# 400ps1-11 - ECON 400 Winter 2011 PROBLEM SET I(for Monday...

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ECON 400 Hartman Winter 2011 PROBLEM SET I (for Monday, January 10) 1. (This is problem 8 in Chapter 1 of the text.) A monopolist faces the demand function x ab p  where x is the quantity sold, p is the price (to buyers), and a and b are given parameters. The monopolist's production costs are given by 2 Ck x where k is a given parameter. There is also a per unit tax on the monopolist's sales at the rate t . The monopolist's objective is the maximization of profit. a. What restrictions on the values of the parameters a , b , and k would you be inclined to assert, a priori ? b. Find the monopolist's output as a function of t , *( ) x xt . Confirm that *( )/ 0 dx t dt for the restricted values of a , b , and k from part a, i . e ., show that output decreases as the tax rate increases. c. What restrictions does the hypothesis of profit maximization place on the parameters a , b , and k ? How do these restrictions compare with those from part a?

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400ps1-11 - ECON 400 Winter 2011 PROBLEM SET I(for Monday...

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