Question: All solutions must be written out.
Please answer all questions.
Q1. Shell and Mobile, in the wake of the recent turbulence in gasoline prices, have to come up with new pricing strategies in order to stay competitive. For simplicity, let's assume that both firms can choose between setting the price at $3/gallon OR $2/gallon. They set their prices at the same time. Because most Shell and Mobile stations, for some reason, are always next to one another, whoever sets the lower price will get ALL the customers. If they set the same price the split the customers in half. Suppose the market demand for a small town, Economiville is given by
P = 6 - 2Q
Where Q is measured by millions of gallons, and consumers in Economiville only have access to Shell or Mobile. Shell and Mobile have no costs of producing the gas (assume they have a prior contract with OPEC (organization of petroleum exporting countries) and have already paid for the gas in stock). This allows us to consider them maximizing their revenue.
a. If Shell charges $3, and Mobile charges $2, what are the revenues for the two firms? (Hint: remember that since Shell is cheaper, consumers will buy gas from Mobile only at $2/gallon.)
b. If Shell charges $3 and Mobile charges $3, what are the revenues?
c. What about if Shell charges $2, Mobile charges $2?
d. Finally, what about Shell charges $2, Mobiles charges $3?
e. In light of your answers in (a)-(d), what is the Nash equilibrium of this price setting game between Shell and Mobile?
f. Briefly discuss how this example compares with the idea in Prisoner's Dilemma we talked about in class. Is the Nash equilibrium the best outcome for the firms, in terms of revenues earned at the Nash equilibrium?
g. Is this oligopolistic competition good for consumers?
Q2. Assume that two stores occupy the Huntington Mall! These stores are facing a decision of whether or not to hire a security guard for the mall. The benefit, in the form of reduced theft, to each store of hiring the guard is 8. The cost of hiring a guard is $10. If either store hires a guard for the mall the other store will benefit just as much as if it had hired the guard (i.e. the guard is non-rival and non-excludable). Additionally, we will assume the one guard is just as good as two guards, thus, if both stores agree to hire a guard they will split the cost of one guard.
The following payoff matrix reflects the payoffs of firms engaged in the game where the stores simultaneously select whether to hire.
|
|
Store #2 |
|
| Store #2 |
|
Hire |
Don't Hire |
|
Hire |
3, 3 |
2, 8 |
|
Don't Hire |
8, -2 |
0, 0 |
a. Is it socially optimal for the stores to hire the guard? Why or why not?
b. What is the Nash Equilibrium of the game? Is the solution a result of free riding?
Explain (Free riding is the benefit one gets from a good or service without paying for it)
c. Now, solve the stores security guard problem (i.e. define a scheme you think would get them to the social optimum).
Q3. A large share of the world supply of diamonds comes from Russia and South Africa. Suppose that the marginal cost of mining diamonds is constant at $1,000 per diamond, and the demand for diamond is described by the following schedule.
| Price |
Quantity |
| 8,000 |
5,000 |
| 7,000 |
6,000 |
| 6,000 |
7,000 |
| 5,000 |
8,000 |
| 4,000 |
9,000 |
| 3,000 |
10,000 |
| 2,000 |
11,000 |
| 1,000 |
12,000 |
(a) If the market for diamonds was perfectly competitive, what would the price and quantity be?
(b) If there were only one supplier of diamonds, what would the price and quantity be?
(c) If Russia and South Africa formed a cartel (or a collusive oligopoly), what would be the price and quantity?
(d) If the countries split the market evenly, what would be South Africa's production and profit?
(e) What would happen to South Africa's profit if it increased its production by 1,000 while Russia stuck to the cartel agreement?
(f) Use your answer to part (e) to explain why cartel agreements are often not successful
Q4. Consider a market where demand is P = 10 - 2Q and supply is P = Q/2. There is a consumption positive externality of $2.50/unit of consumption.
a. Calculate the market equilibrium.
b. What is the social optimum quantity and price?
c. If the government uses a tax to get producers to internalize their externality, what is the net price received by producers?
d. Calculate the total surplus in the market equilibrium, at the social optimum and with the tax.
e. How can government increase the total surplus?
f. Impose the program you indicated in part e and calculate the total surplus.
Q5. Consider a market where demand is P = 10 - 2Q. There is a negative production externality of $2.50/unit of consumption. Supply is equal to P = Q/2
a. What is the market equilibrium?
b. What is the social optimum quantity and price?
c. If the government uses a tax to get producers to internalize the externality what is the net price received by producers?
d. Calculate the total surplus at the market equilibrium.
e. Calculate the total surplus at the Social optimum and with the tax.
Q6. A monopolist in the sugar market faces a demand curve given by Qd = 60 - 2P and has total costs equal to TC = 50 + 2Q2. Quantity is measured in millions of tons and you may assume that units are infinitely divisible.
a. Find the optimal price and quantity for the monopolist.
b. Draw a diagram and carefully label the relevant parts to support your answer to part a.
c. Calculate the consumer surplus and indicate the region representing it in your graph.
d. Calculate the producer surplus and indicate the region representing it in your graph.
Q7. Now, assume that this market becomes perfectly competitive. The production process for the good does not change. So, all firms have the same cost curves as the monopolist.
a. Find the long run equilibrium price and quantity in the competitive market.
b. How many firms are there in the long run equilibrium?
c. What is the consumer and produce surplus in the competitive setting?
Q8. The demand for a new prescription drug is given as Qd = 100 - P, while supply is given by Qs = 3P.
a. What is the equilibrium price and quantity?
b. The U.S. Government, in order to increase access to the drug imposes a price ceiling (the maximum price one can charge) of $20. Is there a shortage or surplus?
c. How big?
d. Suppose the pharmaceutical company refuses to go along with the plan unless the government compensates them. A new member of congress suggests the government pays the manufacturer a subsidy of $5 for each unit sold at $20. Under this plan how much would the government pay?
e. How would the subsidy affect the number of prescriptions filled?
f. Is there a shortage?
Q9. Consider the market for education. The marginal social cost of education (MSC) and the marginal private benefit of education (MPB) are given by the following equations where Q is the number of units of education provided per year.
MSC = 10 + Q MPB = 100 - Q
You are also told that each unit of education provides an external benefit to society of $10 per unit. This external benefit is currently not being internalized in the market.
a) Given the MSC and MPB curves, what is the current number of education units being produced by the market?
b) Is the current level of market production for education the socially optimal amount of education? Explain your answer.
c) What is the value of consumer surplus (CS),
What is the value the value of producer surplus (PS), and the value of the external benefits of the current level of production.
Sum together (CS + PS + external benefits). Draw a diagram illustrating each of these concepts in the market for education.
d) Given the market level of production, what is the deadweight loss in this market?
e) Now suppose that the external benefit is internalized in this market when the government provides a subsidy of $10 per educational unit to consumers. What will be the socially optimal amount of education to provide given this subsidy?
f) Given the subsidy in (e), calculate the value of consumer surplus with the subsidy (CS'), Calculate the producer surplus with the subsidy (PS').
g) With the subsidy, there are no longer any external benefits that the market fails to account for. Sum together CS' + PS' does this total equal the sum of (CS + PS + external benefits) + DWL from parts (c) and (d)?