A single buyer who wields monopoly power in its purchase of an item is called a monopsonist. Suppose that a large firm is the sole buyer of parts from 10 small suppliers. The cost of a typical supplier is given by C = 20 + 4Q + Q2.
a. Suppose that the large firm sets the market price at some level P. Each supplier acts competitively (i.e., sets output to maximize profit, given P). What is the supply curve of the typical supplier? Of the industry?
b. The monopsonist values the part at $10. This is the firm’s break-even price, but it intends to offer a price much less than this and purchase all parts offered. If it sets price P, its profit is simply:
π = (10 - P)Qs,
Where Qs is the industry supply curve found in part (a). (Of course, Qs is a function of P.) Write down the profit expression and maximize profit with respect to P. Find the firm’s optimal price. Give a brief explanation for this price.