21 May ARE COKE AND PEPSI SUBSTITUTES OR COMPLEMENTS?
EconS 301, Dr. Rosenman, Spring 2016. HW 2
1. The New York City Transit system runs both buses and subways. Buses are slow, inefficient
and crowded. Subways are more efficient, fast and underutilized. Suppose the cost for each
is $1.00, and currently the Buses carry 100,000 passengers per day, with subways carrying
200,000 passengers per day. Current revenues are $300,000. The transit authority wants to
cut the number of bus passengers by 10% (that is, by 10,000). Suppose the price elasticity
of demand for buses is 0.9 and the cross price elasticity of demand for subways with respect
to the price of bus is 0.6.
a) By how much must the transit authority raise or lower the price of a bus trip to achieve
its goal?
b) What will happen to the total number of subway riders if the price of a bus trip is raised
as you suggest in part a)?
c) Will total transit revenues go up or down? Explain.
2. Below are the estimated elasticities of Coke and Pepsi.
Price Elasticity of Demand
Income Elasticity
Cross-price elasticity
Coke
-1.74
0.58
0.52
Pepsi
-1.55
1.38
0.64
a) Are the demands for Coke and Pepsi elastic or inelastic? Explain what being elastic or
inelastic means.
b) Does it make economic sense the price elasticity of demand for Coke and Pepsi differ?
Explain why this might be the case?
c) Are Coke and Pepsi normal goods? What does that mean?
d) Are Coke and Pepsi substitutes or complements? How do you know?
e) Does it make sense that the cross price elasticities of demand are different? Why or why
not?
3. To protect the US steel industry, in November 2015 the US Department of Commerce
imposed import duties (tariffs) on Chinese Steel. You can read about it at
http://www.wsj.com/articles/u-s-steel-projects-worse-than-expected-shipments-in-20151446589798.
a)
b)
c)
d)
Using a two-sector graph, explain how this move helps US steel producers?
Does it help US steel consumers? Explain
What is the impact on Chinese steel producers? Explain.
If instead the US imposed import quotas on Chinese steel (to the same quantity
restriction) how would it change the impact on US steel producers, US steel consumers,
and Chinese steel producers?
4. The tax on Gasoline is cut from 50 cents per gallon to 30 cents per gallon. What will happen
to consumer and producer surplus? What will happen to deadweight loss?
Mathematical question
5. Suppose you have the following demand and supply schedules:
Qd = 90 – 5P 2Y and Qs= 10 6P where Qd and Qs are quantity demanded and supplied, respectively, P is
the price of the good, and Y is the average income in the area (in 10,000).
a) Suppose Y = 3.5. Find the equilibrium quantity and price.
b) Find the amount of consumer surplus and producer surplus.
c) Suppose the consumers must pay a 5 cents per unit tax. Explain what happens to the demand curve.
d) Find the new equilibrium price and quantity after the tax.
e) How much tax revenue will be collected? What happens to consumer and producer surpluses?
f) Now the government decides to eliminate the unit tax on this good, and instead imposes a 0.1 income
tax. How will this change the equilibrium price and quantity?
g) How does the income tax affect consumer and producer surplus compared to the unit tax?
h) Find the income elasticity of demand when there is no tax. Then find the income elasticity of demand
when there is per unit tax. Finally, find the income elasticity of demand when there is an income tax. Do they
differ? Why or why not?
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