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Introduction to Industrial Organization Perfect Competition, Monopoly, and Dominant Firm

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Introduction to Industrial Organization Perfect Competition, Monopoly, and Dominant Firm Introduction to Industrial Organization Perfect Competition, Monopoly, and Dominant Firm Jian-Da Zhu National Taiwan University September 19, 2019 Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 1 / 40 Outline Perfect Competition - Assumptions - Shutdown decision for firms - Short-run and long-run equilibrium - Elasticities - Efficiency and welfare Monopoly - Assumptions - Elasticity - Welfare and deadweight loss Dominant Firm - Assumptions - Equilibrium Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 2 / 40 Perfect Competition Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 3 / 40 Perfect Competition Assumptions: - Homogeneous products (only one single good) - Perfect information: All consumers and producers know the price and utilities for each person. - No transaction costs - No externalities - Many (infinite) buyers (consumers) and sellers (firms). - All firms and buyers are price takers. Price is determined by the market. Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 4 / 40 Profit Maximization The profit maximization problem for a single firm: max π = max P · q − c(q) q q First-order condition (F.O.C.): ∂π ∂c(q) = 0 ⇒ P − = 0 ⇒ P = MC(q) ∂q ∂q Given a price P0, the firm produces at the quantity level q0, where P0 = MC(q0). Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 5 / 40 Figure for Perfect Competition $ profits MC P0 AC AV C q Cost 0 q Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 6 / 40 Shutdown Decisions (I) Total cost is C(q0)= q0AC(q0). Supply curve: As price increases, the firm increase the production along the curve MC(q). Shutdown decision: ◮ The firm produces only if the revenues are higher than avoidable costs. ◮ In the short run, avoidable costs are variable costs V C(q) if all fixed costs are sunk. If P · q<VC(q) ⇒ P < AV C(q), then the firm will shut down. ◮ In the long run, avoidable costs are total costs C(q). If P · q < C(q) ⇒ P < AC(q), then the firm will shut down. ◮ In the short run, if proportion α of fixed costs are not sunk, such as refundable rent, then avoidable costs are V C(q)+ αF . The firm will αF shut down if P · q<VC(q)+ αF ⇒ P < AV C(q)+ q Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 7 / 40 Shutdown Decisions (II) Short-run shutdown point Ps. (All the fixed costs are sunk.) Long-run shutdown point Pl. $ MC AC AV C Pl Ps q Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 8 / 40 Short-Run Equilibrium There are n identical firms. Short-run market supply curve, S; Short-run equilibrium price, P0, and quantity, Q0 = nq0. (Qs = nqs) Firms are making a positive profit. $ MC $ Supply, S AV C P0 P0 Ps Ps Demand qs q0 q Qs Q0 q Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 9 / 40 Long-Run Equilibrium Firms are free to enter into the market. ∗ replacementsThe equilibrium price, P = minimum of AC; the equilibrium number of firms, n∗; the equilibrium output Q∗ = n∗q∗. Firms make zero profit because of free entry. $ $ MC AC ∗ Long-Run Supply Curve P AV C Demand ∗ ∗ q q Q q Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 10 / 40 Long-Run Equilibrium Note: The long-run supply curve need not be flat. It may be upward-sloping. - Case 1: minimum of AC is rising in market demand. Example: An expansion of output causes the prices of some key inputs to increase. - Case 2: A few firms can produce at low costs. Example: Two types of firms: n1 low-cost, efficient firms with smaller AC1, and n2 high-cost firms with higher AC2. Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 11 / 40 Residual Demand Curve Definition: The demand curve facing a particular firm is called the residual demand curve, Dr(p) Dr(p) ≡ D(p) − So(p); Dr(p) = 0 if So(p) > D(p), where So(p) is the supply of other firms. $ $ So L 10 10 9 9 D Dr 200 300 Q 100 q Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 12 / 40 Elasticities Price Elasticity of Demand/Supply ∆Q(P ) Q(P ) ∆Q(P ) P ǫ = = ∆P P Q P P ∆ ( ) Example: - The slope of demand is very steep ⇒ inelastic demand |ǫ| < 1 - The slope of demand is very flat ⇒ elastic demand |ǫ| > 1 Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 13 / 40 Elasticities and the Residual Demand Curve (I) The elasticity of demand facing firm i is ǫi. Dr(p)= D(p) − So(p) dD (P ) dD(P ) dS (P ) ⇒ r = − o dP dP dP dD (P ) P dD(P ) P dS (P ) P ⇒ r = − o dP q dP q dP q dD (P ) P dD(P ) P Q dS (P ) P Q ⇒ r = − o o dP q dP Q q dP Qo q ǫi ǫ n η0 n−1 | {z } | {z } |{z} | {z } |{z} ⇒ ǫi = nǫ − (n − 1)η0, where ǫ is the market elasticity of demand, and η0 is the elasticity of supply of the other firm. (Qo = (n − 1)q; Q = nq) Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 14 / 40 Elasticities and the Residual Demand Curve (II) The residual demand curve facing the firm is much flatter than the market demand curve. The single firm’s demand elasticity is much higher than the market elasticity. ǫi = nǫ − (n − 1)η0 Given the supply of other firms is completely inelastic (η0 = 0), ǫi = nǫ. For instance, if ǫ = −1 and n = 500, then ǫi = −500. The elasticity of demand facing a single firm is very large. In a perfect competition market, n = ∞. The elasticity of demand facing a firm is infinite, so the demand curve facing a competitive firm is horizontal at the market price. A competitive firm is a price taker. Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 15 / 40 Efficiency and Welfare P Welfare = consumer surplus S (CS) + producer surplus (PS) In the competitive equilibrium CS - Firms: P = MC(q). Profits PS are maximized, so producer D surplus is maximized. P q Q - Consumers: consumer surplus S is maximized. Deadweight loss is defined as Deadweight Loss the welfare loss from the competitive equilibrium. D Q Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 16 / 40 Summary and Example Summary: - Welfare is maximized under perfect competition. - Free entry is a crucial factor for perfect competition market, so the firms make zero profits in the long run. - All the firms are price takers. Example: U.S. agricultural markets ◮ Many farms as sellers, and no farm has even 1 percent of total sales. ◮ The elasticity of demand facing each farm is extremely large. Estimated Market Each Farm’s Residual Crop Demand Elasticity Number of Farms Demand Elasticity Fruits apples -0.2 28,160 -5,620 grapes -1.03 19,961 -20,560 Vegetables asparagus -0.65 2,672 -11,140 cucumbers -0.30 6,821 -2,046 Sources: Carlton and Perloff (2005) Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 17 / 40 Monopoly Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 18 / 40 Monopoly (I) Assumptions: - Only one firm in the market - Facing the downward-sloping demand curve(P (Q)) Profit maximization problem: max π = P (Q)Q − C(Q) Q Revenue Cost | {z } | {z } First-order condition: ∂π ∂P (Q) ∂C(Q) = 0 ⇒ Q + P (Q) − = 0 ∂Q ∂Q ∂Q Marginal revenue Marginal cost | {z } | {z } Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 19 / 40 Monopoly (II) From F.O.C, ∂P (Q) Q + P (Q)= MC(Q) ∂Q ∂P (Q) Q ⇒ P (Q) + P (Q)= MC(Q) ∂Q P (Q) 1 ⇒ P (Q) 1+ = MC(Q), ∂Q P (Q) ∂P Q ∂Q P (Q) where ∂P Q is the demand elasticity. We obtain 1 P 1+ = MC. ǫ Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 20 / 40 Example Deciding the price for monopoly is equivalent to deciding the quantity. There is no supply curve for monopoly. Example: - Inverse demand function: P = a − bQ - Cost function: cQ (constant marginal cost) - Maximization problem: max(a − bQ)Q − cQ = aQ − bQ2 − cQ Q - First-order condition: a − 2bQ − c =0 MR MC | {z } |{z} - Marginal revenue: a − 2bQ; marginal cost: c. a−c a+c - Optimal output: Qm = 2b ; optimal price: Pm = 2 . Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 21 / 40 Figure for Monopoly P Pm P = a − bQ(Inverse demand function) MC=c profits Q Qm MR: P = a − 2bQ Jian-Da Zhu (National Taiwan University) Introduction to Industrial Organization September 19, 2019 22 / 40 Elasticity (I) From F.O.C: 1 P (1 + )= MC ǫ P − MC 1 ⇒ = − P ǫ price-cost margin positive | {z } |{z} The price-cost margin is also called the Lerner Index of market power. If the demand is very elastic, ǫ = −100, then the price-cost margin is 1 P −MC 100 . As ǫ → −∞, P → 0 ⇒ P → MC. 1 If the demand is less elastic, ǫ = −2, then the price-cost margin is 2 . The optimal price is much higher than the marginal cost.
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