Name:____________________
FE431: PUBLIC FINANCE
Assignment 5: Due Friday 2/19/16
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Make sure you show your work and that ALL answers are complete and neatly
written.
Only work that follows these instructions and represents a “Good Faith Effort” to
answer the questions posed will receive a check. (Copying answers from a classmate
without working through the problems is unacceptable conduct).
Stop by during my office hours (MWF period 4, Thurs period 9) if you have
questions, or set up another time to meet with me. A “Review of Numerical
Problems” is posted at www.usna.edu/Users/econ/swope/FE431/homeworks.html
Part I - Answer the following questions which cover material from Chapters 1 and 2
of your textbook:
1. Jane has preferences over two goods, P and F, given by
UJ  P*F
Tarzan’s utility function over P and F is
UT  P  F
a. Calculate Jane’s marginal rate of substitution if she has 6 F and 24 P.
b. Assuming the price of a unit of P is 3, and the price of a unit of F is 1,
how much of each good would you expect Jane to purchase if she has
income of 42?
c. Calculate Tarzan’s marginal rate of substitution if he has 6 F and 24 P.
d. Assuming the price of a unit of P is 3, and the price of a unit of F is 1,
how much of each good would you expect Tarzan to purchase if he has
income of 42?
Part II - Answer the following questions which cover material from Chapter 2 of
your textbook (Externalities) and imperfect competition / monopoly power:
2. Assume that a fuel-cell powered vehicle is developed that has zero hazardous
emissions. Let the marginal private benefit (i.e. the market demand) for these
vehicles be
MPB = 50,000 – Q
where Q is the total quantity of fuel-cell vehicles purchased. Given their ability to
reduce pollution, these vehicles are considered to have a marginal external
benefit of
MEB = 0.2Q
Furthermore, assume there is a constant marginal (private) cost of producing
such vehicles of 30,000. There are no marginal external costs.
a. What is the economically efficient number of fuel-cell vehicles that should
be produced and purchased each year?
b. Calculate the equilibrium market quantity and price if such vehicles are
produced in perfectly competitive markets. Show (by calculation) that the
DWL at the perfectly competitive outcome is $10 million (per year). How
large of a Pigouvian subsidy would be necessary to lead to the efficient
number of vehicles being purchased?
c. Suppose such vehicles were produced by a single-price monopoly. Calculate
the monopoly’s price and quantity of vehicles sold, and demonstrate that the
deadweight loss (per year) in this case would be $90 million per year.