6- Consider a consumer with a utility function U(X,Y) = 4√x + √Y a) Evaluate whether marginal utilities of X and Y are diminishing or not. b) Compute marginal rate of substitution (MRS). What is the value of MRS when the consumer is consuming 4 units of X and 64 units of Y. d) c) Provide an interpretation of the value of MRS you found in part (c). Evaluate whether this consumer has diminishing marginal rate of substitution or not
6- Consider a consumer with a utility function U(X,Y) = 4√x + √Y a) Evaluate whether marginal utilities of X and Y are diminishing or not. b) Compute marginal rate of substitution (MRS). What is the value of MRS when the consumer is consuming 4 units of X and 64 units of Y. d) c) Provide an interpretation of the value of MRS you found in part (c). Evaluate whether this consumer has diminishing marginal rate of substitution or not
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:5-
6-
For this question, consider that the letter "A" denotes the last 4 digits of your
student number. That is, for example, if your student number is: 12345678, then
A = 5678.
Suppose that the consumer has a utility function given by U(X,Y) = X0,2 y0,8
The prices of goods X and Y are given by px=4 TL and py=2 TL. The total
budget the consumer has is given by I = A TL.
a. Write down the consumer's optimization problem (formally, as we wrote in the
lectures).
b. Apply the Lagrangian method. Find the necessary condition (NC) for the
consumer's optimization problem. Then find the values of X and Y that maximize
consumer's utility.
C. Illustrate your results by using a graph.
d. In the graph you drew for part (c), mark a consumption bundle that is not optimal
(i.e. does not satisfy the NC) and discuss why it is not optimal.
Consider a consumer with a utility function U(X,Y)= 4√x + √Y
a) Evaluate whether marginal utilities of X and Y are diminishing or not.
b) Compute marginal rate of substitution (MRS). What is the value of MRS
when the consumer is consuming 4 units of X and 64 units of Y.
c) Provide an interpretation of the value of MRS you found in part (c).
d) Evaluate whether this consumer has diminishing marginal rate of
substitution or not.
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