# Microeconomics, Monopoly Pricing, Game Theory

**Section I: Monopoly pricing (50 points)**

Milwaukee Utilities has a complete monopoly over the generation and transmission of energy. The following information on this company is given as follows:

Demand = 750 – 10Q

Average cost = 500 – 2Q

Where Q is measured in megawatts and prices and costs are measured in dollars.

a.) Does this firm’s production process satisfy the condition for a natural monopoly? When explaining your answer assume two hypothetical smaller firms q1 and q2 generate 5 and 10 megawatts of energy, respectively. (Hint, Milwaukee Utilities is a monopolist so it generates the sum of the energy generated by the two smaller firms. Hence, the smaller firms’ output is a subset of Milwaukee Utilities’ output.) (Hint, the term’production process’ used in question Ia, is interpreted as ‘cost characteristics’, i.e, do the cost characteristics satisfy the condition for a natural monopoly)

b.) How much energy would be sold and at what price if the monopolist sets price as a profit maximizing monopolist? Note: The marginal cost curve is twice as steep as the average cost curve.

c.) What is the firm’s profits at the monopoly price determined in part b?

d.) Now, suppose the monopolist adopts a two-part tariff pricing scheme for its customers such that the access fee is equal to the profit-maximizing marginal cost and the user fee is the difference between the profit maximizing monopoly price and marginal cost. Please calculate the user and access fees based on this information.

e.) Now suppose the monopolist practices 3rd degree price discrimination and charges the profit-maximizing price to the high reservation price customers and charges a 10 percent discount on the monopoly price to low reservation price customers. Note, low reservation price customers are those who would never pay the monopoly price. What is the price charged to the low reservation price customers? What is the profit generated by charging these prices? Are the profits greater than the profits in part ‘c’? Please explain.

f.) Now suppose the state public utility commission requires this monopolist to charge the competitive price, how much energy would be sold and at what price? What are the monopolist’s profits?

g.) Based on the profits obtained when forcing this monopolist to charge a competitive price, the regulator now requires this monopoly to set price equal to average cost (this is called second-best pricing). What is the monopolist’s profits when charging second-best prices?

**Please show all work to receive full credit.**

**Section II: Game theoretic approach toward analyzing output behavior of rivals (50 points)**

Firms X and Y are duopolists facing the same two strategy choices. They can either tacitly collude or they can compete in a Cournot fashion. The market demand for their product, as well as their respective cost curves are as follows:

C(qx) = C(qy) =25qi (firm X and Y’s total cost curves), where i=x or y

MC(qy) =MC(qy) = 25 (firm X and Y’s marginal cost curves)

P=50-Q, (market demand), where Q = qx + qy .

C(q) and have the same cost structure: marginal cost and average cost both=25

a.) Calculate the respective output levels of each firm if they collude to set monopoly prices.

b.) Calculate the respective output levels of each firm if they adhere to the Cournot model.

c.) What four possible output combinations are available in this game?

d.) Derive the for possible profit outcomes for each firm that arise from producing the four possible output combinations available in this game.

e.) Use these profit outcomes to construct a 2×2 normal representative matrix for this game.

f.) Does either firm have a dominant strategy? If so, what is it?

g.) Is there a Nash equilibrium for this game? If so, what is it?

h.) Is the outcome of this game a prisoner’s dilemma? Please Explain?

**Please show all work to receive full credit.**