Monopoly and Market power

Monopoly and Market power - PGP I Term I Suppose you are...

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PGP I Term I
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Suppose you are the manager of a watch making firm operating in a competitive market. Your cost of production is given by C = 200 + 2q2, where q is the level of output and C is total cost. (The marginal cost of production is 4q; the fixed cost is $200.) a. If the price of watches is $100, how many watches should you produce to maximize profit? b. What will the profit level be? c. At what minimum price will the firm produce a positive output?
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a. Profits are maximized where price equals marginal cost. Therefore,100 = 4q, or q =25. b. Profit is equal to total revenue minus total cost: π = Pq (200 + 2q 2 ) Thus, π = (100)(25) – (200 + 2(25)2)= Rs.1050.
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At what minimum price will the firm produce a positive output? Ans. A firm will produce in the short run if its price is greater than equal to AVC. The firm’s short -run Supply curve is its MC curve above minimum AVC. Here, AVC = VC/q = 2q 2 / q = 2q . Also, MC = 4q. So, MC is greater than AVC for any quantity greater than 0. This means that the firm produces in the short run as long as price is positive.
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10. Suppose you are given the following information about a particular industry: QD = 6500 −100P :Market demand QS =1200P :Market supply C(q) = 722 + q 2 /200 :Firm total cost function MC(q) =2q/ 200 : Firm MC function Assume that all firms are identical, and that the market is characterized by pure competition
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a. Find the equilibrium price, the equilibrium quantity, the output supplied by the firm, and the profit of each firm. Equilibrium price and quantity are found by setting Market supply equal to market demand: 6500 100P = 1200P Solve to find P = 5 and substitute into either equation to find Q = 6000. To find the output for the firm set price equal to marginal cost: 5 = 2q/200 and therefore q = 500. Profit=Pq-Cq=5(500)-(722+500 2 /200)=528
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C. What is the lowest price at which each firm would sell its output in the long run? Is profit positive, negative, or zero at this price? Explain. In the long run profit falls to zero, which means price falls to the minimum value of AC. To find the minimum average cost, set marginal cost equal to average cost and solve for q: 2q/200= 722/q+ q/200 q/200=722/q q 2 = 722(200) q = 380 AC(q = 380) = 3.8. Therefore, the firm will not sell for any price less than Rs.3.80 in the long run. The long-run equilibrium price is therefore Rs.3.80, and at a price of Rs.3.80, each firm’s economic profit equals zero because P = AC.
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d. What is the lowest price at which each firm would sell its output in the short run? Is profit
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Monopoly and Market power - PGP I Term I Suppose you are...

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