Intermediate Microeconomics
HW 5
Homework 5: Indifference Curves
1. Colby Popik’s happiness, or utility, depends only on the bags of candy corn, x,
and Peeps, y, that he eats. His happiness, v, is measured by his utility function,
which is a function of x and y, v = u(x,y). Specifically, v = x∙y. With this
function, how happy is Colby if he owns two bags of candy corn and four Peeps?
2. Write out the set of all possible combinations of x and y that give Colby a
happiness of 8 in set notation. This set is called Colby’s indifference curve.
3. Graph Colby’s indifference curves for v = 8. Hint: first rearrange the equation 8 =
x∙y for y with y on the left-hand side.
4. Write out the set of all combinations of x and y for which Colby’s happiness is 8
or greater in set notation. This is called to upper contour set of the utility function.
5. Graph the upper contour set for which Colby’s happiness is 8 or greater.
6. Colby’s friend Monica is willing to trade one bag of candy corn for one Peep, so
Colby would have three bags of candy corn and three Peeps. How happy would
this make Colby? Should Colby accept Monica’s offer?
7. Draw Colby’s indifference curves for v = 8 and v = 9 on the same graph. You
may use the same graph as in question 3.
8. Arielle’s happiness depends on bags of candy corn and Peeps in a different way.
For Arielle, v = x + y. Draw Arielle’s indifference curves for v = 5 and v = 6 on
the same graph.
9. John-Paul’s happiness also differs from both Colby’s and Arielle’s. For JohnPaul, v = min(x,y). This means that John-Paul happiness is measured by the
minimum of the number of bags and Peeps that he owns, so if he owns two bags
of candy corn and three Peeps, then his happiness is two. Draw John-Paul’s
happiness for v = 2 and v = 3 on the same graph.