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Handout #10 Monopoly Characteristics: 1. Key resource owned by a single firm 2. government gives a single firm the exclusive right to produce some goods or services 3. The costs of production make a single firm more efficient than a large number of producers Individual Demand and Marginal revenue Curve In the monopoly market, firms demand curve is the market demand curve (of course, since there is only one firm in this market). As for Marginal revenue curve, if the demand function is linear, the marginal revenue function has “same” y-intercept as demand function but its slope = 2 x slope of demand function. Suppose that the demand function is given by P = b-mQ. Then the marginal revenue function is MR = b-2mQ. P,revenue MR Demand=AR q Firm’s demand and MR curves Profit Maximization Condition As usual, firm maximizes its profit at MC = MR. and also always P > MR except when quantity is zero. Monopolist’s profit is then Profit = TR – TC = (TR/Q – TC/Q)Q = (P – ATC )Q Inefficiency of Monopoly Since monopoly charges a price above MC, not all consumers who value the good more than its cost will buy it. The quantity produced and sold by monopolist is then lower than socially optimal level. The socially optimal level of quantity is where demand intersects MC, or Price=MC. price MC Qm=monopoly output DWL Q* = efficient output Monopoly price MR demand Qm Q* e Example: A profit maximizing monopolist has cost function TC=10+2Q. Demand in this market is given by the equation Q=14-P. Calculate the firm’s profit. From the TC function, you can find MC. As MC = slope of TC function, MC =$2. Next, you can find the MR function from the demand function. From demand function, P=14-Q (note that you need to rewrite demand function so that “P” is on the right-hand side of the demand function). The marginal revenue function is MR = 14-2Q. The profit maximizing level of output is such that: MC = MR; therefore, 14-2Q = 2 Qm = 6. Monopolist chooses to produce 6 units. Substitute quantity into the demand function to find the profit maximizing price (as there is only one firm in the industry, the monopolist quantity is also the market quantity. You can substitute profit maximizing quantity into the demand function to find the price). P = 14-Q = 14-6 = 8. Therefore, TR = PxQ = 8x6 = $48. TC = 10+2Q = 10+2x6 = $22. Profit= TR-TC = $48-$22 = $26. Natural Monopoly Characteristics: A Natural Monopoly has declining average total cost. Therefore, marginal cost is always less than average total cost. The following picture shows the natural monopoly in case that the marginal cost is constant. ATC MC Demand quantity Therefore, for a natural monopoly, if the government requires it to charge a price equal to marginal cost (The price that brings about allocatively efficient quantity), price will be below average total cost, and the monopoly will get loss. The shaded area is the loss for monopolist if the government enforces marginal cost pricing. ATC MC Demand quantity Price Discrimination This is the situation in which the monopolist can sell different price to different buyers. The key idea is to convert consumer surplus into economic profit. 1. First-degree (perfect) price discrimination The monopolist can extract the entire consumer surplus. This is the case that the monopolist can set price differently for every unit of goods sold. Recall that, for a single monopoly, marginal revenue (MR) is less than price since when the price is cut in order to sell a larger quantity, the price is lower on all units sold. However, for the first-degree price discrimination, MR= P. In other words, the demand curve is also the marginal revenue curve. The monopolist can obtain greater profit by increasing output up to the point that P=MC. Consider the following picture. If the monopolist set single price (set price that MR=MC to maximize its profit), the monopolist has revenue equal to the rectangular PB0Q* and consumers get consumer surplus equal to the triangle AP*B. When there is prefect price discrimination, the monopolist has total revenue equal to the rectangular AB0Q*, so he can extract all consumer surplus. In this case, consumers get nothing. Price MC A B P* Demand= MR 0 Quantity Q* Note that, with the first-degree price discrimination, the quantity that the monopolist chooses to produce is the same level as the perfectly competitive quantity, the allocative efficient. Recall that the allocative efficient quantity is the quantity that MC=P. In the case of first-degree price discrimination, the monopolist maximizes his profit at the quantity Q*, where MC=P. 2. Second-degree price discrimination The second-degree price discrimination occurs when the monopolist can discriminate among units of good (buy not for every unit like the first degree one). A discount for bulk buying is an example of this type of discrimination. The larger the order, the larger is the discount and the lower is price. Example 1: Suppose that the monopolist can discriminate price in the way that if a consumer buys less than Q1 units, he has to pay P1 per unit. If he buys more than Q1 units, he has to pay P2 per unit. Then the monopolist can sell totally Q2 units. His revenue is [P1xQ1+P2x(Q2-Q10)]. In case that he can set only a single price, he will produce Q1 units to maximize his profit and get the revenue equal to P1xQ1. Therefore, from the picture, you can see that the monopolist gets higher profit when he uses price discrimination. 3. Third-degree price discrimination The third-degree price discrimination occurs when the monopolist can discriminate among groups of buyers. In other words, the monopolist can charge different prices from different groups of consumers. Example 2: Men and women have different demand functions for pretzels. Specifically, the demand function for men is given by Q=10-P; for women, demand is given by Q=5-P. Assume a monopolist supplies the pretzel market and has no fixed or marginal costs associated with producing pretzels (this just simplifies the math a little bit). i) Derive the aggregate demand curve in the market for pretzels and graph it (Hint: this is the horizontal summation of the two demand curves for P<=5, and it is just the demand curve for men for P>5. Can you explain why?)