w8sol - Economics 11: Microeconomic Theory 1 Professor...

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Economics 11: Microeconomic Theory 1 Professor Christian Hellwig Exercises Week 8 ANSWERS 1) A perfectly competitive industry has a large number of potential entrants. Each firm has an identical cost function and their cost functions are C (q) = 100 + q 2 /4. Total market demand is given by Q = 1,500 - 50P . a) What is the long-run equilibrium price, the output of each firm (q), the number of firms in the industry, the total industry output (Q), and the profits of each firm? We find the equilibrium price and the quantity each firm produces from the no profit condition. If profit equals zero: P=MC=AC. With the above cost function; MC=q/2; AC = (100/q) + q/4 q/2= (100/q) + q/4, and from this we find that the quantity each firm supplies should equal q = 20, and P = 10 The total output should equal total demand. Denoting N as number of firms in the economy: N*q=1,500 - 50P N*20 = 1,500 – 50*10, so the number of firms is equal to N=50. Profits of each firm will equal to 0. b) What is the long run industry supply schedule? LR supply is horizontal at P=MC=AC=10 Now suppose that the number of firms in the market is equal to what you have found in part (b) for the long-run equilibrium. In addition, in the short-run each firm’s cost is equal to C(q)=q 2 /4, so his fixed cost which is equal to 100 is sunk cost, meaning they are already paid for. And in the short-run no-additional firm can enter the market. c)
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w8sol - Economics 11: Microeconomic Theory 1 Professor...

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