Problem Set 1
You can work in groups of up to 3 students. Each group should submit only one solution.
You can get up to 3 points.
1. Key concepts:
a. When we say that preferences are rational, what does this imply?
b. What is the Marginal Rate of Substitution between x and y? What does it mean when
MRS𝑥,y(B) = 3?
2. For each case state whether the preferences are rational (i.e. complete and transitive)
and monotone, or not. Why?
a. John is indifferent between bundles (6,1), (1,6) and (2,2)
b. Suzan prefers bundle (6,1) to bundle (4,4), prefers bundle (4,4) to bundle (1,6), and is
indifferent between bundles (6,1) and (1,6)
c. David prefers bundle (2,3) to bundle (1,8), and is indifferent between bundle (1,8) and
bundle (4,4)
3. Suppose Bill is indifferent between bundles (2,6), (4,4) and (6,2) and Claire is indifferent
between bundles (2,6), (3,3) and (6,2). They both have smooth, monotonic indifference
curves. At bundle (2,6) who has the higher MRS? What about bundle (6,2)?
4. Suppose that Johanna, Linda, and Michelle rank all the guys in their class by brains and
looks. Albert received the grades (brains=9, looks=2), Leonardo (brains=1, looks=8.5), and
Gunter (brains=4,looks=5).
a. Johanna says “I only cares for brains and don’t care for looks”. Draw Johana’s indifference
curves.
b. Linda says “I only cares for looks and don’t care for brains”. Draw Linda’s indifference
curves.
c. Michelle says “my preferences for brains (x) and looks (y) can be expressed by u(x,y)=xy”.
Draw Michelle’s indifference curves.
d. Which guy will each girl choose?
5. Suppose Dina consumes sneakers, denoted by x, and skinny jeans, denoted by y. She has
the following utility function: u(x,y)=xy.
a. Calculate her utility from the following bundles: (3,6),(4,2), (1,10).
b. Find another bundle for which she is indifferent between this bundle and the bundle
(3,7).
c. Sketch Dina’s indifference curves.
d. Suppose that Dina consumes 6 sneakers and 4 pairs of jeans. How many jeans is she
willing to give up for 2 more sneakers? How many jeans is she willing to give up for 1 more
sneaker? How many sneakers is she willing to give up for 2 more jeans? How many sneakers
is she willing to give up for 1 more jeans?
d. Suppose Dina consumes 4 sneakers and 6 pairs of jeans. One day, she loses 1 pair of
sneakers, so she only has 3. You would like to compensate her, but can only give her jeans.
How many jeans should you give her to make her just as happy as before?
What if her initial bundle was 4 sneakers and 2 pairs of jeans, how many jeans would you
have to give her then?
e. Calculate her MRS at the bundles: (4,6),(3,7), (1,10).
6. Calculate the marginal rate of substitutions for the following utility functions
1
3
a. u(𝑥,y)=2𝑥 4 𝑦 4
b. u(𝑥,y)=(x+5)(y+7)
c. u(𝑥,y)= 3𝑥 + 4𝑦
d. u(𝑥,y)= √𝑥 + 4𝑦
e. u(𝑥,y)=2𝑥2+2𝑦2
7. David and Ella are planning a holiday together to Hawaii. David says that he can only enjoy
a day of sightseeing if it is followed by a day on the beach, and he can only enjoy a day on the
beach if it follows a day of sightseeing. Ella says that one day of sightseeing is equally good
to one day on the beach. The price of one day of sightseeing is €20 and the price of one day
on the beach is €10. Their joint budget is €240.
a. Draw a graph that illustrates all the possible combinations of days of sightseeing and days
on the beach that they can afford.
b. Draw the indifference curves of Ella and David.
c. . If they end up choosing to spend 7 days of sightseeing and 10 days on the beach, does
there exist another bundle that makes both better off?
d. If they end up choosing 9 days of sightseeing and 6 days on the beach, does there exist
another bundle that makes both better off?
e. Suppose that Ella replaced David with Freddi. Freddi says that one day of sightseeing is
equally good to four days on the beach. Answer parts c. and d. for Ella and Freddi.