Assignment:
1. The demand curve for a certain chemical is given by Qd = 120 - 2P, where Qd is quantity demanded (measured in tons) per week and P is the price per ton of that chemical. The supply curve for that chemical that reflects the private MC of the firms in that industry is Qsp = 20 + 3P, where Qsp is quantity supplied (measured in tons) per week. However, a certain pollutant is generated in producing this chemical. When one takes into consideration the social MC of the firms in that industry, the supply curve for this chemical is given by Qss = -30 + 3P, where Qss is quantity supplied (measured in tons) per week.
a. Construct a table with four columns, P, Qd, Qsp, and Qss. Start the P-column at 10 but then raise it to 50 at increments of 5. Then figure out the Q's that correspond to each price-level.
b. In a market situation where there is no government intervention and the firms only consider their private marginal costs, what is the equilibrium price and quantity from the table?
c. Were the firms to act socially responsibly and consider the social marginal costs, what is the equilibrium price and quantity from the table?
d. Making use of the algebraic expressions that are given, solve for the equilibrium price and quantities in the two scenarios in 1.b and 1.c respectively.
e. Sketch the results in one large diagram, with all relevant curves clearly labeled.
f. Sketch and calculate the Dead Weight Loss when the firm produces at the output level when it only considers its private marginal cost.
g. How do the equilibrium prices and equilibrium quantities in the two scenarios compare with each other? Is there overproduction or underproduction from society's stand point?
2. Suppose that Cindy-Loo-Sue and Joe-Who are the only residents of the city of Whoville. They need to determine the number of fire fighters Whoville should have. Fire workers satisfy the characteristics of a pure public good. The marginal benefit that each person receives (in dollar terms) is given by the following table.
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Marginal benefit for Cindy-Loo-Sue
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Marginal benefit for Joe-Who
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Marginal Benefit to both
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# of Fire Fighters
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Marginal Cost of Fire Fighters
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16
|
9
|
|
1
|
|
|
12
|
8
|
|
2
|
|
|
8
|
5
|
|
3
|
|
|
7
|
2
|
|
4
|
|
(a) If each fire fighter cost $10 to hire and If Cindy-Loo-Sue and Joe-Who individually decide to provide fire fighters, how many will be hired? Will there be any "free riders?" Who will pay for the fire fighters?
(b) Fill in the column labeled "marginal benefit to both." What is the socially optimal number of fire fighters to hire in Whoville?
(c) Explain why the private market has a hard time providing the optimal number of firefighters from society's standpoint in Whoville.