Problem Set 1: Due 8/31/2020 at noon (EDT on Brightspace)
1. Vanya and Leonard make up a simple exchange economy where the only goods are violins and
figurines.
Total violins = 4
Total figurines = 16
a. Leonard has 12 figurines and 2 violins. Draw the Edgeworth box. Label the endowment
with ω and how much each person is consuming at that point. Also label Leonard’s
origin (OL) and Vanya’s origin (OV), and label along which axis each good is increasing for
each person.
b. On your graph from part a, draw an indifference curve for each person (label them IL
and IV) such that the endowment is NOT Pareto Efficient.
c. On your graph from part a, draw a point that represents a Pareto improvement relative
to the endowment. Label it P1.
d. Define Pareto improvement and explain how P1 satisfies that definition.
e. At a Pareto Efficient allocation in this type of exchange economy, what must be true of
the agents’ Marginal Rates of Substitution (MRS)?
f. Given the following utility functions for the two individuals over the two goods, is the
allocation where Leonard has 12 figurines and 3 violins Pareto Efficient? Justify your
answer fully.
UL(vL,fL) = 4vLfL
UV(vV,fV) = 2𝑣𝑉2 𝑓𝑉
g. Find a Pareto Efficient allocation where they each have 2 violins.
h. What does the First Fundamental Theorem of Welfare Economics tell us about all initial
allocations in a simple exchange economy? Under what (2) assumptions?
2. Luther and Allison are superheroes who just saved the world (yay!) but they made a huge mess
(boo!) Fortunately, there was no structural damage, but there is debris on all of the sidewalks in
Dallas. Luther and Allison are considering cleaning up the mess they made. This affects all of the
residents of Dallas, but for now, just consider Luther and Allison. The marginal cost of cleaning
one block of sidewalk is MC = 45 + 2Q. Use the following demand curves in your answer as
needed, suppose that Q is blocks of sidewalk:
Allison’s: PA = 90 – 2Q
Luther’s: PL = 60 – 3Q
a. What 2 criteria must a public good meet? List and define them.
b. Explain how clean sidewalks meet these two criteria.
c. Would either Luther or Allison decide to privately provide any of the public good? Justify
your answer.
d. Draw the market demand for the public good. Denote the area where both consumers
are willing to pay for additional clean sidewalks “A” and the area where only one of
them is willing to pay “B.” Label all axes, intercepts, kink points, and slopes.
e. What is the socially optimal quantity of clean sidewalks?
f. Explain the free rider problem.
g. Explain how the free rider problem can undermine Pareto Efficiency in the market for
public goods. Your answer should refer to the Samuelson Condition.