Question

. Short answer/definitional questions:

a. Suppose there are only two goods in the world, X and Y. The price of X is $4. The price of Y is $2. Assume that a consumer chooses to purchase some X and some Y at these prices. What is the marginal rate of substitution between X and Y for this consumer at her purchased combination of X and Y, assuming that she is maximizing her utility? How do you know?

b. Consider this demand curve for a good X: QX = 100 - PX . What is the approximate price elasticity of demand for X at PX = 5? What is the approximate price elasticity of demand at PX = 90? Show your calculations.

c. Describe what is meant by the assumption that consumer preferences are “transitive.” (You may use an indifference curve graph to support your answer if you’d like, but you don’t need to.

Answer 1

a. At the utility maximizing bundle, slope of indifference curve equals the slope of the budget line. Slope of the indifference curve is Marginal Rate of Substitution, MRS, and slope of the budget line is Price of X/Price of Y = 4/2 = 2
So, MRS = 2
Thus, the marginal rate of substitution between X and Y for this consumer at her purchased combination is 2.

b. At PX = 5; QX = 100 - 5 = 95
QX = 100 - PX
So, dQX/dPX = -1
Approximate price elasticity of demand = (dQX/dPX)*(PX/QX) = (-1)*(5/95) = -.05

At PX = 90; QX = 100 - 5 = 10
QX = 100 - PX
So, dQX/dPX = -1
Approximate price elasticity of demand = (dQX/dPX)*(PX/QX) = (-1)*(90/10) = -9

c. Preferences are transitive means that if a consumer prefers bundle a over bundle b and bundle b over bundle c, then he will always prefer bundle a over bundle c because a gives him the highest utility.