Question

Question) The shape of indifference curves tells you something about the relationship between consumption goods.

A. Define (in your own words) the meaning of MRS_SB where S indicates steaks and B indicates beer. What does the MRS have to do with the construction of indifference curves? (4)

B. Suppose an individual’s marginal rate of substitution of steak for beer (MRS_SB) is 2:1. Suppose also that the price of steak is $ 4 and the price of beer is $ 1. In order to increase the individual’s level of utility, should he/she buy more steak, buy more beer, or purchase the same consumption bundle? Explain. (4)

C   If we have the utility function U (X₁,X₂) = X₁^1/3 X₂^2/3 , what is the marginal rate of substitution between X₁ and X₂ if X₁ = 1 and X₂ = 1? What is MRS if X₁ = 2 and X₂ = 1? Would the indifference curves generated from this utility function exhibit diminishing marginal rates of substitution as X₁ increases? (4)

Answer 1

A)MRS(sb) refers to substitution of good B to consume one additional unit of S, to maintain the utility level unchanged.

MRS is slope of indifference curve , so MRS decide the shape of indifference curve.

B) Utility maximizing condition:

MRS(sb)=Ps/Pb

MRS(sb)=2/1

Ps/Pb=4/1

So MRS(sb)<Ps/Pb, so per MRS marginal utility from B is greater than per dollar marginal utility from s, so Consumer should increase consumption of B to maximize the utility.

C)MRS(x1,X2)=MUx1/MUx2

MUx1=(x2^2/3)/(3*X1^2/3)

MUx2=(2*X1^1/3)/(3*X2^1/3)

MRS(x1,x2)=(x2)/(2*x1)

When x1=1 and x2=1

MRS=1/(2*1)=1/2=0.5

When x1=2 and X2=1

MRS=1/(2*2)=1/4=0.25

Yes , as X1 increases from 1 to 2, MRS Decreases from 0.5 to 0.25 .