Question

(Use this information to answer a, b, c below) Suppose Mary’s utility function for two goods X and Y is given by:

U(X,Y) = 3X^1/2Y^1/2 . Suppose consumption bundle A consists of 10 units of X and 30 units of Y, and consumption bundle B consists of 40 units of X and 20 units of Y.

a. Consumption bundle A lies on a higher/lower/same indifference curve than consumption bundle B. Show computations.

b. Compute Mary’s MRSxy at consumption bundle A. What does this number tell you?

c. If Mary chose consumption bundle B, her MRSxy would be a higher or lower compared to MRSxy at A? Please explain why.

d. Mary’s preference is transitive. Could two of Mary’s IC’s intersect? Please explain using a graph below.

e. State the equi-marginal principle. Suppose Jane is consuming a bundle of X and Y where MUx = 3,  MUy = 4, Px = $1, Py = $2. To maximize utility, Jane should increase the consumption of good ___ and decrease the consumption of good ____. Explain your answer by using the equi-marginalprinciple.

f. True or False and briefly explain: If at any consumption bundle, MRSxy <Px/Py, a consumer can enjoy a higher level of utility by increasing the consumption of X and decreasing the consumption of Y.

2. (12*3 = 36 pts) Suppose Mary’s utility function for two goods X and Y is given by: U(X,Y) = 6X^1/3Y^2/3

1. If Px = $3, Py = $5, and Income I = $600, compute Mary’s utility maximizing consumption bundle. Show the utility maximizing consumption bundle on a graph. Show computations using the calculus approach.

b. Suppose Px and Py are the same as in part (a), but Mary’s income falls to $300. Construct Mary’s Income Consumption Curve, and Mary’s Engel Curve for Good Y. Is good Y a normal good? Briefly explain (Can use either calculus or solver to do computations.)

c. Define Price Consumption Curve. Suppose Px and Income are the same as in part (a), but Py falls to $2. On a graph, construct Mary’s demand curve for good Y. ((Can use either calculus or solver to do computations.)

Answer 1

A)At budle A ,

U=3*√10*√30=51.96

At bundle B

U=3*√40*√20=84.85

So lower utility shows consumption bundle A is lies on lower indifference curve than consumption bundle B.

B)MRSxy=MUx/MUy

MUx=1.5√y/(√x)

MUy=1.5√x/(√y)

MRS=MUx/MUy=y/x

MRS at bundle A,

MRS=30/10=3

This tells CONSUMER is willing to trade 3 units of y foe one unit of x.

C)MRS at bundle B,

MRSxy=y/x=40/2=20

MRS at bundle be is 2 ,which tells CONSUMER is willing to trade 2 y for 1 x.

So MRS at bundle B is lower than bundle A

D)NO,

IC curve shows different combination of two goods athat gives same utility.if curves intersect means at some point different IC curve shows same utility.

Which also suggest that with same number of X , increasing y has has no effect on utility ,which is not possible.

So it can't be true.