Consider a market with one large firm and many small firms. The supply curve of the small
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S(p) = 100 + p.
The demand curve for the product is
D(p) = 200 − p.
The cost function for the one large firm is
c(y) = 25y.
(a) Suppose that the large firm is forced to operate at a zero level of output. What will be the equilibrium price? 50. What will be the equilibrium quantity? 150.
(b) Suppose now that the large firm attempts to exploit its market power and set a profit-maximizing price. In order to model this we assume that customers always go first to the competitive firms and buy as much as they are able to and then go to the large firm. In this situation, the equilibrium price will be $37.50. The quantity supplied by the large firm will be 25. and the equilibrium quantity supplied by the competitive firms will be 137.5.
(c) What will be the large firm’s profits? $312.50.
(d) Finally suppose that the large firm could force the competitive firms out of the business and behave as a real monopolist. What will be the equilibrium price? 225/2. What will be the equilibrium quantity? 175/2. What will be the large firm’s profits? (175/2)2.
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