A firm sells two goods (X and Y)that are related in consumption.The estimated inverse demand and cost functions are: $$\begin{array} { l } P _ { X } = 105 - 0.5 Q _ { X } - 0.75 Q _ { Y } \ P _ { Y } = 120 - Q _ { Y } - 0.5 Q _ { X } \ M C _ { X } = 10 + 0.25 Q _ { X } \ M C _ { Y } = 16 + 0.5 Q _ { Y } \end{array}$$ What are the profit-maximizing prices for the two goods? A) $P _ { X }$ = $40, $P _ { y }$ = $32.50 B) $P _ { X }$ = $53.50, $P _ { y }$ = $61 C) $P _ { X }$ = $80, $P _ { y }$ = $55 D) $P _ { X }$ = $112.50, $P _ { y }$ = $87.75 E)none of the above

Question

Quizplus · Accepted Answer

The profit-maximizing prices are found by setting marginal revenue equal to marginal cost for each good and solving the system of equations. The correct prices are $P _ { X }$ = $53.50 and $P _ { Y }$ = $61.

A Firm Sells Two Goods (X and Y)that Are Related