468_ps4_sol_2008

468_ps4_sol_2008 - ECON 468: Industrial Organization...

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Unformatted text preview: ECON 468: Industrial Organization Problem Set 4 Due date: May 8th 2008 May 8, 2008 1. Consider the problem of a cofee-shop who wants to set the price and the optimal size of cup of coffee. The market is composed to two types of consumers i { L,H } with the following utility from buying a cup of size q : u i ( q ) = i q- p ( q ) , where L < H and p ( q ) is the price of cup of size q . The proportion of consumers of type H in the population is 1 / 2 (the other half is of type L ). Moreover the cost of producing and selling a cup of size q is given by: C ( q ) = 1 2 q 2 . (a) Assume that the stores owner is constrained to offer only one type of cup (i.e. q u ), and is not able to price discriminate between consumers. What is the optimal cup size and price such that both types of consumers are buying the good? (hint: solve for the maximum price such that both participation constraints are satisfied and then maximize the suppliers profits to find the optimal cup size). Only PC L will bind: L q = p . Substituting in the profits of the firm the optimal size solves: max q L q- 1 2 q 2 q u = L The optimal solution is therefore: ( p u ,q u ) = ( 2 L , L ) . (b) Assume now that the owner is perfectly able to discriminate across consumers. What is the optimal cup size and price offered to each consumer type?...
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468_ps4_sol_2008 - ECON 468: Industrial Organization...

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