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Assignment_3 - where& 2 f 1 2 g denotes the consumer...

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EC 501 Micro Assignment 3 Due 4/5/10 in class 1. 7.2 ("Show that if an individual°s..") 2. 7.4 ("Suppose there is a 50-50 chance..") 3. 7.10 ("In some cases individuals may care..") 4. 13.4 ("Suppose that Robinson Crusoe..") 5. 13.6 ("In the country of Ruritanina..") 6. 14.2 ("A monopolist faces a market demand curve..") 7. 14.6 ("Suppose a monopoly can produce..") 8. Suppose a monopolist who produces an output y at marginal cost c wants to implement a non-linear pricing scheme to maximize pro±ts in a market where there are two kinds of consumers. The utility functions for the two types of consumers are: °u (
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Unformatted text preview: ) where & 2 f 1 ; 2 g denotes the consumer type, and where u is a concave function. The seller cannot tell the type of any one consumer, but he estimates that Pr ( & = 1) = q 2 (0 ; 1) : (a) Set up the seller&s maximization problem and ±nd the conditions for the optimal pricing schedule. (b) Suppose that the seller&s marginal cost c = 1 and that the consumers&utility functions take the form: &u ( y ) = 5( & + 1) log (1 + y ) Suppose also that q = 1 = 2 : Find the optimal pricing schedule in this special case. Verify that the solution entails a quantity discount. 1...
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