spend on butter and margarine, and if butter costs $2 per pound and margarine costs $1 per pound, what is his optimal bundle of butter and margarine? Selected Answer: Incorrect [None Given] Answers: a. 3 butter and 4 margarine b. 5 butter and 0 margarine Correctc. 0 butter and 10 margarine d. 2 butter and 6 margarine e. none of the above

Answer 1

Option (c).

A linear utility function means butter and margarine are perfect substitutes. The isoquant will be linear, touching both axes, and optimal consumption is at one of the corner points, so either butter or margarine will be consumed.

U = 5M + 2B

Total cost (TC) ($): 10 = M + 2B. From this function we get

When M = 0, B = 10/2 = 5 and U = 5 x 0 + 2 x 5 = 10

When B = 0, M = 10 and U = 5 x 10 + 2 x 0 = 50

Since utility is higher (50 > 10) when M = 10 and B = 0, this is the optimal bundle.