The goods in the next question are not ale and bread. To solve this question, you are going to have to evaluate the condition The price p is defined for you, but you will have to define the marginal rate of substitution for yourself. What ratio of marginal utilities should you use? You will know the answer to this question once you have defined the marginal rate of

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.15P
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The goods in the next question are not ale and bread. To solve this question, you are going to have to evaluate the condition

The price p is defined for you, but you will have to define the marginal rate of substitution for yourself. What ratio of marginal utilities should you use? You will know the answer to this question once you have defined the marginal rate of substitution – that is, decided which good is being given up and which good is being given in compensation. When making this decision, remember that both sides of this equation refer to the same kind of trade. The right-hand side describes the rate at which one good can be traded for the other in the marketplace; and the left-hand side describes the rate at which someone is willing to trade that good for the other. Thus, the definition of the price determines the manner in which the marginal rate of substitution must be defined.

Pierre lives on red wine and blue cheese. His utility function is.

where w is his consumption of wine and c is his consumption of cheese. He is endowed with 4 kilograms of cheese and 8 bottles of wine. He can trade these commodities in a marketplace, where the price of red wine, measured in blue cheese, is p.

a) Find Pierre’s optimal consumption of wine and cheese at any given price p.

b) Find the quantity of wine that Pierre would like to buy at any given price p.

c) Suppose that Pierre trades with Gabrielle, whose excess demand for wine is

Find the market-clearing price.

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