1. (15 marks) Suppose in a duopoly market there are two firms, 1 and 2, each with a cost function given as TC₁ = 10Q₁ and TC₂ = 10Q₂.The inverse demand in the market is P = 100 - 2(Q₁ + Q₂).

The firms are homogeneous product duopoly.

1. Suppose the market is characterized by Cournot oligopoly. Calculate each firm's profit maximizing output, price, and profit. Be sure to show all steps needed for this question.
2. Now suppose the market is characterized by Stackelberg oligopoly. Calculate each firm's profit-maximizing output, price, and profit.
3. Now suppose each firm colludes in its price and output decision. Calculate each firm's profit maximizing output, price and profit.

1. (15 marks)
   1. Cournot

A. Give a real world example of a market that looks like each of the following oligopoly setting, and explain your reasoning. a.Stackelberg

1. Bertrand

B. Give 3 real world examples of group price discrimination and explain your reasoning.

1. (15 marks) A water supply company faces the following inverse demand function: P = 100 - 2Q. Its cost function is C = 100+2Q. Note P is the water rate per thousand litres of water and Q is the quantity measured in thousand liters of water.
   1. Calculate the firm's profit-maximizing output and price. What profit it will make? Will there be a deadweight loss to the society? How much?
   2. Suppose a government regulator regulates the price following the marginal cost pricing rule. What price and water consumption will result? How much profit the monopoly will now make? What cost will the regulator incur? What deadweight loss will result due to this regulation?
   3. Now suppose the regulator wants the monopoly to follow the average cost pricing rule. What price and quantity will result? What will be the deadweight loss?
2. (15 marks) Consider a monopolist whose total cost function is TC = Q³ - 30Q² + 301Q, whose inverse demand function is P = 1501 - 30Q where Q is output and P is price.
   1. If the firm were to act as a single price monopolist, how much will it produce? What price it will charge? How large will be its profit? Calculate the firm's Lerner Index of monopoly power.
   2. Now suppose this firm can practice perfect price discrimination. How much does it produce? If the firm produces Q = 25, what is the lowest price it charges for any unit and what are its profits?
3. (15 marks) Consider a firm whose total cost function is q³ - 6q² + 13q.
4. If the price of a unit of output is $13, what is the profit-maximizing value of q?
5. Find the average cost function of the firm? What is the firm's minimum average cost?
6. What is the equilibrium price of output? How much does each firm produce at equilibrium price? What is each firm's profit at the equilibrium price?

6.(15 marks) In 2003, Saudi Arabia and Venezuela produced an average of 8 million and 3 million barrels of oil a day, respectively. Production costs were about $10 a barrel and the price of oil averaged $28 per barrel. Each country had the capacity to produce an additional 1 million barrels per day. At that time, it was estimated that each country 1-million-barrel increase in supply would depress the average price of oil by $3. Copy the following Table on your answer sheet :

		Venezuela
Saudi Arabia	8 M barrels	3 M barrels	4 M barrels
____, ____	____, ____
9 M barrels	____, ____	____, ____

Answer the following questions:

1. Fill in the missing profit entries in the payoff Table.
2. What action should each country take and why?
3. Does the asymmetry in the countries' sizes cause them to take different attitudes towards expanding out? Explain why or why not.