Micro Theory, 2005 Chapter 2 Industrial Organization References: Varian(1992)Chapters 13-16 and MWG(1995)Chapter 12 The firm is assumed to maximize profit, which implies f MR(")=MC(y*) This formula applies to any type of firms in the output market 1. Competitive Output Market Competitive industry: Many firms: Firms are independent of each other in decision making Identical product: Each firm faces a horizontal demand curve at the market price Free entry: Zero profit in the long run A competitive firm takes the market price as given. For a given market price p, firm i faces demand. t if Pi>p 0, oo] if Pi=p if pi0. (22)
Chapter 2 Industrial Organization Micro Theory, 2005 References: Varian (1992) Chapters 13—16 and MWG (1995) Chapter 12. The firm is assumed to maximize profit, which implies † MR(y∗ ) = MC(y∗ ). (2.1) This formula applies to any type of firms in the output market. 1. Competitive Output Market Competitive industry: • Many firms: Firms are independent of each other in decision making. • Identical product: Each firm faces a horizontal demand curve at the market price. • Free entry: Zero profit in the long run. A competitive firm takes the market price as given. For a given market price p, firm i faces demand: † qd i = ⎧ ⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎩ 0 if pi > p [0, ∞] if pi = p ∞ if pi 0. (2.2) 2—1
The industry supply v)=∑() i.e., the industry supply curve is the horizontal sum of the firms' supply curves f Remarks The industry faces a downward sloping market demand 2. The behavior of each firm in the input market is assumed away by the given c(y) 3. The supply curves for the short run and long run are similar(LeChatelier Principle The equilibrium is where industry demand equals industry supply. t If time horizon comes into play, when entry and exit stop, the industry reaches a ong-run equilibrium t Example 2. 1. Consider a decrease in demand. t Example 2.2. Find the equilibrium for f Industry denand: y=a-bp, Firms cost: ci(yi)=yi+1 Example 2. 3. Consider a sales tax t on producers, where p(y) and p(y) are industry demand and supply. f 2. Monopoly Monopoly one firm: the firm industry downward-sloping demand: control price and quantity no entry: possible long- run profit Three types of monopolies 1. single-price monopoly: charges the same price for each and every unit
The industry supply: y(p) ≡ [m i=1 yi(p), i.e., the industry supply curve is the horizontal sum of the firms’ supply curves. † Remarks: 1. The industry faces a downward sloping market demand. 2. The behavior of each firm in the input market is assumed away by the given c(y). 3. The supply curves for the short run and long run are similar (LeChatelier Principle). The equilibrium is where industry demand equals industry supply. † If time horizon comes into play, when entry and exit stop, the industry reaches a long-run equilibrium. † Example 2.1. Consider a decrease in demand. † Example 2.2. Find the equilibrium for † Industry demand : yd = a − bp, Firms’ cost : ci(yi) = y2 i + 1. Example 2.3. Consider a sales tax t on producers, where pd(y) and ps(y) are industry demand and supply. † 2. Monopoly Monopoly: • one firm: the firm = industry. • downward-sloping demand: control price and quantity. • no entry: possible long-run profit. Three types of monopolies: 1. single-price monopoly: charges the same price for each and every unit. 2—2
2. price-discriminating monopoly: charges different prices to different people or to different quantities demanded 3. monopoly under asymmetric information: incentives for truthful choices 2.1. Single-Price Monopoly The demand: p=p(y). The revenue: R(y)=p(y)y Profit maximization p(y)+p(y)y*=( Discussion: MR=P11、 where n=-2 is price elasticity of demand. If Mc>0, then n>1 2. Zero profit or loss is possible 3. No supply curve Example 2.4. Consider p=A-a 2.2. Price-Discriminating Monopoly Perfect price discrimination: charge a different price for each different unit A monopoly does better by charging multiple prices. t Perfect price discrimination gives the maximum revenue for a given y Since MR=p(y), profit maximization implies f p(y)=MC(y) 1. Monopoly price generally exceeds competitive price 2. Monopoly quantity is generally less than competitive quantity 3. The more perfectly the monopoly can price discriminate, the closer its output is to the competitive output
2. price-discriminating monopoly: charges different prices to different people or to different quantities demanded. 3. monopoly under asymmetric information: incentives for truthful choices. 2.1. Single-Price Monopoly The demand: pd = p(y). The revenue: R(y) ≡ p(y)y. Profit maximization: † p(y∗ ) + p0 (y∗ )y∗ = c0 (y∗ ). Discussion: 1. MR = p 1 − 1 η , where η = −p y dyd dp is price elasticity of demand. If MC ≥ 0, then η ≥ 1. 2. Zero profit or loss is possible. 3. No supply curve. Example 2.4. Consider pd = A − ay. 2.2. Price-Discriminating Monopoly Perfect price discrimination: charge a different price for each different unit. A monopoly does better by charging multiple prices. † Perfect price discrimination gives the maximum revenue for a given y.† Since MR = p(y), profit maximization implies † p(y∗ ) = MC(y∗ ). Discussion: 1. Monopoly price generally exceeds competitive price. 2. Monopoly quantity is generally less than competitive quantity. 3. The more perfectly the monopoly can price discriminate, the closer its output is to the competitive output. 2—3
2.3. Monopoly under Inc complete information Suppose now that the monopolist can practice price discrimination but it doesnt know the demand curve of each consumer. More specifically, the monopolist only knows ll existing types of consumers but it doesn't know which consumer belongs to which pe. What should the monopolist do Consider a simple case in which there are two types of consumers and there is no production cost 3. Allocative Efficiency Given ordinary demand p(a), for consumption x at price p, define the consumer surplus CS(a)=/[p(t)-pldt It is the amount that the consumer is willing to pay for minus what the consumer actually pays, po Given marginal cost MC(y), for output y at price p, define the producer surplus: t PS(y)=/p-MC(t)] dt It is the gain without taking into account the fixed cost, i.e. r(y)=PS(y)-c(0) Social Welfare Consumer Surplus Producer Surplus A market equilibrium is allocatively efficient if the social welfare is maximized The competitive equilibrium is allocatively efficient. t a single-price monopoly has a deadweight loss. t a perfectly price-discriminating monopoly is allocatively efficient. t Example 2.5. Consider the welfare aspect of Example 2.3. In the short run, the tax is shared by consumers and producers, with a deadweight loss. t In the long run, the tax revenue is paid solely by consumers, also with a deadweight loss Gains from monopoly: economies of scale, economies of scope, incentive to innovate
2.3. Monopoly under Incomplete Information Suppose now that the monopolist can practice price discrimination but it doesn’t know the demand curve of each consumer. More specifically, the monopolist only knows all existing types of consumers but it doesn’t know which consumer belongs to which type. What should the monopolist do? Consider a simple case in which there are two types of consumers and there is no production cost. 3. Allocative Efficiency Given ordinary demand pd(x), for consumption x at price p, define the consumer surplus: † CS(x) ≡ ] x 0 [pd (t) − p] dt. (2.3) It is the amount that the consumer is willing to pay for x minus what the consumer actually pays, px. Given marginal cost MC(y), for output y at price p, define the producer surplus: † P S(y) ≡ ] y 0 [p − MC(t)] dt. (2.4) It is the gain without taking into account the fixed cost, i.e., π(y) = P S(y) − c(0). Define Social Welfare ≡ Consumer Surplus + Producer Surplus. A market equilibrium is allocatively efficient if the social welfare is maximized. The competitive equilibrium is allocatively efficient. † A single-price monopoly has a deadweight loss. † A perfectly price-discriminating monopoly is allocatively efficient. † Example 2.5. Consider the welfare aspect of Example 2.3. In the short run, the tax is shared by consumers and producers, with a deadweight loss. † In the long run, the tax revenue is paid solely by consumers, also with a deadweight loss. † Gains from monopoly: economies of scale, economies of scope, incentive to innovate. 2—4
4. Monopolistic Competition Monopolistically competitive industry: Many firms: Firms are independent of each other in their decisions Product differentiation: Each firm faces a downward-sloping demand curve Free entry: Zero profit in the long run The key difference between monopoly and monopolistic competition is free entry. Firm i faces demand Pi=Pi (91, 92,.. yn). Its problem max Ti=pi(yi, y_i) -Ci(yi) FOC n1(,)+9p(,张读=() Equilibrium(,…,) n(G,)+(G:,y w=d(2),V When the time horizon comes into play,(2.5 )defines a short-run equilibrium. t In the long-run, firms will enter or exit until the profit is zero: t P2(3,)=c(2), 1. By(2.5) and(2.6), the demand and AC curves are tangent at the optimal point in the long run 2. In the long run, firms have excess capacity, caused by product differentiation 3. Monopolistic competition is allocatively inefficient 4. Firms will attempt to differentiate the consumers' perception of the product, princi- pally by advertising, which incurs costs 5. Social gains: greater product variety and product innovation
4. Monopolistic Competition Monopolistically competitive industry: • Many firms: Firms are independent of each other in their decisions. • Product differentiation: Each firm faces a downward-sloping demand curve. • Free entry: Zero profit in the long run. The key difference between monopoly and monopolistic competition is free entry. Firm i faces demand pi = pi(y1, y2,...,yn). Its problem: max yi πi ≡ pi(yi, y−i)yi − ci(yi). FOC: pi(y∗ i , y−i) + ∂pi(y∗ i , y−i) ∂yi y∗ i = c0 i(y∗ i). Equilibrium (y∗ 1,...,y∗ n) : pi(y∗ i , y∗ −i) + ∂pi(y∗ i , y∗ −i) ∂yi y∗ i = c0 i(y∗ i), ∀ i. (2.5) When the time horizon comes into play, (2.5) defines a short-run equilibrium. † In the long-run, firms will enter or exit until the profit is zero: † pi(y∗ i , y∗ −i)y∗ i = ci(y∗ i), ∀ i. (2.6) Discussion: 1. By (2.5) and (2.6), the demand and AC curves are tangent at the optimal point in the long run. 2. In the long run, firms have excess capacity, caused by product differentiation. 3. Monopolistic competition is allocatively inefficient. 4. Firms will attempt to differentiate the consumers’ perception of the product, principally by advertising, which incurs costs. 5. Social gains: greater product variety and product innovation. 2—5
