ProblemSet2_Key - Problem Set 2 Market Power and Price...

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Problem Set 2: Market Power, and Price Discrimination Question 1: A monopoly faces market demand given by Q d ( P ) = 100 - 1 2 P . It has marginal costs that are constant at $20. Fixed costs are $100. (i) What is the firm’s revenue function? The first thing we need is inverse demand. We get this by inverting the given demand function: P d ( Q ) = 200 - 2 Q . Now write revenue: R ( Q ) = P d ( Q ) · Q = 200 Q - 2 Q 2 . (ii) What is the firm’s marginal revenue function? MR ( Q ) = 200 - 4 Q (iii) What is its profit-maximizing price and quantity? MR ( Q ) = MC ( Q ) 200 - 4 Q = 20 Q = 45 , P = P d (45) = 110 (iv) What is the deadweight loss from the monopoly? First find the competitive equilibrium for comparison: 200 - 2 Q = 20 Q = 90 , P = P d (90) = 20 Forgone social surplus is: CS = 1 2 · (90 - 45) · (110 - 20) = 2025 (v) If the government offers to sell the right to be the monopolist, what is the most that firm is willing to pay for this right? 4050 is an approximation of the monopoly rents. Ignoring setup costs, this is the most the firm would be willing to pay the government, for instance, to become the monopolist. If there are large startup costs, this number would be less. Here, setup costs are 100 – the potential monopolist would only be willing to pay 3950. Question 2: Often, agricultural markets feature a large number of raw producers and a small number of processors. Consider here the guacamole market which takes avocados as input and produces guacamole as output for consumption. Suppose a large number of small farms produce avocados and supply the guacamole market according to Q s ( P ) = - 92+4 P . The manufacturers of guacamole decide to form a purchasing group; in other words, this market is monopsonized. Their input demand for avocado is given by: Q d ( P ) = 100 - 2 P . (i) What is the purchasing group’s marginal outlay schedule? First, find the outlay schedule. The monopsonist has market power so may choose his own price. His outlay will be the price multiplied by the amount of avocado that would be supplied to him at that price. Phrased differently, his outlay is the quantity supplied multiplied by the inverse supply of that quantity: Outlay = Q · P s ( Q ) = Q ( 1 4 Q + 23) = 1 4 Q 2 + 23 Q MO = 1 2 Q + 23. (ii) Graph inverse demand, supply and marginal outlay. 1
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0 10 20 30 40 50 10 20 30 40 50 60 70 A C B Quantity Price Demand Supply Marginal Outlay (iii) What will be the price and quantity sold with the purchasing group? The purchasing group will choose a price-quantity such that marginal outlay equals marginal benefit or, inverse demand: 1 2 Q + 23 = 50 - 1 2 Q Q = 27 , p = 29 . 75. (iv) What is the deadweight loss from the monopsony? For a basis of comparison, calculate the competitive market equilibrium. This occurs where supply equals demand: 1 4 Q + 23 = 50 - 1 2 Q Q = 36 , p = 32. The deadweight loss is given by: Δ ABC = 1 2 · (36 - 27) · (36 . 5 - 29 . 75) = 30 . 375 Question 3: An industry produces a homogenous product and consists of a dominant firm with output Q and costs given by: C ( Q ) = 28 Q + Q 2 . There are eight identical fringe firms each with output q and costs given by: c ( q ) = 40 q + 2 q 2 . Market demand is given by: Q d ( p ) = 100 - p .
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