ECON 311 Problem Set 4 - Suppose we have the following inverse

1.? Suppose we have the following inverse Demand and Supply function:
PD = 200 ? 2QD PS = 20 + QS (a) Graph the Supply and Demand curves, be sure to label all important points (b) What is the
Consumer Surplus =
Producer Surplus = 1 ? Now suppose the government imposes a $15 Excise tax on the consumer.
(c) Graph the Shadow Demand curve on the same graph as part (a). Be sure to label all
important points. (d) What is the
Tax Revenue =
Deadweight loss =
New Consumer Surplus =
New Producer Surplus =
(e) What percentage of the Tax Revenue is “paid” by the consumer in the form of lost
Consumer Surplus? What about the Producer?
Percentage of Consumer Surplus =
Percentage of Producer Surplus = 2.? Suppose we have a monopolist that faces an inverse demand function and total cost
function of
PD = 100 ? 2QD
C(QS ) = Q2S + 8QS + 50
Note that the last part of this question asks you to graph much of your answers to the first
parts of this question.
(a) Find the profit maximizing level of output (Q) and the corresponding price charged (P ). 2 (b) Find the Socially optimal level of output and price. (hint: this is the case when we
assume perfect competition) (c) Graph the Demand, Marginal Revenue, and Marginal Cost curves. Find the Deadweight
Loss, loss to Consumer Surplus and gain to Producer Surplus due to monopolistic power.
DWL =
Loss to CS =
Gain to PS = 3 3.? Explain why in the long run, perfectly competitive firms will make no profit. What is
the long run equilibrium condition for a firm? (Hint: Do this both by first assuming that
some firm are making positive profits and then by assuming some firms are making negative
profits...some graphs may be helpful). 4 4.? Give an intuitive explanation of the following terms:
• Marginal Product of Labor: • Marginal Product of Capital: • Technical Rate of Substitution: • The slope of an Isocost line: • Marginal Cost: • Marginal Revenue: 5 

5.? The Corleone and Chung families are the only providers of good h in the United States.
The market demand for good h is h = 1, 200 ? 20p. The costs of production for each of
them are represented by the cost functions C1 (h1 ) = 10h1 and C2 (h2 ) = 20h2 , respectively.
Suppose both families must choose their output level simultaneously.
(a) Derive their reaction functions. (b) Calculate the Cournot equilibrium in this market. Indicate output levels, market price,
and individual profits. (c) Now suppose the Chung family can choose their output first (before the Corleone family).
Find the new equilibrium output levels, prices, and individual profits. 6 Do the rest, but do not hand in.

6. Suppose that all consumers view red pencils and blue pencils as perfect substitutes. Suppose that the supply curve for red pencils is upward sloping. Let the price of red pencils
and blue pencils be pr and pb . What would happen if the government put a tax only on red
pencils? 

7. The United States imports about half of its petroleum needs. Suppose that the rest of
the oil producers are willing to supply as much oil as the United States wants at a constant
price of $25 a barrel. What would happen to the price of domestic oil if a tax of $5 a barrel
were placed on foreign oil? 

8. Explain why price elasticity of demand and/or supply is important in tax policy. 

9. The government is considering subsidizing the marginal costs of a monopolist. What level
of subsidy should the government choose if it wants the monopolist to produce the socially
optimal amount of output? (I’m not asking for an actual number here and it may be helpful
to graph this out) 7