Econ_274_Fall_2011_PS_2_Solutions - Econ 274 Fall 2011...

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Unformatted text preview: Econ 274 Fall 2011 Problem Set 2 Glandon Due: Wednesday, September 28 by 5:00 PM 1. If monopolies are always bad, why does the government award firms with monopolies (such as for public utilities and patents)? Optimistic answer: Natural monopolies mean that a single firm is the most efficient way to produce. Also, temporary monopolies (patents) give firms incentive to innovate. Pessimistic view: Rent seeking behavior is linked to the election of politicians. 2. What would a monopoly’s marginal revenue be if it chose a point on the demand curve where the price elasticity of demand equals -1? Why would it never be optimal to choose such a point, given positive marginal costs? Would the monopoly rather produce less or more? MR = 0. There are two ways to show this. One is to differentiate the revenue function: () ( )( () If ) , the marginal revenue is zero. The other approach is to note that Thus, if which means that This could never be optimal because the monopolist could reduce quantity, (and reduce cost) while leaving revenue unchanged. So reducing quantity increases profits. 3. If a single firm with constant marginal costs of $8 monopolizes a market with demand Q = 100 - 2p, how large is the deadweight loss from monopoly? How large is the additional social loss if, in order to obtain the monopoly, the firm spent an amount equal to half of its current profits? The monopolist selects a price (or quantity) that equates MR to MC. ( Now set MR = MC ) The socially optimal quantity would set inverse demand equal to MC: Dead weight loss is a triangle with the base equal to the difference in monopoly price and socially optimal price and the height equal to the difference in monopoly quantity and socially optimal quantity: ( )( ) ) The monopolist’s profits are: ( spends 441 in real resources protecting this monopoly, then the additional DWL = 441 4. If all n identical firms in a market belong to a cartel, how much total output will be produced relative to the monopoly output, and how much will each firm produce? The cartel will try to maximize total profit, which is exactly what the monopolist does so cartel output will equal monopolist output – assuming the cartel is successful and nobody cheats. Since all firms are identical, they will most likely split output equally. 5. Can the combined profits of oligopolistic firms ever be higher than those of a monopoly with the same costs as those of the firms combined? No. A monopolist maximizes profits so there is not quantity that c ould result in higher profits, given that the costs of the combined firms is the same as the monopolist. 6. An industry consists of three firms with identical costs ( ) demand is ( ) . . Market a. What is the industry equilibrium (price, output and profits) if the firms have Cournot beliefs? We’ll solve for firm 1: ( Set MR = MC ) Firm 1’s best response function is: In equilibrium, because the firms are symmetric: Each firm produces units Sells them at a price of Profits are b. Would it pay for Firm 1 and Firm 2 to merge, if, after the merger, the remaining firm plays Cournot? (Hint: carefully consider if the merged firm would produce using both original firms’ plants or just those of one firm.) The trick here is to first find what the combined firm’s cost function is. We argued in class that since marginal cost is rising at the two plants, the merged firm will allocate production between the two plants so that marginal cost is equal, which implies that the output of the two plants is equal. Let be the quantity produced at each plant and be the merged firm’s total quantity. We know that . Now we need to write the merged firm’s total cost function: ( ) ( ( )) So marginal cost of the new firm is: Now that there are just 2 firms, let’s denote the quantity of the other firm as Here we just have Cournot duopoly and need to compute marginal revenue: ( ) So the merged firm will set marginal revenue equal to marginal cost: Firm 3’s best response is also found by setting its marginal cost equal to its marginal revenue: To find equilibrium, both firms must be playing a best response simultaneously so we can now solve for and : Equilibrium price is The profits of the combined firm are: This is much more than the sum of profits of two individual firms in part a, so yes it is profitable for the firm to merge. ...
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