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Problem Set5 - BPUB250 Problem Set5 Due April 4-5 2012 in...

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BPUB250 Problem Set5 Due: April 4-5, 2012 in Class Question 1 Hugh is planning to open a Shabu Shabu restaurant in Philadelphia. It is the only restaurant in Philly specialized in Shabu Shabu, so it has a monopoly (in at least a narrowly defined market). Demand is predicted to be q=100-2p , and Hugh’s total cost function is given by C(q) = q 2 +5q . (a) Hugh stopped attending BPUB250 class before the midterm, and he insisted that a firm should always produce where price equals marginal cost. Compute Hugh’s quantity choice, price, and profits under this assumption. (b) Now compute the profit-maximizing quantity, price and profits. Why do the values you calculated in (a) and (b) differ? (c) Hugh has the option to build a second kitchen with a onetime construction cost of F. The second kitchen, which is equipped with state-of-the-art cooking utensils, will operate at a constant marginal cost of $25. With this option, Hugh can serve the Shabu Shabu demand, q=100-2p, with two kitchens. What is the maximum cost F you would advise Hugh to pay for building the second kitchen? Question 2 Steve Jobs has been very successful in selling the iPad3 . He has two manufacturing plants, one in the US ( U ) and the other in China ( C ). The phones produced by each plant are identical, and Steve is a monopolist in both countries. The demand curve in each country is given by (respectively): Q c = 100 – P c Q u = 200 – 2P u The total cost function of each plant is given by (respectively): C c (Q c ) = 2Q c 2 C u (Q u ) = F +10Q u + Q u 2 where F is a fixed cost. Unless suggested otherwise, assume F is such that Steve chooses to manufacture at the US plant. (a) Initially Steve is only permitted to sell an iPad3 manufactured in one country to consumers in that country. How many units does each plant produce? What price does Steve charge in each country? What are Steve’s total profits ( as a function of F )?
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