Suppose Joe’s utility for lobster (L) and soda (S) can be represented

Suppose Joe’s utility for lobster (L) and soda (S) can be represented as U = L0.5 S0.5. Joe walks into a restaurant with $72. Lobsters cost $18 each and sodas cost $2 each.

How much lobster and soda will Joe consume if he intends to spend all his money? (There are no tax and no tips.)

ANSWER

Maximizing Joe’s utility subject to his budget constraint yields:

U = L0.5 S0.5 + q(72 – 18L – 2S)
1 ). dU/dL = 0.5 L-0.5 S0.5 – 18q = 0
2 ). dU/dL = 0.5 L0.5 S-0.5 – 2q = 0
3 ). dU/dq = 72 – 18L – 2S = 0

From 1 ) and 2 ), S/L = 9 or S = 9L. Substituting into 3 ) yields 72 – 36L = 0 or L = 2. Since S = 9L, S = 18. Thus, Joe will buy 2 lobsters and wash it all down with 18 sodas.