5. Consider a consumer whose utility function isu(x,y) = sqrt(xy) (MRS(x,y)=y/x)a. Assume the consumer has income $120 and initially faces the prices px = $1 and py = $1. Howmuch x and y would they buy? Draw the budget constraint and the demands. b. Next, suppose the price of x were to increase to $2. How much would they buy now? Draw thisin the same figure.c. Decompose the total effect of the price change on demand for x into the substitution effect and theincome effect. That is, determine precisely how much of the change is due to each of thecomponent effects. (Hint: See the lecture notes for the two properties that determine the locationof “z”, the reference point for distinguishing the income and substitution effects.) 5. Consider a consumer whose utility function isu(x, y) = Vxy (MRS(x, y) =2)a. Assume the consumer has income $120 and initially faces the prices px= $1 and py= $1. Howmuch x and y would they buy? Draw the budget constraint and the demands.b. Next, suppose the price of x were to increase to $2. How much would they buy now? Draw thisin the same figure.c. Decompose the total effect of the price change on demand for x into the substitution effect and theincome effect. That is, determine precisely how much of the change is due to each of thecomponent effects. (Hint: See the lecture notes for the two properties that determine the locationof “z", the reference point for distinguishing the income and substitution effects.)

Optimal consumption point for a consumer is achieved at the point where the marginal rate of…

Answered: 5. Consider a consumer whose utility…

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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5. Consider a consumer whose utility function is
u(x,y) = sqrt(xy) (MRS(x,y)=y/x)
a. Assume the consumer has income $120 and initially faces the prices px = $1 and py = $1. How
much x and y would they buy? Draw the budget constraint and the demands.
b. Next, suppose the price of x were to increase to $2. How much would they buy now? Draw this
in the same figure.
c. Decompose the total effect of the price change on demand for x into the substitution effect and the
income effect. That is, determine precisely how much of the change is due to each of the
component effects. (Hint: See the lecture notes for the two properties that determine the location
of “z”, the reference point for distinguishing the income and substitution effects.)

5. Consider a consumer whose utility function is
u(x, y) = Vxy (MRS(x, y) =2)
a. Assume the consumer has income $120 and initially faces the prices px= $1 and py= $1. How
much x and y would they buy? Draw the budget constraint and the demands.
b. Next, suppose the price of x were to increase to $2. How much would they buy now? Draw this
in the same figure.
c. Decompose the total effect of the price change on demand for x into the substitution effect and the
income effect. That is, determine precisely how much of the change is due to each of the
component effects. (Hint: See the lecture notes for the two properties that determine the location
of “z", the reference point for distinguishing the income and substitution effects.)

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