ECON 562: Public Finance Problem Set 1 Problem sets must be turned in class. Lat

ECON 562: Public Finance
Problem Set 1
Problem sets must be turned in class. Late problem sets are assessed a 10 percentage point
penalty per day.
Question 1 (20 pts)
Suppose that demand for a coffee is given by QD = 7500 − 3P, and the supply of coffee is given
by QS = −1500 + 12P.
a. Find the market equilibrium quantity and price. What is the consumer and producer sur-
plus?
b. Calculate the elasticities of supply and demand at the market equilibrium price.
c. Using the elasticities you found in part b, calculate how much gross prices paid for con-
sumers and after-tax prices received by firms will change if a tax of $60 is implemented on
consumers. (Hint: Use the tax incidence formula.)
d. Verify your calculations from part c using the supply and demand curves.
e. Calculate the consumer surplus, producer surplus, and total surplus after the tax. Show
that you can also calculate tax incidence using the changes in the consumer and producer
surplus.
f. What is the deadweight loss of the $60 tax?
g. (+3 UG Bonus) Return to a situation without tax. Now suppose that the government im-
poses a mandate forcing suppliers to use only premium organic coffee beans. This increases
the cost of making coffee by $60. However, consumers value organic coffee beans only $45.
Compute the deadweight loss with the mandate. How does it compare to the deadweight
loss found in part b?
Question 2 (10 pts)
(From Gruber, p. 84–85) State A introduced a tax cut in the year 2017. You are interested in
seeing whether this tax cut has led to increases in personal consumption within the state. You
observe the following information:
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Year Consumption in State A
2012 330
2014 350
2016 370
2018 430
A colleague argues that the best estimate of the effect of the tax cut is an increase in consump-
tion of 60 units, but you think that the true effect is smaller because consumption was trending
upward prior to the tax cut. You find information on a neighboring state (State B) that did not
change its tax policy during this time period. You observe the following information in that state:
Year Consumption in State B
2012 300
2014 320
2016 340
2018 350
Given this information, what is your best estimate of the effect of the tax cut on consumption?
What assumptions are required for you to interpret your estimates as causal?
Question 3 (10 pts)
Consider the following market. Demand is given by QD = 1600 − 3P where QD is the quantity
demand and P is the price. Supply is given by QS = 2P − 400 where QS is the quantity supplied.
a. What is the market equilibrium quantity and price?
b. Calculate consumer, producer, and total surplus. Depict your answer in a graph.
c. Suppose the government imposes a price floor of P = 500. Calculate the consumer surplus
and the producer surplus and deadweight loss. Depict your answer in a graph.
Question 4 (10 pts)
Listen to “Episode 453: What Causes What?” of NPR’s Planet Money podcast. (Link here.) Write
a short response (2-4 college-level sentences will do) to the following questions.
a. What were the results of the randomized controlled trial studying the causal relationship
between heart disease and estrogen replacement therapy? Why do you think researchers
initially find the opposite result in the statistical panel data (longitudinal) study?
b. Why might a statistical study find a positive correlation between the number of police and
the number of crimes? Describe the quasi-experiment that the researchers discussed in
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the podcast used to overcome any possible bias in their study of the relationship between
police and crime. What were their results?
c. Why is it hard for researchers to determine the value-added from going to a highly-selective
college versus going to a less selective college? Describe the treatment and control groups
used by researchers of this study (Dale and Kruger, 2002). Briefly describe their results.
d. Discuss the reasons why the treatment and control groups in Dale and Kruger (2002) may
not be directly comparable.
Question 5 (10 pts G, +10 UG pts)
Consider an new ad valorem tax (a tax t levied on the percentage of price paid) the government
imposes on the market to be paid by consumers. Now the price paid by the demand side of
the market is Pd = (1 + t)Ps where Ps is the price received by the supply side. The government
receives t · Ps. Using implicit differentiation, derive that the change in Ps after the tax is
dPs
dt = Ps · εD
εs − (1 + t)εD
.
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