ps2_ans

# ps2_ans - Department of Economics University of California...

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Department of Economics Fall 2004 University of California Woroch/Lopez/Sydnor Economics 121: PROBLEM SET 2 Due: Thursday, October 7, 2004, 12:30 PM (in lecture) 1. True/False/Uncertain: Decide whether the following statements are true, false or uncertain, and then explain the reasoning behind your answer. a) The Bertrand Paradox will arise for a duopoly on the Hotelling line as transportation costs go to zero. UNCERTAIN. - Recall that price in the model is P + tx. If t = 0, then each consumer will only pay the price regardless of its position on the Hotelling line. - If t=0, we can assume that consumers view the products as perfect substitutes. In this case, the price will converge to the marginal cost. - However, if marginal costs differ across firms, then firms will compete on price. If we assume two firms with different costs, say MC1 > MC2. Then, when the firms compete on price, firm 2 will be able to price just below MC1 b) If production exhibits learning by doing , then a scope economy arises between the product produced at different points in time. TRUE. Assume there are two periods and define 1 q and 2 q as output in the first and second periods, respectively. The cost of producing either output alone without the other would be the same, but when some of 1 q has been produced in the first period, then the cost of producing 2 q in the second period is lower than when q 2 is produced stand alone. Note that the source of the scope economy here is not a shared input since production in the second period does not affect cost in the first, but rather a cost complementarity: more produced in the first period, the less the cost in the second. c) When firms in an industry act as price takers, their index of scale economies, s, will be less than 1 when the industry reaches equilibrium. FALSE: s = AC/MC. When firms act as price takers (i.e. a competitive industry), when s < 1 then AC < MC and firms are making a profit. In equilibrium, however, profits will be zero, since firms enter until profits are zero. Profits are just zero when AC = MC, or when s = 1. 2. Engineering economists have found that the cost of producing small cars (S) and trucks (T) can be expressed as follows: * C(S, T) = 10 + S + 2T + ST if S > 0 and T > 0 * C(S, T) = 8 + 2T if S = 0 and T > 0 * C(S, T) = 4 + S if S > 0 and T = 0 Both S and T are measured in thousands of vehicles per year. a) Find the incremental cost function of producing trucks when a positive amount of small cars are produced: S > 0. IC T (S,T) = C(S,T) - C(S,0) )= 10 + S + 2T + ST - (4 + S) = 6 + 2T + ST b) Evaluate incremental cost of trucks at T = 10 when S = 10 and then again when S = 20. IC

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ps2_ans - Department of Economics University of California...

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