Consider two consumers, each having income of $300 that can be used to purchase two goods: X and Y. The price per unit of X is $5, and the price per unit of Y is $4. Ms. A’s preferences can be described by the utility function: U = (X^2)Y and her marginal rate of substitution is given by MRS X,Y = 2Y/X. Mr. B’s preferences can be described by the utility function: U = X(Y+100) and his marginal rate of substitution is given by MRS X,Y = (Y+100)/X. Calculate the amounts of X and Y each of these consumers will purchase if each is trying to make her- or himself as well off as possible.
Consider two consumers, each having income of $300 that can be used to purchase two goods: X and Y. The price per unit of X is $5, and the price per unit of Y is $4. Ms. A’s preferences can be described by the utility function: U = (X^2)Y and her marginal rate of substitution is given by MRS X,Y = 2Y/X. Mr. B’s preferences can be described by the utility function: U = X(Y+100) and his marginal rate of substitution is given by MRS X,Y = (Y+100)/X. Calculate the amounts of X and Y each of these consumers will purchase if each is trying to make her- or himself as well off as possible.
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.2P
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1. Consider two consumers, each having income of $300 that can be used to purchase two goods: X and Y. The price per unit of X is $5, and the price per unit of Y is $4. Ms. A’s preferences can be described by the utility function:
U = (X^2)Y
and her marginal rate of substitution is given by
MRS X,Y = 2Y/X.
Mr. B’s preferences can be described by the utility function:
U = X(Y+100)
and his marginal rate of substitution is given by
MRS X,Y = (Y+100)/X.
Calculate the amounts of X and Y each of these consumers will purchase if each is trying to make
her- or himself as well off as possible.
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