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ECO380H1 (2)


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Carlos Serrano

UNIVERSITY OF TORONTO Faculty of Arts and Science October 2010 MIDTERM EXAMINATION PRACTICE QUESTIONS ECO380F Non-programmable calculators are allowed No other aids allowed Question 1 [Product differentiation] (40 points) Consider the "Not so easy" Hotelling model we discussed in the lecture. That is where transportation costs are quadratic and there is a marginal cost  0 of production. To study location (product) compe- tition, we considered a two period game. In the first period firms chose location simultaneously. In the second period firms chose prices simultaneously. To solve the model, we started solving it from its second period. You proved in the homework that proved that the demand function offirm1and2were  () and  (). Immediately after, you solved 1 2 that the second period equilibrium prices were 1() and 2() whichdependonthelocationof firm 1 and2. ethensolvedthe first period problem of the firms. You also showed that when the firms chose location there was a trade-off between moving to the center or to the extremes. In this question, I want to focus on this trade-off. (a) Explain what this trade-off is about. Please, be specific and use the technical terms (including the sign of the derivatives) that appeared in the homework whenever possible. These technical terms (including sign of the derivatives) were the results that you were supposed to prove. Note: here you don’t have to proveanything,youjusthavedescribeandusetheseresultsinyouranswer.(25points) (b) Did the firms find it optimal to move to either the center, locate at the extremes or stay somewhere in between? Explain. (10 points) Question 2: [Price discrimination] (20 points) 1 Consider the maximization problem of a telephone company, Telefonica S.A. Assume that Telefonica, a monopolist, has fixed costs  0 of operation and a cost  =10 per unit supplied of telephone services. There are two type of customers: There are 2 type-1 customers with individual (inverse) demand (1)=50 −  1 and there are 5 type-2 customers with individual (inverse) demand (2)=50 − 10 2 where  s the quantity demanded by customer type- and  is the price per unit of telephone services. Suppose that each customer pays a connect fixed fee charge to use the telephone system and a usage price per unit of telephone services. Assume that the telephone company must charge to all customers the same fixed fee and same usage price per unit of telephone services. Assume that the telephone company is serving both type of customers. Consider that the telephone company hires you as an economic advisor. The telephone company wants to maximize profits under the conditions specified above. Suppose that the fixed cost are sufficiently low that the firm will operate. (a) Calculate what is the optimal fixed fee charged, , as a function of the price per unit of telephone services ?7o)t (b) Write the maximization problem that the telephone company solves to maximize profits? Please, write the profit function as a function of . You don’t have to calculate the speficic  (7 points) (c) After making your proposal to management, a MBA graduate suggests that profits are maximized when marginal revenue equals marginal cost, and consequently Telefonica should charge the monopoly price  and set  =0 (  is the uniform monopoly price). Explain in simple terms, as if you had to convince the management team, whether or not the MBA graduate is correct. It is not necessary to make calculations. (6 points) 1 According to my final exam policy, an answer-key to this question will not be available. 1 Question 3: [Third Degree Price Discrimination] Suppose there are two kinds of consumers,  and . The inverse demand curves for the two markets are =16 − an   =20 − The seller in the market is a monopolist with cost function ()=2 . (a) Suppose the firm can discriminate between the two markets and practice third degree price discrim- ination. Suppose in market  ∈ {},the firm offers a uniform price  . Sol
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