Econ170SQ5FALL07

Econ170SQ5FALL07 - Economics 170 UCLA E. McDevitt Study...

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Economics 170 UCLA E. McDevitt Study Questions Set #5 Complements and Mergers 1. Assume two complementary goods that buyers always buy in pairs—perhaps operating systems (O) and browsers (B). The demand for this pair is Q= 100- (P O + P B ). Marginal cost for good O is MC O = 2 and the marginal cost for good B is MC B = 0. Ignore fixed costs. a. Suppose the two goods are sold by separate firms. Find prices, quantity and profits. b. Suppose the two firms merge and sell the two goods a package. Find price, quantity and profit. How does the merger affect consumers? c. Suppose the two goods are again sold separately but that good B is sold in a perfectly competitive market. Find price, quantity and profit. How does this result compare with the outcome in part b? Durable-goods Monopoly 1. Using graphs, present Coase’s argument concerning the outcome in a durable-goods monopoly when the monopolist sells the good (rather than renting). What are some possible solutions to this problem for the monopolist? 2. Suppose there is a monopoly that sells a durable good . Assume that the duration of the good is two periods. Demand for the services of the product is constant over the two periods and is given by Q i = 100 – R i , where is the R i is the rental rate in period i. Assume that marginal cost is zero and that the interest rate is zero. Finally, it is assumed that the monopoly cannot credibly commit to selling zero units in period two, and that consumers anticipate any price cut that may take place in period two. a. Suppose the monopolist decides to sell the product rather than rent it. Find the profit-maximizing values for Q 1 , Q 2 , R 1 , R 2 . Calculate profit for each period. b. Find profit when the monopolist adopts a policy of only renting the good. Incentive to Innovate, Patents, and the Optimal Life of Patents 1. Using graphs, compare the incentives to innovate in the following cases: a. Competitive industry (before innovation) vs. monopoly, minor invention case. b. Competitive industry (before innovation) vs. monopoly, major invention case. 2. Assume a market demand curve of P = 100 –Q. Each firm in a competitive industry faces a constant marginal cost of $70. An innovation is defined as a mechanism that reduces marginal cost by some amount X. Greater expenditures on research and development will yield greater reductions in MC (that is, larger values for X). The R&D costs of achieving a given value for X for some firm is described by the cost function r = 15X 2 . The interest rate is i = 10% (so the discount factor is δ = 1/(1+i) = 1/1.1 = 0.9091). a. Find the initial outcome in a competitive economy. Show this outcome on a graph. b. Suppose one firm conducts research that leads to a “minor” innovation. The impact of the innovation is to lower its marginal cost to 70 – X. What is output and price after this innovation. Show this result on a graph. Indicate on the graph the increase in profit to the innovating firm. What happens to
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Econ170SQ5FALL07 - Economics 170 UCLA E. McDevitt Study...

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