1. Jim's preferences for pears and apples can be summarized by the following utility function: U(Xa,Xp)=XaXp where xa is the quantity of apples and xp is the quantity of pears. a) Draw an indifference curve for Jim by calculating a series of bundles that all produce the same level of "utility" and plotting them. Interpret the slope of the indifference curve (the marginal rate of substitution). b) Calculate the formula for Jim's marginal rate of substitution, as a function of apples and pears consumed.¹ c) What happens to the numeric value of Jim's marginal rate of substitution along an indifference curve (i.e., holds his utility constant) as he increases the number of pears he consumes and decreases the number of apples? For example, compare his MRS for a bundle consisting of 9 apples and 4 pears to his MRS for a bundle consisting of 9 pears and 4 apples and interpret the change. d) Suppose something increases Jim's desire for apples (for example, apples are found to reduce the risk of cancer), and thereby reduces his willingness to trade apples for pears. Write down a new MRS that would express this change, and plot a new indifference curve. Come up with a utility function that reflects Jim's new marginal rate of substitution.
1. Jim's preferences for pears and apples can be summarized by the following utility function: U(Xa,Xp)=XaXp where xa is the quantity of apples and xp is the quantity of pears. a) Draw an indifference curve for Jim by calculating a series of bundles that all produce the same level of "utility" and plotting them. Interpret the slope of the indifference curve (the marginal rate of substitution). b) Calculate the formula for Jim's marginal rate of substitution, as a function of apples and pears consumed.¹ c) What happens to the numeric value of Jim's marginal rate of substitution along an indifference curve (i.e., holds his utility constant) as he increases the number of pears he consumes and decreases the number of apples? For example, compare his MRS for a bundle consisting of 9 apples and 4 pears to his MRS for a bundle consisting of 9 pears and 4 apples and interpret the change. d) Suppose something increases Jim's desire for apples (for example, apples are found to reduce the risk of cancer), and thereby reduces his willingness to trade apples for pears. Write down a new MRS that would express this change, and plot a new indifference curve. Come up with a utility function that reflects Jim's new marginal rate of substitution.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:1. Jim's preferences for pears and apples can be summarized by the following utility
function:
U(Xa,Xp)=XaXp
where xa is the quantity of apples and xp is the quantity of pears.
a) Draw an indifference curve for Jim by calculating a series of bundles that all produce
the same level of "utility" and plotting them. Interpret the slope of the indifference
curve (the marginal rate of substitution).
b) Calculate the formula for Jim's marginal rate of substitution, as a function of apples
and pears consumed.¹
c) What happens to the numeric value of Jim's marginal rate of substitution along an
indifference curve (i.e., holds his utility constant) as he increases the number of pears
he consumes and decreases the number of apples? For example, compare his MRS
for a bundle consisting of 9 apples and 4 pears to his MRS for a bundle consisting of
9 pears and 4 apples and interpret the change.
d) Suppose something increases Jim's desire for apples (for example, apples are found
to reduce the risk of cancer), and thereby reduces his willingness to trade apples for
pears. Write down a new MRS that would express this change, and plot a new
indifference curve. Come up with a utility function that reflects Jim's new marginal
rate of substitution.
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