Problem set #5 – Competitive Equilibrium – Microeconomics 701 A beginning market equilibrium problem: Firms have production function kl A x = . Consumers have demand function p I x / α = . In the short run, there are m firms, each with one unit of capital. The costs of labor are given by w , while the costs of capital are given by r . There are n consumers in the market. 1. Find the short run cost function of firms (assume throughout that the industry is competitive). 2. Find each firm’s supply function, and find the market supply function. Also, find the market demand function. 3. Find market output and price by equating quantity demanded and supplied, given your answers in 2 above. 4. A trickier question: In the long run, what must be the price of the good, given freedom of entry? What will be the total market quantity produced? 5. Can you figure out the number of firms that will be in the industry in the long run? Explain why or why not.
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