Models of Competition Review

S Lines are noted with arrows. Please use letters to define areas: B J K Q I H F D C R L G M A E S Z Lines are noted with arrows. Please use letters to define areas: 1. Long-run competitive supply A 2. Monopolist marginal revenue K 3. Total welfare (producer + consumer) in a competitive market in the short run. I,F,L 4. Producer surplus in the long-run competitive market. S None! 5. Consumer surplus in a single price monopoly. I,H,K 6. Producer surplus in a single price monopoly. H,K,R,F More questions: What line is the short-run supply curve? What line is the long-run supply curve? What are producers on line Q above point L doing? Why? What are consumers on line J below point L doing? Why Would production at C be allocatively efficient? Why or why not? 7. Dead-weight loss due to monopoly power K,R,L 8. What is the monopolist profit maximizing mark-up (Learner Index) K-R 9. Which would consumers prefer – a tax equal to (H-G) or a single-price monopoly? Consumers are indifferent in the long-run; better with tax in the short run.

The market consists of the following firms: 5 firms with TC = 500 + 2.5Q2 + 20Q; MC = 5Q + 20 1 firm with TC = 1,000 + 5Q2 + 100Q; MC = 10Q + 100 1 firm with TC = 5,000 + 0.5Q2 + 600Q; MC = Q + 600 What is the market supply? P = 300 + (10/21)Q If the demand is P = 2400 – 11/21Q What is the perfectly competitive equilibrium price and quantity? Q = 2100, P = $1,300 5 firms with Q = 256 1 firm with Q = 120 1 firm with Q = 700 How much will each firm make? ((P – 20)/5)* 5 = P – 20 = Q (P – 100)/10 = P/10 – 10 P – 600 (21/10)P – 630 = Q P = 300 + (10/21)Q For quantities plug in market price to MC functions Avc is vc/Q at q found in prior question 2400 – (11/21)Q= Q + 20 2380 = (32/21)Q Q = 1,562 (rounded) P = 2400 - (11/21)(1562) =1582 Which firm(s) can cut their price to what $ to put the others out of business? 2.5(256) + 20 = $660 5(120) + 100 = $700 0.5(700) + 600 = $950 The five firms with AVC $660 can cut to $699

Demand: P = 200 -4Q MC = 4Q1 MC = 6Q2 If there are two (2) firms in the market with different cost structures (Cournot Oligopoly): How would you express the marginal revenue for firm #1? What is Firm #1’s response function? (How much would they make depending on how much Firm #2 makes?) How much will each firm make? What will be the equilibrium price

Industry supply & demand For a perfectly competitive market: What is the producer surplus? ½ x 25 x 500 = 5,250 What is the consumer surplus? ½ x 50 x 500 = 12,750 Draw a graph and explain in words what would happen in this market in the long-run Producer surplus attracts supply, increasing Q decreasing P, forcing some firms to shut down until all firms produce identically at long run min AVC For a single-price monopoly: What would be the monopolist’s marginal revenue function? P = 100 – Q/10; MR = 100 - Q/5 In the long run consumers would enter the market increasing quantity, decreasing price, pushing high cost producers out of the market. In the long run equilibrium supply would be perfectly elastic at the long run minimum average variable cost. What would be the monopolist’s optimal price and quantity at a marginal cost of $50? Q = 250 P = 75 What would be the monopolist’s producer surplus at the optimal P & Q? 25 x 250 = 6,250 What would be the consumers’ surplus at the optimal P & Q? ½ x 25 x 250 = 3,125

Demand: P = 200 -4Q TC = 10 +2Q2 MC = 4Q Q = 25, P = $100 $1,250 What is the optimal price and quantity in a perfectly competitive market? Q = 25, P = $100 $1,250 What is the producer surplus in a perfectly competitive market? What will happen to price and quantity in the long run (just direction, not actual numbers.) New competitors will enter increasing Q and decreasing P. What is the optimal price and quantity in a monopoly market? (round to nearest whole Q) Q = 17, P = $132 $1,666 What is the producer surplus for the monopolist? What is the consumer surplus with the monopolist’s market power? 200 – 4Q = 4Q 200 = 8Q Q = 25 P = 200 – 4(25) = $100 AVC = 2(25) = 50 PS = 25(100 – 50) = $1,250 200 – 8Q = 4Q Q = 17 (rounded) P = 200 – 4(17) = $132 17(132 – 34) = 1666 ** also try computing with a graph! Dead weight – draw the graph. Y for producer P = 4(17) = $68. 132 – 68 = 64 MC = 4Q+10 = 200 – 4Q 8Q = 190 Q = 23.75 = 24 P = 200 – 4(24) = $104 ½ (200 – 132)(17) = $578 What is the dead-weight loss associated with the monopolist’s market power? ½ (64 x 8) = $256 What will happen to the monopoly market in the long run? Nothing if there are barriers to entry and the monopolist is producing at min AVC

MR = MC MR = MC = AVC P = MR = MC = LAC=ATC Yes No No P < minAVC Please answer the following with math notation What is the short-run profit maximizing condition? MR = MC What is the long-run profit maximizing condition? MR = MC = AVC P = MR = MC = LAC=ATC What is the equilibrium price in the long run? Can a firm have an economic loss but stay in business in the short run? Yes Can a firm have an economic loss but stay in business in the long run? No Is producer surplus the same as economic profit? No What is the shut-down condition? P < minAVC

A B A is perfect, B is monopoly Similarity: profit max condition is MR = MC Difference: MR = price for perfect competition; MR = f(demand) for monopoly Short term b/c TC curve starts above zero. Which panel shows perfect competition and which monopoly competition? What is one difference and one similarity between perfect and monopoly competition? Are these short or long term graphs? How do you know? Answers in notes section below

Good Luck!!