MONOPOLY Prepared by Kwabena N. Darfor

Topics Monopoly Profit Maximization. Market Power. Market Failure Due to Monopoly Pricing. Causes of Monopoly. Government Actions That Reduce Market Power. Networks, Dynamics, and Behavioral Economics.

Monopoly Profit Maximization Monopoly – the only supplier of a good for which there is no close substitute. A monopoly can set its price – not a price taker. All firms, including competitive firms and monopolies, maximize profits by setting marginal revenue equal to marginal cost.

Marginal Revenue and Price A firm’s revenue is: R = pq. A firm’s marginal revenue, MR, is: the change in its revenue from selling one more unit. MR = ΔR/Δq. If the firm sells exactly one more unit, Δq = 1, its marginal revenue is MR = ΔR.

Marginal Revenue and Price (cont.) The marginal revenue of a monopoly differs from that of a competitive firm because the monopoly faces a downward-sloping demand curve unlike the competitive firm. Thus, the monopoly’s marginal revenue curve lies below the demand curve at every positive quantity.

Figure 11.1 Average and Marginal Revenue

Deriving the Marginal Revenue Curve For a monopoly to increase its output by ΔQ, the monopoly lowers its price per unit by Δp/ΔQ, the slope of the demand curve. By lowering its price, the monopoly loses: (Δp/ΔQ) x Q on the Q units it originally sold at the higher price, but it earns an additional p on the extra output it now sells.

Deriving the Marginal Revenue Curve (cont.) Thus, the monopoly’s marginal revenue is:

Figure 11.2 Elasticity of Demand and Total, Average, and Marginal Revenue

Solved Problem 11.1 Derive the marginal revenue curve when the monopoly faces the linear inverse demand function, p=24 – Q, in Figure 11.2. How does the slope of the marginal revenue curve compare to the slope of the inverse demand curve?

Solved Problem 11.1: Answer The slope of this marginal revenue curve is ΔMR/ΔQ = −2, so the marginal revenue curve is twice as steeply sloped as is the demand curve.

Marginal Revenue and Price Elasticity of Demand At a given quantity, the marginal revenue equals the price times a term involving the elasticity of demand: Marginal revenue is closer to price as demand becomes more elastic.

Marginal Revenue and Price Elasticity of Demand (cont.) Where the demand curve hits the price axis (Q = 0), the demand curve is perfectly elastic, so the marginal revenue equals price: MR = p. Where the demand elasticity is unitary, ε = −1, marginal revenue is zero: MR = p[1 + 1/(−1)] = 0. Marginal revenue is negative where the demand curve is inelastic, −1 < ε ≤ 0.

Table 11.1 Quantity, Price, Marginal Revenue, and Elasticity for the Linear Inverse Demand Curve p = 24 - Q

Choosing Price or Quantity Any firm maximizes its profit by setting its marginal revenue equal to its marginal cost. Unlike a competitive firm, a monopoly can adjust its price – it has a choice of setting its price or its quantity to maximize its profit. The monopoly is constrained by the market demand curve. Because the demand curve slopes downward, the monopoly faces a trade-off between a higher price and a lower quantity or a lower price and a higher quantity.

Figure 11.3 Maximizing Profit

Profit-Maximizing Output Because a linear demand curve is more elastic at smaller quantities, monopoly profit is maximized in the elastic portion of the demand curve. Equivalently, a monopoly never operates in the inelastic portion of its demand curve.

Shutdown Decision In the short run, a monopoly shuts down to avoid making a loss if its price is below its average variable cost at its profit-maximizing quantity. In the long run, the monopoly shuts down if the price is less than its average cost.

Mathematical Approach The monopoly faces a short-run cost function of: C(Q) = Q2 + 12 where Q2 is the monopoly’s variable cost as a function of output and $12 is its fixed cost. Given this cost function the monopoly’s marginal cost function is MC = 2Q.

Mathematical Approach (cont.) The average variable cost is: AVC = Q2/Q = Q, so it is a straight line through the origin with a slope of 1.

Mathematical Approach (cont.) We determine the profit-maximizing output by: MR = 24 − 2Q = 2Q = MC. Solving for Q, we find that Q = 6. Substituting Q = 6 into the inverse demand function: p = 24 − Q = 24 − 6 = $18.

Mathematical Approach (cont.) At that quantity, AVC = $6, which is less than the price, so the firm does not shut down. The average cost is AC = $(6 + 12/6) = $8, which is less than the price, so the firm makes a profit.

Solved Problem 11.2 When the iPad was introduced, Apple’s constant marginal cost of producing this iPad was about $220. We estimate that its average cost was about AC = 220+ 2,000/Q , and that Apple’s inverse demand function for the iPad was p = 770 - 11Q , where Q is measured in millions of iPads purchased. What was Apple’s marginal revenue function? What were its profit-maximizing price and quantity? What was its profit?

Solved Problem 11.2: Answer

Effects of a Shift of the Demand Curve Unlike a competitive firm, a monopoly does not have a supply curve. A given quantity can correspond to more than one monopoly-optimal price. A shift in the demand curve may cause the monopoly optimal price to stay constant and the quantity to change or both price and quantity to change.

Figure 11.4 Effects of a Shift of the Demand Curve

Market Power Market power - the ability of a firm to charge a price above marginal cost and earn a positive profit. and rearranging the terms: so the ratio of the price to marginal cost depends only on the elasticity of demand at the profit-maximizing quantity.

Table 11.2 Elasticity of Demand, Price, and Marginal Cost

Lerner Index Lerner Index - the ratio of the difference between price and marginal cost to the price: (p − MC)/p. In terms of the elasticity of demand: Because MC ≥ 0 and p ≥ MC, 0 ≤ p − MC ≤ p, so the Lerner Index ranges from 0 to 1 for a profit-maximizing firm.

Solved Problem 11.3 Initially, Apple sold its iPad for $500 and its marginal cost was approximately $220. What was its Lerner Index? If it was operating at the short-run profit-maximizing level, what was the elasticity of demand for the iPad?

Solved Problem 11.3: Answer Calculate the Lerner Index by substituting the iPad’s price and marginal cost into the definition. Apple’s Lerner Index for the iPad was ( p - MC)/ p=(500 - 220)/500 = 0.56. Determine the elasticity by substituting the iPad’s Lerner Index into equation 11.9.

Sources of Market Power All else the same, the demand curve a firm faces becomes more elastic as: better substitutes for the firm’s product are introduced, more firms enter the market selling the same product, or firms that provide the same service locate closer to this firm.

Market Failure Due to Monopoly Pricing Welfare, W, is lower under monopoly than under competition. Competition maximizes welfare because price equals marginal cost. By setting its price above its marginal cost, a monopoly causes consumers to buy less than the competitive level of the good, so a deadweight loss to society occurs.

Figure 11.5 Deadweight Loss of Monopoly

Solved Problem 11.4 In the linear example in Figure 11.3, how does charging the monopoly a specific tax of t = $8 per unit affect the monopoly optimum and the welfare of consumers, the monopoly, and society (where society’s welfare includes the tax revenue)? What is the incidence of the tax on consumers?

Solved Problem 11.4: Answer

Causes of Monopoly Why are some markets monopolized? A firm has a cost advantage over other firms or A government created the monopoly.

Cost Advantages Reasons for cost advantages: the firm uses a superior technology or has a better way of organizing production. the firm controls an essential facility: a scarce resource that a rival needs to use to survive.

Natural Monopoly Natural monopoly - situation in which one firm can produce the total output of the market at lower cost than several firms could. Believing that they are natural monopolies, governments frequently grant monopoly rights to public utilities to provide essential goods or services such as water, gas, electric power, or mail delivery.

Natural Monopoly (cont.) If the cost for any firm to produce q is C(q), the condition for a natural monopoly is where Q=q1+q2+…+qn is the sum of the output of any n≥2 firms.

Figure 11.6 Natural Monopoly 40 , $ per unit MC , C A 20 A C = 10 + 60/ Q 15 10 MC = 10 6 12 15 Q , Units per da y

Solved Problem 11.5 A firm that delivers Q units of water to households has a total cost of C(Q) = mQ + F. If any entrant would have the same cost, does this market have a natural monopoly? Answer Determine whether costs rise if two firms produce a given quantity.

Barriers to Entry Governments create many monopolies. Sometimes governments own and manage monopolies, forbidding other firms from entering. In the United States, as in most countries, the postal service is a government monopoly. Frequently, however, governments create monopolies by preventing competing firms from entering a market.

Patents Patent - an exclusive right granted to the inventor to sell a new and useful product, process, substance, or design for a fixed period of time. The length of a patent varies across countries. Question: If a firm with a patent monopoly sets a high price that results in deadweight loss then why do governments grant patent monopolies?

Application: Botox Patent Monopoly

Optimal Price Regulation In some markets, the government can eliminate the deadweight loss of monopoly by requiring that a monopoly charge no more than the competitive price.

Figure 11.7 Optimal Price Regulation

Problems in Regulating Problems that governments face in regulating monopolies: because they do not know the actual demand and marginal cost curves, governments may set the price at the wrong level. Second, many governments use regulations that are less efficient than price regulation. Third, regulated firms may bribe or otherwise influence government regulators to help the firms rather than society as a whole.

Nonoptimal Price Regulation If the regulated price is not optimal, a deadweight loss results. If the price is set below the firm’s minimum average cost, the firm will shut down. The deadweight loss equals the sum of the consumer plus producer surplus under optimal regulation.

Solved Problem 11.6 Suppose that the government sets a price, p2, that is below the socially optimal level, p1, but above the monopoly’s minimum average cost. How do the price, the quantity sold, the quantity demanded, and welfare under this regulation compare to those under optimal regulation?

Solved Problem 11.6: Answer

Application: Natural Gas Regulation

Increasing Competition Encouraging competition is an alternative to regulation as a means of reducing the harms of monopoly.

Solved Problem 11.7 How did the presence of me-too rival products produced by firms with higher marginal costs affect Apple’s iPod pricing in more recent years? Assume that Apple has a constant marginal cost MC . The large number of identical, higher-cost rivals—the competitive fringe—act like (competitive) price takers so that their collective supply curve is horizontal at p2 = MC + x .

Solved Problem 11.7: Answer

Networks, Dynamics and Behavioral Economics In some markets, decisions today affect demand or cost in a future period, creating a need for a dynamic analysis, in which firms explicitly consider relationships between periods. In such markets the monopoly may maximize its long-run profit by making a decision today that does not maximize its short-run profit.

Network Externalities Network externality - the situation where one person’s demand for a good depends on the consumption of the good by others.

Direct Size Effect Many industries exhibit positive network externalities where the customer gets a direct benefit from a larger network. Example: the larger an ATM network such as the Plus network, the greater the odds that you will find an ATM when you want one, so the more likely it is that you will want to use that network.

Indirect Effect In some markets, positive network externalities are indirect. They stem from complementary goods that are offered when a product has a critical mass of users. The more applications (apps) available for a smart phone, the more people want to buy that smart phone; however, many of these extra apps will be written only if a critical mass of customers buys the smart phone.

Network Externalities and Behavioral Economics Bandwagon effect - the situation in which a person places greater value on a good as more and more other people possess it. Snob effect - the situation in which a person places greater value on a good as fewer and fewer other people possess it.

A Two-Period Monopoly Model A monopoly may be able to solve the chicken-and-egg problem of getting a critical mass for its product by initially selling the product at a low introductory price. By doing so, the firm maximizes its long-run profit but not its short-run profit.

A Two Period Monopoly Model (cont.) Suppose that a monopoly sells its good only two periods. If the monopoly sells less than a critical quantity of output, Q, in the first period, its second-period demand curve lies close to the price axis. However, if the good is a success in the first period—at least Q units are sold—the second-period demand curve shifts substantially to the right.

A Two Period Monopoly Model (cont.) Should the monopoly charge a low introductory price in the first period? The firm chooses to charge a low introductory period in the first period if its first period loss (from charging a less than optimal price) is less than its extra profit in the second period.

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