Question

This problem set is partitioned into four sections. Section I examines price discrimination in the airline industry. Section II uses game theory to analyze output behavior of rivals. Section III uses game theory to examine output behavior of rivals for a multi-period game.

Section I: Monopoly pricing

4. Firm X has a complete monopoly over the production of nutmeg. The following information is given:

Marginal revenue = 1500 -20Q

Marginal cost = 300 +10Q

Where Q equals the output of nutmeg per unit of time. How much nutmeg would be sold and at what price if

1. the firm sets price as a monopoly?
2. What is the firm’s profits at the monopoly price determine in part a?
3. Now suppose the industry (firm) behaves perfectly competitively, how much nutmeg would be sold and at what price?
4. What is the firm’s profits at the monopoly price and at the competitive price?

Please show all your work to receive full credit

Section II: Game theoretic approach toward analyzing output behavior of rivals

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 presented below.

P = 100 - Q                                         (Market demand), where Q = q_x + q_y

C(q_x) =C(q_y) = 50q_j                            (Firm X and Y’s total cost curves), where j=x or y.

and MC(q_x) =MC(q_y) = 50                 (Firm X and Y’s marginal cost curves)

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 are the four possible output combinations available in this game?

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

e.) Use these profit outcomes to construct a 2x2 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 an example of the prisoners’ dilemma? Explain.

Answer 1

Answering only first section