Monopoly Monopoly Definition Herbert Stocker [email protected] A firm is considered a monopoly if . Institute of International Studies University of Ramkhamhaeng it is the sole seller of its product. & Department of Economics University of Innsbruck its product does not have close substitutes. Repetition Repetition Remember: Technological restrictions are the same for Remember: monopolies and for firms on perfectly Firms maximize their profits subject to the competitive markets. restrictions they face. These are embedded in the cost function: There are two kinds of restrictions: Remember that we did not need the price of Technological restrictions. output for the derivation of the cost function! Market restrictions. Only market restrictions differ between monopolies and firms on perfectly competitive markets. 1 Monopoly & Perfect Competition Monopoly & Perfect Competition Monopoly: A Monopolist is the only supplier and there are no close substitutes for his Perfect Competition: Every supplier product. Therefore he perceives that the perceives demand for his own product as demand for his product is falling when he perfectly elastic, he can sell every unit of increases price. output for the same price. Monopolistic firms are price-seekers; if they Therefore, marginal revenue is simply the price, want to sell more, they can do so only at a and firms are price-takers! lower price! This has important implications for the marginal revenue of a monopoly, e.g. marginal revenue no longer equals price! Perfect Competition vs. Monopoly Total and Marginal Revenue Perfect Competition: Monopoly: Example: P P ‘perceived’ ‘perceived’ Market Demand Market Demand Q = 6 − P Total Marginal Average Price Quantity Revenue Revenue Revenue PQ R = P × Q MR AR = P 6 0 0 – – 5 1 5 5 5 4 2 8 3 4 Q Q 3 3 9 1 3 Each producer perceives the Monopolist perceives demand 2 4 8 −1 2 to be less than perfectly demand for his product as 1 5 5 −3 1 elastic. perfectly elastic. 0 6 0 −5 0 2 Marginal Revenue Marginal Revenue If a monopolist increases output there are two Demand: Q = 6 − P ⇒ Inverse Demand: P = 6 − Q effects: [Inverse Demand allows us to express revenue as a function of Q only] he can sell the additional produced units of output Revenue: only at a lower price P: P × ∆Q P R = PQ = (6 − Q)Q but he has to sell also all other units of output at MR this lower price: Q × ∆P = 6Q − Q2 6 The resulting change in total revenue is 5 Marginal Revenue: therefore 4 dR ∆R = Q × ∆P + P × ∆Q 3 MR ≡ = 6 − 2Q 2 dQ Marginal Revenue is 1 Linear demand curves ⇒ MR ∆R ∆P 0 ≡ MR = Q × + P Q curve is double as steep as de- 0 1 2 3 4 5 6 mand curve! ∆Q ∆Q Marginal Revenue Marginal Revenue With Calculus: In detail: Market Demand is a function of price: Q = Q(P) R = P Q 1 1 1 We rewrite this and express price as a function R = P Q /− 2 2 2 of quantity: P = P(Q). ∆R ≡ R − R = P Q − P Q 1 2 1 1 2 2 This is called inverse demand function. P Q Q P Q P Q = 1( 1 − 2) + 1 2 − 2 2 Revenue R can then be expressed as a function = P (Q − Q ) + Q (P − P ) 1 1 2 2 1 2 of Q only, i.e. = P1∆Q + Q2∆P ≈ P∆Q + Q∆P R = P(Q) × Q ∆R ∆P For differentiating this use the product rule: MR= ∆Q = P + Q ∆Q dR dP MR ≡ = × Q + P dQ dQ 3 Marginal Revenue Marginal Revenue Rearranging terms gives Therefore, marginal revenue depends in a very specific way on the price elasticity of demand: ∆P MR = P + Q × Q ∆R 1 ∆ MR ≡ = P 1 − Q ∆P ∆Q |EQ P | = P + P , P ∆Q Q ∆P = P 1 + When demand is elastic (|EQ,P | > 1) increasing P ∆Q output will increase revenue (MR > 0). 1 1 = P 1 + = P 1 − When demand is inelastic (|EQ,P)| < 1 EQ,P |EQ,P | increasing output will decrease revenue (MR < 0). Output, Price Elasticity & Revenue Monopoly What happens with monopolist’s revenue, when he Example reduces output? We can see from this simple analysis that a P −∞ P −∞ E = E = monopolist will never produce a quantity in the bc elastic elastic ∆P bc inelastic portion of the demand curve. Why? If demand is inelastic a decrease of quantity E = −1 E = −1 would increase revenue. inelastic inelastic bc Producing less would lower cost. ∆P bc E = 0 E = 0 This implies he could make higher profits by ∆Q Q ∆Q Q reducing the quantity, therefore this cannot be a maximum! Elastic Demand: Inelastic Demand: Q ↓ ⇒ P ↑ ⇒ R ↓ Q ↓ ⇒ P ↑ ⇒ R ↑ More generally . 4 Profit Maximization Profit Maximization Monopolists like all firms maximize profit, and profit is the difference between revenue and cost π = R − C Perfect Competition For a maximum it must be true that For a firm on a perfectly competitive market dπ dR dC demand is perfectly elastic, this implies MR = P. = − =! 0 dQ dQ dQ Therefore, profit maximizing firms choose output MR MC where MR = P = MC Therefore profit maximization|{z} |{z} implies MR = MC This result is true for monopolists and for firms on perfectly competitive markets! Profit Maximization Monopoly: Profit Maximization Monopoly Which quantity For a monopolist marginal revenue is P should a monopolist 1 produce? MR = P 1 − Lost MC |EQ,P | Profit When marginal rev- therefore a monopolist chooses output and price enue is higher than marginal cost the firm where D(P) should produce more! 1 AC MR = P 1 − = MC ⇒ ⇐ When marginal rev- |EQ,P | MC MR MR MC MR enue is is smaller than Q marginal cost the firm MR = MC holds generally, but MR is different for firms under should produce less! perfect and imperfect competition! 5 Monopoly: Profit Maximization Monopoly: Profit Maximization Which quantity P should a monopolist P Monopolies are produce? ‘price-seekers’: MC MC Profits are maximized Monopolist chooses ∗ b b when the cost of the PM the output where D(P) last unit are equal the bc bc D(P) MR = MC, and revenue of the last AC AC charges the maximum unit, price consumers are MC MR MR MR willing to pay for this MR = MC b ∗ ∗ output. QM Q QM Q Monopoly: Profit Maximization Monopoly: Profit Maximization Profits: Profits: P P AC b MC Profits are defined as MC Loss If AC are high profits P∗ b b P∗ b b M π = (P − AC)Q M become negative, the D(P) D(P) monopoly runs a loss! π bcbc bcbc AC i.e. profits depend b (Still, this output level on average cost and minimizes losses.) MR price! MR b b ∗ ∗ QM Q QM Q 6 Monopoly In perfect competition, the market supply curve is determined by marginal cost. For a monopoly, output is determined by marginal cost and the shape of the demand Example curve (demand elasticity). Since supply depends on the demand curve, there is no supply curve for monopolistic market. Shifts in demand usually cause a change in both price and quantity. Monopoly Monopoly Profits of a monopolist: Profits of a monopolist: P P bc Market demand: P = 4 − Q bc 4 4 − ↔ − Revenue: R = 4Q − Q2 Q = 4 P P = 4 Q R R R = 4Q − Q2, MR = 4 − 2Q ∗ Marginal revenue: MR = 4 − 2Q ∗ 3 π C Cost:0 C = .2Q2 + 0.5 3 π C C = 0.2Q2 + 0.5, MC = 0.4Q ∗ bc Marginal cost: MC = 0.4Q ∗ bc P P QPR MR C MC π 2 2 0.00 4.00 0.00 4.00 0.50 0.00 -0.50 Condition for profit maximum: 0.50 3.50 1.75 3.00 0.55 0.20 1.20 1.00 3.00 3.00 2.00 0.70 0.40 2.30 MC MC 1.50 2.50 3.75 1.00 0.95 0.60 2.80 MR bc MR = MC MR bc 1.67 2.33 3.89 0.67 1.06 0.67 2.83 1 1 2.00 2.00 4.00 0.00 1.30 0.80 2.70 bcbc Q . Q bcbc 2.50 1.50 3.75 -1.00 1.75 1.00 2.00 4 − 2 = 0 4 3.00 1.00 3.00 -2.00 2.30 1.20 0.70 ∗ 3.50 0.50 1.75 -3.00 2.95 1.40 -1.20 Q = 1.667 4.00 0.00 0.00 -4.00 3.70 1.60 -3.70 ∗ ∗ ∗ 0 ∗ π = R − C = 2.833 0 ∗ 0 1Q 2 3 4Q 0 1Q 2 3 4Q 7 Monopoly: Alternative Presentation Long-Run Profit Maximization Profit with Total Cost: Profit with Average Cost: P P 4 bc 4 Attention: In the long run ... R AC(Q∗) = 0.63˙ ∗ 3 π∗ C 3 MC(Q ) = 0.66˙ Monopolist maximizes profit by choosing to ∗ bc ∗ P P bc 2 2 produce output where MR = LMC, as long as MC π∗ MC P > LAC 1 MR bc bcbc 1 bcbc AC Will exit industry if P < LAC! MR Monopolist will adjust plant size to the optimal 0 ∗ 0 ∗ 0 1Q 2 3 4Q 0 1Q 2 3 4Q level. ∗ π∗ = R(Q) − C(Q) π = (P − AC)Q Long-Run Profit Maximization A General Rule for Pricing Optimal plant is where the short-run average cost curve is tangent to the long-run average cost at the profit-maximizing output level.