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Consider a consumer with the utility function U(X,Y) = In(vX + vY) and suppose that the prices of goods and income level are given by px = $2, py = $4 and the income of consumer is I = $120. a) Compute this consumer's optimal consumption levels of goods X and Y and the maximum utility level that she can attain. b) Now, consider another consumer with utility U (X, Y) = vX + VY, facing the same prices and income level. Compute this consumer's optimal consumption levels of goods X and Y and the maximum utility level that she can attain. c) Finally, consider a different consumer with utility U (X,Y) = 3(vX + vY) facing the same prices and income level. Compute this consumer's optimal consumption levels of goods X and Y and the maximum utility level that she can attain. d) Compare your findings in parts (a),(b) and (c). What difference does having the "In" in the utility function make? How does multiplying a utility function with a constant affect the solution of the utility maximization problem?

Consider a consumer with the utility function U(X,Y) = In(vX + vY) and suppose that the prices of goods and income level are given by px = $2, py = $4 and the income of consumer is I = $120. a) Compute this consumer's optimal consumption levels of goods X and Y and the maximum utility level that she can attain. b) Now, consider another consumer with utility U (X, Y) = vX + VY, facing the same prices and income level. Compute this consumer's optimal consumption levels of goods X and Y and the maximum utility level that she can attain. c) Finally, consider a different consumer with utility U (X,Y) = 3(vX + vY) facing the same prices and income level. Compute this consumer's optimal consumption levels of goods X and Y and the maximum utility level that she can attain. d) Compare your findings in parts (a),(b) and (c). What difference does having the "In" in the utility function make? How does multiplying a utility function with a constant affect the solution of the utility maximization problem?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Please solve all the options. (a,b,c,d).

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Consider a consumer with the utility function U(X,Y) = In(vX + VY) and suppose that the prices of goods and income level are given by px = $2, py = $4 and the income of consumer is I = $120. a) Compute this consumer's optimal consumption levels of goods X and Y and the maximum utility level that she can attain. b) Now, consider another consumer with utility U (X, Y) = VX + VY, facing the same prices and income level. Compute this consumer's optimal consumption levels of goods X and Y and the maximum utility level that she can attain. c) Finally, consider a different consumer with utility U (X,Y) = 3(VX + vY) facing the same prices and income level. Compute this consumer's optimal consumption levels of goods X and Y and the maximum utility level that she can attain. d) Compare your findings in parts (a).(b) and (c). What difference does having the "In" in the utility function make? How does multiplying a utility function with a constant affect the solution of the utility maximization problem?
Transcribed Image Text:Consider a consumer with the utility function U(X,Y) = In(vX + VY) and suppose that the prices of goods and income level are given by px = $2, py = $4 and the income of consumer is I = $120. a) Compute this consumer's optimal consumption levels of goods X and Y and the maximum utility level that she can attain. b) Now, consider another consumer with utility U (X, Y) = VX + VY, facing the same prices and income level. Compute this consumer's optimal consumption levels of goods X and Y and the maximum utility level that she can attain. c) Finally, consider a different consumer with utility U (X,Y) = 3(VX + vY) facing the same prices and income level. Compute this consumer's optimal consumption levels of goods X and Y and the maximum utility level that she can attain. d) Compare your findings in parts (a).(b) and (c). What difference does having the "In" in the utility function make? How does multiplying a utility function with a constant affect the solution of the utility maximization problem?
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