A consumer has Cobb-Douglas preferences for beer and pizza. She spends 50% of her budget on New Belgium Fat Tire ale, 20% on Coors Light, and 30% on pizza. Her budget is $500. The price of New Belgium is $9, the price of Coors is $6, and the price of pizza is $12. Suppose Coors acquires New Belgium, and now charges $7.50 for both types of beer. In order to quantify by how much this consumer is better off or worse off because of the merger:Solve for their demand functions for each good, as functions of generic prices and budget. Note that the budget shares tell you what the exponents are in the Cobb-Douglas utility function.Use the demand functions to calculate their optimal quantities demanded for each good at pre-merger prices.Plug these quantities into the utility function and calculate their utility level for the quantities demanded at pre-merger prices.Now put the demand functions (not quantities demanded) into the utility function. What budget level is required at the post-merger prices in order to achieve the pre-merger utility? The difference between this and the original budget ($500) is the impact of the merger on this consumer’s welfare, valued in dollars.

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Answered: A consumer has Cobb-Douglas preferences…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A consumer has Cobb-Douglas preferences for beer and pizza. She spends 50% of her budget on New Belgium Fat Tire ale, 20% on Coors Light, and 30% on pizza. Her budget is $500. The price of New Belgium is $9, the price of Coors is $6, and the price of pizza is $12. Suppose Coors acquires New Belgium, and now charges $7.50 for both types of beer. In order to quantify by how much this consumer is better off or worse off because of the merger:
1. Solve for their demand functions for each good, as functions of generic prices and budget. Note that the budget shares tell you what the exponents are in the Cobb-Douglas utility function.
2. Use the demand functions to calculate their optimal quantities demanded for each good at pre-merger prices.
3. Plug these quantities into the utility function and calculate their utility level for the quantities demanded at pre-merger prices.
4. Now put the demand functions (not quantities demanded) into the utility function. What budget level is required at the post-merger prices in order to achieve the pre-merger utility? The difference between this and the original budget ($500) is the impact of the merger on this consumer’s welfare, valued in dollars.

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