Ian views playing Wartcraft and drinking soda as perfect complements (

Ian views playing Wartcraft and drinking soda as perfect complements (one soda with one hour of playing Wartcraft). Currently, sodas are $1 each and Wartcraft costs $1 per hour. Ian has $12 of income.

a. Compute Ian’s Compensating Variation if the price of Wartcraft rises to $2.
b. Compute Ian’s Equivalent Variation if the price of Wartcraft rises to $2.
c. Compute Ian’s change in Consumer Surplus if the price of Wartcraft rises to $2.

ANSWER

a. Ian initially will purchase six units of each. When the price of Wartcraft rises to $2, the only bundle which will return Ian to the same indifference curve is (6,6 ). This bundle now costs $18. Thus the CV = $12 – $18 = -$6. We need to pay Ian $6 to return him to the initial utility level following the price change.
b. After the price change, with an income of $12, Ian will purchase 4 units of each good. If the prices were still $1 each, then the income level that puts Ian at the bundle (4,4 ) is $8. So the
EV = $8 – $12 = -$4.
c. Denote W and S as the quantities of each good. Perfect complements implies that W=S in the optimum. The budget constraint implies that pW + S = 12, where p is the price of Wartcraft and the price of soda is 1. Solve for W = 12/(1 + p). The CS is the integral of 12/(1 + p) between p = 1 and p = 2. This solves to be $4.87 (approx.).