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?
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.11P
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Please solve all the options. (a,b,c,d).
Thank you from now.
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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