Chapter 9: Monopoly and Imperfect Definition: Competition total revenue = total amount received A. Total revenue and marginal revenue from selling product Definition: Definition: total revenue = total amount received marginal revenue = amount received from selling product from selling one more unit of product P = price of product Q = number of units sold PQ = total revenue Firm with downward-sloping Definition: demand curve marginal revenue = amount received from selling one more unit of product Demand for firm's product 17 16 15 ∆(PQ) d(PQ) 14 or 13 ∆Q dQ (P) Price 12 11 10 012345 Quantity (Q) 1 Example: Firm with downward- Example: Firm with downward- sloping demand curve sloping demand curve Q P Q P TR Demand for firm's product 1 16 Demand for firm's product 1 16 16 17 17 16 16 15 15 14 2 15 14 2 15 30 13 13 Price (P) 12 Price (P) 12 11 11 10 10 012345 3 14 012345 3 14 42 Quantity (Q) Quantity (Q) 4 13 4 13 52 Example: Firm with downward- Example: Firm with downward- sloping demand curve sloping demand curve Q P TR MR Demand for firm's product Marginal revenue 17 17 16 16 15 15 14 14 Demand for firm's product 13 (MR) 13 1 16 16 16 (P) Price 12 12 11 11 17 10 revenue Marginal 10 16 012345 012345 15 Quantity (Q) Quantity (Q) 14 2 15 30 14 13 Price (P) 12 11 Q P TR MR Note: MR < P 10 3 14 42 12 012345 1 16 16 16 Quantity (Q) Reason: more quantity 2 15 30 14 4 13 52 10 means lower price 3 14 42 12 4 13 52 10 Special case: linear demand curve Special case: linear demand curve Demand for firm’s product: P = a - bQ P Demand curve: slope = -b P = a + bQ a is the intercept Intercept = a -b is the slope Q 2 P = a+ bQ total revenue: Marginal revenue: PQ = (a - bQ)Q a − 2bQ = aQ - bQ2 This is equation of a line where marginalrevenue: a is the intercept −2b is the slope d(PQ) = a -2 bQ dQ Chapter 9: Monopoly and Imperfect Competition Demand for firm’s product: P = a - bQ A. Total revenue and marginal revenue P Demand curve: slope = -b B. Marginal revenue for a perfectly competitive firm Marginal revenue curve: slope = -2b Intercept = a Q Extreme case: Firm with perfectly Extreme case: Firm with perfectly elastic demand curve elastic demand curve Q P TR MR Demand for firm's product 15 Demand for firm's product 1 10 13 15 13 11 11 2 10 9 9 Price (P) Price (P) Price 7 7 5 012343 10 5 Quantity (Q) 01234 Quantity (Q) 4 10 3 Extreme case: Firm with perfectly Extreme case: Firm with perfectly elastic demand curve elastic demand curve Q P TR MR Q P TR MR Demand for firm's product 1 10 10 Demand for firm's product 1 10 10 10 15 15 13 13 11 2 10 20 11 2 10 20 10 9 9 Price (P) Price (P) 7 7 5 5 012343 10 30 012343 10 30 10 Quantity (Q) Quantity (Q) 4 10 40 4 10 40 10 Conclusion: if demand is perfectly elastic, Question: but don’t demand curves always then MR = P slope down (i.e., always less than perfectly elastic)? If demand is less than perfectly elastic, then MR < P Answer: yes, but it’s a question of degree Key issue: how much of market does each firm control? Chapter 9: Monopoly and Imperfect Competition A. Total revenue and marginal revenue Consider entire U.S. market for tomatoes B. Marginal revenue for a perfectly competitive firm • More than 5 million tons C. The difference between individual firm’s produced each year demand curve and market demand curve • Sell wholesale for about $50/ton 4 Consider entire U.S. market for tomatoes • More than five million tons produced each year • Sell wholesale around $50/ton Consider individual tomato farm • Suppose demand has elasticity of -1 • Produces 1,000 tons per year • Means 10% increase in U.S. production (500,000 more tons) would lower price by 10% (from $50 to $45) Comparison of industry-wide demand curve with individual producer’s demand curve Consider individual tomato farm • Produces 1,000 tons per year Industry-wide demand curve Individual farm's demand curve • 10% increase in one farm’s production is 65 65 55 55 100 tons 45 45 35 35 25 25 • This is 1/50,000 = 0.002 % of U.S. market 15 15 Price ($ per ton) per ($ Price Price ($ per ton) per ($ Price 5 5 • U.S. price would drop 0.002% (from 35790 500 1000 1500 2000 2500 Quantity (millions of tons) Quantity (tons) $50/ton to $49.99/ton) Example: earth is approximately flat Perfect competition: firm for all practical purposes ignores any potential effect of its actions on the market price • Represent as: perfectly elastic demand curve • Justification: this firm is a very small part of the total market 5 Comparison of industry-wide and individual producer’s demand curve when there is a monopoly • Imperfect competition: firm takes into account the effect of its actions on price Industry-wide demand curve Individual firm's demand curve • Monopoly: firm is the only seller in the 65 65 55 55 entire market 45 45 35 35 25 25 15 15 Price ($ per ton) Price ($ per ton) 5 5 35793579 Quantity (millions of tons) Quantity (millions of tons) Chapter 9: Monopoly and Imperfect Competition A. Total revenue and marginal revenue B. Marginal revenue for a perfectly competitive firm C. The difference between individual firm’s demand curve and market demand curve D. Total cost and marginal cost Definition: total cost total expensesfirm would Q Total cost incur in order to produce quantityQ 1 4 marginalcost additionalcost of 2 10 producingone more unit 3 18 4 28 Δ(TC) d(TC) 5 40 or ΔQ dQ 6 54 6 Chapter 9: Monopoly and Imperfect Competition Q Total cost Marginal cost A. Total revenue and marginal revenue 1 4 4 B. Marginal revenue for a perfectly 2 10 6 competitive firm C. The difference between individual firm’s 3 18 8 demand curve and market demand curve 4 28 10 D. Total cost and marginal cost 5 40 12 E. Profit maximization 6 54 14 First method of proof: calculus Proposition: any firm maximizes profit by TR total revenue setting marginal revenue equal to marginal cost TC total cost TR − TC profit Firm maximizes profit by finding derivative of profit with respect to Q and setting it to zero dTR − TC 0 dQ Second method of proof: intuition requires dTR dTC Suppose the firm wasn’t following our dQ dQ advice, and operated at a level where MR > MC or marginal revenue marginal cost 7 Then if it produced one more unit: Or, suppose instead the firm wasn’t • its revenues would go up by MR following our advice, and operated at a • its costs would go up by MC level where MR < MC • if MR > MC, its revenues would go up by more than its costs if it produced one more unit • Conclusion: if MR > MC, firm can increase profits by producing one more unit Then if it produced one less unit: Combined implication: firm is only • its revenues would go down by MR (bad) maximizing profits if it sets MR = MC • its costs would go down by MC (good) • if MR < MC, its cost savings more than make up for lost revenue • Conclusion: if MR < MC, firm can increase profits by producing one less unit Any firm will try to set MR = MC Any firm will try to set MR = MC • For a perfectly competitive firm, MR = P • For an imperfectly competitive firm or • Therefore, a perfectly competitive firm will monopolist, MR < P set P = MC • Therefore, an imperfectly competitive firm • That is, it will choose a level of production will set MC < P at which the marginal cost of producing • That is, it will choose a level of production one more unit is equal to the price at which the marginal cost of producing one more unit is less than the price 8 Chapter 9: Monopoly and Imperfect Supply decisions for farm 1 Competition E. Profit maximization If P = 10, farm 1 F. Price and output under perfect produces 1 unit Marginal Cost for farm 1 competition If P = 12, farm 1 16 produces 2 units 14 12 If P = 14, farm 1 Price (P) 10 produces 3 units 8 012345 Quantity (Q) Supply decisions for farm 2 If P = 10, farm 2 Suppose there are 100 different farms like produces 2 units farm 1 and 100 farms like farm 2 Marginal Cost for farm 2 If P = 12, farm 2 If P = 10, type 1 farms produce 1 unit each 16 produces 4 units 14 (100 total), type 2 farms produce 2 units 12 If P = 14, farm 2 Price (P) each (200 units total) 10 produces 6 units 8 02468 So if P = 10, all farms together produce 300 Quantity (Q) units If P = 12, type 1 farms produce 2 units each If P = 10, all farms (200 total), type 2 farms produce 4 units together produce 300 each (400 units total) units Supply curve for entire industry If P = 12, all farms 16 So if P = 12, all farms together produce 600 14 together produce 600 12 units Price (P) units 10 8 If P = 14, all farms 0 500 1000 together produce 900 Quantity) units 9 Supply curve for MC for type 1 MC for type 2 whole industry Conclusion: under perfect competition, MC1 industry-wide supply curve is horizontal MC2 supply summation of each firm’s individual PPP marginal cost curve Q1 Q2 Q total = 100 x Q1 + 100 x Q2 Market equilibrium under perfect Chapter 9: Monopoly and Imperfect competition Competition E.