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The market demand curve for a good is given by Q = A + bY − cP, where Q denotes the quantity demanded, Y denotes aggregate income, P denotes the market price, and A, b, and c are positive constants.
(a)Suppose this good is produced in an industry that is made up of N identical profit-maximizing, perfectly competitive firms, each of which has a cost function, Ci(qi) = 144 − 20qi + qi^2, where qi denotes the output of firm i. Derive the short-run market equilibrium price.
(b)What is the long-run market equilibrium price?
(c)Suppose that N = 2 and the firms behave as Cournot duopolists. Further suppose that the values of A, b, c, and Y are such that the demand curve becomes Q = 100 − P . What is the market equilibrium price?
(d)Entrepreneurial talent is scarce. Suppose the supply curve for entrepreneurs is given by Qe = 0.25w,
where w is the annual wage paid. Suppose also that each firm requires one (and only one) entrepreneur (hence the quantity of entrepreneurs hired is equal to the number of firms), and market demand shifted to Q = 1500 − 50P . Long-run total costs for each firm are hence given by
Ci(qi, w) = 0.5qi^2 − 10qi + w.
What is the long-run equilibrium output and market price? How many firms will
there be? How many entrepreneurs will be hired, and what is their wage?
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