4/8/2016 1 Intermediate Microeconomics W3211 Lecture 17: Equilibrium with Firms Introduction Columbia University, Spring 2016 Mark Dean: [email protected] 2 3 4 The Story So Far…. Today • We have now thought a lot about what a single firm will • Think about what happens when firms are not on their do in a perfectly competitive market own • We know how to maximize profits • How many firms combine to make an industry • In the short and long run • What happens when firms and consumers interact • This second point will take us back to the study of equilibrium • Equilibrium will now come in two flavors • Partial Equilibrium • General Equilibrium 6 Supply From A Competitive Industry So far we have thought about the behavior of a single firm But typically an industry will consist of many firms In fact, we pretty much assumed that when we started talking about perfect competition Industry Supply How are the supply decisions of the many individual firms in a competitive industry combined to discover the market supply curve for the entire industry? 5 1 4/8/2016 7 8 Supply From A Competitive Industry Short-Run Supply Since every firm in the industry is a price-taker, total quantity In a short-run the number of firms in the industry is, temporarily, supplied at a given price is the sum of quantities supplied at fixed. that price by the individual firms. Let n be the number of firms; i = 1, … ,n. Si(p) is firm i’s supply function. 9 Supply From A Competitive 10 Short-Run Supply Industry In a short-run the number of firms in the industry is, temporarily, fixed Firm 1’s Supply Firm 2’s Supply Let n be the number of firms; p p i = 1, … ,n. Si(p) is firm i’s supply function. The industry’s short-run supply function is n S1(p) S2(p) S(p) Si (p). i1 11 12 Supply From A Competitive Industry Supply From A Competitive Industry Firm 1’s Supply Firm 2’s Supply Firm 1’s Supply Firm 2’s Supply p p p p p” p’ S (p’) S (p) S (p) S (p”) S (p) S (p”) S (p) p 1 1 2 p 1 1 2 2 p” p’ S1(p’) S(p) = S1(p) + S2(p) S1(p”)+S2(p”) S(p) = S1(p) + S2(p) Industry’s Supply Industry’s Supply 2 4/8/2016 13 14 Supply From A Competitive Industry Short-Run Industry Equilibrium Firm 1’s Supply Firm 2’s Supply p p In a short-run, neither entry nor exit can occur. Consequently, in a short-run equilibrium, some firms may earn positive economics profits, others may suffer economic losses, and still others may earn zero economic profit. S (p) S (p) p 1 2 S(p) = S1(p) + S2(p) Industry’s Supply 15 16 Short-Run Industry Equilibrium Short-Run Industry Equilibrium Firm 1 Firm 2 Firm 3 AC Short-run industry s AC MCs s supply ACs MC MC s p e s s e ps Market demand * * * e y1 y1 y2 y2 y3 y3 Ys Y Short-run equilibrium price clears the market and is taken as given by each firm. (We will talk more about this in a minute) 17 18 Short-Run Industry Equilibrium Long-Run Industry Supply Firm 1 Firm 2 Firm 3 ACs AC In the long-run every firm now in the industry is free to exit and MCs s ACs firms now outside the industry are free to enter MCs MCs e ps (Notice: not true in all markets. There are cases in which firms are not free to enter. Examples?) > 0 < 0 = 0 * * * y1 y1 y2 y2 y3 y3 The industry’s long-run supply function must account for entry and exit as well as for the supply choices of firms that choose to be in the industry. How is this done? 3 4/8/2016 19 20 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm pp Positive economic profit induces entry. Mkt. Demand 2 e S (p) MC(y) AC(y) Economic profit is positive when the market price ps is higher than a firm’s minimum av. total cost; Mkt. p e > min AC(y). s Supply e Entry increases industry supply, causing ps to fall. When does entry cease? For simplicity, let’s assume that all firms have identical costs Y y Suppose the industry initially contains only two firms. 21 22 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand S2(p) MC(y) AC(y) S2(p) MC(y) AC(y) p2 p2 p2 p2 Y y Y y2* y Then the market-clearing price is p2. Then the market-clearing price is p2. Each firm produces y2* units of output. 23 24 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand S2(p) MC(y) AC(y) S2(p) MC(y) AC(y) S3(p) p2 p2 p2 p2 > 0 Y y2* y Y y2* y Each firm makes a positive economic Market supply shifts outwards. profit, inducing entry by another firm. 4 4/8/2016 25 26 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand S2(p) MC(y) AC(y) S2(p) MC(y) AC(y) S3(p) S3(p) p2 p2 p3 p3 Y y2* y Y y3* y Market supply shifts outwards. Each firm produces less. Market price falls. 27 28 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand S2(p) MC(y) AC(y) MC(y) AC(y) S3(p) S3(p) p p p p 3 3 > 0 3 3 > 0 Y y3* y Y y3* y Each firm produces less. Each firm’s economic profit is positive. Each firm’s economic profit is reduced. Will another firm enter? 29 30 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand MC(y) AC(y) MC(y) AC(y) S3(p) S3(p) S4(p) S4(p) p3 p3 p3 p3 Y y3* y Y y3* y Market supply would shift outwards again. Market supply would shift outwards again. Market price would fall again. 5 4/8/2016 31 32 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand MC(y) AC(y) MC(y) AC(y) S3(p) S3(p) S4(p) S4(p) p4 p4 p4 p4 < 0 Y y4* y Y y4* y Each firm would produce less again. Each firm would produce less again. Each firm’s economic profit would be negative. 33 34 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm pp Mkt. Demand The long-run number of firms in the industry is the largest MC(y) AC(y) number for which the market price is at least as large as the minimum of the AC(y). S3(p) Now we can construct the industry’s long-run supply curve S4(p) Remember, this measures how industry supply changes with p4 p4 < 0 price For example because demand changes Y y4* y Each firm would produce less again. Each firm’s economic profit would be negative. So the fourth firm would not enter. 35 36 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm pp Suppose that market demand is large enough to sustain only Mkt. Demand two firms in the industry. S2(p) MC(y) AC(y) S3(p) p2’ p2’ Y y2* y 6 4/8/2016 37 38 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm pp Suppose that market demand is large enough to sustain only Mkt. Demand two firms in the industry. S2(p) MC(y) AC(y) Then if market demand increases, the market price rises, each S3(p) firm produces more, and earns a higher economic profit. p2’ p2’ Y y2* y 39 40 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand S2(p) MC(y) AC(y) S2(p) MC(y) AC(y) S3(p) S3(p) p2” p2” p2” p2” Y y2* y Y y2* y 41 42 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm pp Mkt. Demand As market demand increases further, the market price rises 2 MC(y) AC(y) further, the two incumbent firms each produce more and earn S (p) still higher economic profits -- until a 3rd firm becomes S3(p) indifferent between entering and staying out. p2” p2” Y y2* y Notice that a 3rd firm will not enter since it would earn negative economic profits. 7 4/8/2016 43 44 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand S2(p) MC(y) AC(y) S2(p) MC(y) AC(y) S3(p) S3(p) p2’” p2’” p2” p2” Y y2* y Y y2* y 45 46 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm pp Mkt.