The Paul H. Nitze School of Advanced International Studies
The Johns Hopkins University
PROBLEM SET III
Due on Dec 3
and Dec 4
(Professor Alvisi and Carbonara)
Exercise 5 of Problem Set 2. Part e.
Let the long run cost function of each firm have the same algebraic expression of the short
run cost function, that is
࠵?࠵?(࠵?) = 5࠵?
+ 50࠵? + 500
. Market demand is unchanged. What is
the long run equilibrium in terms of price and quantity? How many firms are active in the
market? Compare the result with the one in part
and discuss briefly.
Taxes and Social Welfare in Perfect Competition.
A country is considering the introduction of a per-case tax t=2.5$ in the market of canned
fruit. The economic advisors to the country estimate the supply and demand curves for
canned fruit as:
= 3600 – 400P
= -600 + 400P,
Where P is the price per case and Q are cases per-day.
What are the equilibrium price and quantity in the current environment with no tax? Illustrate
your results in a graph, indicating the values of the intercepts.
What price and quantity would prevail after the imposition of the tax?
Illustrate your results
in the graph of part a. What portion of the tax would be borne by buyers and sellers
respectively? Discuss your results using the values of the price elasticities of demand and
supply at the pre-tax equilibrium.
What tax revenue will be generated? Calculate the deadweight loss from the tax as the
difference between pre-tax and post-tax total surplus. Can you obtain the DWL from the
graph using a different method?
General Equilibrium in a Pure Exchange Economy.
Consider a pure exchange economy
with two consumers, Harry and Meghan, who consume two commodities, pudding and
salmon. Harry’s initial endowment is 16 puddings and 2 salmons. Meghan’s endowment is 8
salmons and 4 puddings. Their utility functions are