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ajaz_eco_204_2012_2013_chapter_17__18_PP

Eco 204 s ajaz hussain do not distribute substitute

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Unformatted text preview: r’s budget constraint is: Assume the customer has monotonic preferences so that: The consumer chooses by solving the UMP: ( ( ) ) Solve the UMP by the Langragian method: ( ) [ The FOCs are: ( The 1st FOC implies that ) which substituted in 2nd FOC yields: ( ( ) ) 51 ECO 204 Chapter 17 & 18: Practice Problems & Solutions for Firms with Market Power: Business Apps and Price Discrimination in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ( ) Substitute this in 3rd FOC: ( ) ( ) The complete solution to the UMP is: 52 ECO 204 Chapter 17 & 18: Practice Problems & Solutions for Firms with Market Power: Business Apps and Price Discrimination in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. (c) Use your answers in parts (a) and (b) to deduce the parameters and in the utility function. Does this consumer have monotonic preferences over D & H jackets (good 1)? Show all calculations and state any assumptions. Answer From part (b) we had: From part (a) we had: This implies that: The consumer has utility function: ( ( ( ) ) ( ) ) ( ( ) ) ( ) Observe that: ( ) The consumer has monotonic preferences when: ( ( ) ) 53 ECO 204 Chapter 17 & 18: Practice Problems & Solutions for Firms with Market Power: Business Apps and Price Discrimination in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. (d) For what price of D & H jackets will a NYC customer maximize or minimize savings? Prove whether savings are maximized or minimized. Show all calculations and state any assumptions. Hint: Use the expression for from part (b).\ Answer: We know that: ( ) ( ) Substituting: We have: ( ) ( ) Ceteris paribus, assuming an interior solution, savings are maximized/minimized when: To see if savings are maximized or minimized check the SOC: Since the SOC > 0 it means that saving...
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