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Graph your solution below. [Do 1st degree price discrimination in this part only].
Answer
Under 1st degree price discrimination, each jacket is sold at a unique price. The optimal number of jackets is found by
setting:
57
ECO 204 Chapter 17 & 18: Practice Problems & Solutions for Firms with Market Power: Business Apps and Price Discrimination in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Under 1st degree price discrimination the demand curve is the curve so that: Here each jacket is sold according to: MC $ 1,000 AVC 1st Degree Price
Discrimination Prices 720
Individual demand curve
and
MR curve 300
2.8 q (g) [This part assumes uniform prices] Suppose that in April 2010,
utility function:
( ) ( . Consider a typical NYC consumer with the
) Here is savings in dollars and is the number of D & H jackets. Suppose this consumer has an income of
Using values for and from part (c), solve the UMP for the optimal
and (any) Lagrange multipliers given that
. Calculate the marginal utility of relaxing the savings limit constraint. Show all calculations and state any
assumptions. . Answer
Earlier we saw that:
58
ECO 204 Chapter 17 & 18: Practice Problems & Solutions for Firms with Market Power: Business Apps and Price Discrimination in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Assuming monotonic preferences (so that (
( ) the consumer chooses
( ) ) by solving the UMP: ) ( ) With an equality and inequality constraint, the UMP can be solved by:
( [ ) [ The FOCs and KuhnTucker conditions are: ( ) ( ) Start by checking:
(
Possibility #1: ) . From the FOC: This implies that: 59
ECO 204 Chapter 17 & 18: Practice Problems & Solutions for Firms with Market Power: Business Apps and Price Discrimination in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. The 2nd FOC implies:
( ) ( )
( ) The 1st FOC implies: All the KuhnTucker solutions are satisfied. Thus one solution is: Possibility #2: . The 1st FOC implies:
60 ECO 204 Chapter 17 & 18: Practice Problems & Solutions for Firms with Market Power: Business Apps and Price Discrimination in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. The 2nd FOC implies:
( ) ( ) () ( ) ( ) The 3rd FOC implies: () This violates the condition that and therefore cannot be a solution. 61
ECO 204 Chapter 17 & 18: Practice Problems & Solutions for Firms with Market Power: Business Apps and Price Discrimination in ECO 204 (this version 20122013)...
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This document was uploaded on 01/19/2014.
 Fall '14

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