468_ps4_2008 - ECON 468 Industrial Organization Problem Set...

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ECON 468: Industrial Organization Problem Set 4 Due date: May 8th 2008 May 2, 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 ) = θ i q - p ( q ) , where θ L < θ 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 store’s 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 supplier’s profits to find the optimal cup size).
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