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. The Marginal Rate of Substitution indicates the rate at which the consumer is willing to give up beer in order to increase the consumption of steak by 1 unit. The value of MRS keeps on decreasing as we move downwards along the indifference curve. This tells us that the shape of the indifference curve is convex because MRS is diminishing.

B. The above data shows that MRS = 2/1 and P s / P b = 4. This shows that rate of substitution is less than price ratio. In order to increase the rate of substitution along the indifference curve and equate it to price ratio, the consumption of steak should decrease and consumption of beer should increase. Decrease in the consumption of steak will increase marginal utility derived from steak and reduce marginal utility derived derived from beer which will increase the marginal rate of substitution and thus equate the MRS with Price ratio.

Thus, the person should buy more steak to increase utility.

C.