Job is a smoker. He has a utility function for cigarettes smoked in ba

Job is a smoker. He has a utility function for cigarettes smoked in bars (q1 ) and a composite good (q2 ) given by U(q1,q2 ) = 10q1.5 + q2 Job’s income is $100 and faces prices p1 = 5 and p2 = 1. The government is planning to ban smoking in bars.

Compute the compensating variation.

ANSWER

Find the utility before the smoking ban. Set MRS = MRT (or use Lagrangian method) to compute the optimal bundle. Solving yields q1 = 1 and q2 = 95. The utility = 105. To reach the same utility when q1 = 0, the consumer would need an additional $5 of income, i.e., CV = 5.