Question

Consider two firms are performing Cournot price competition in
two differentiated goods markets. Firm 1 produces goods 1, and firm
2 produces goods 2, and two market demand functions are given by
q1(p1,p2) = 12 - 2p1 +p2 and q2(p1,p2) =
15q_{2}^{2} + 45Q . Furthermore, assume that the
two firms have the same cost function such that fixed cost is $20
and variable cost is zero.

(10pts) Calculate the equilibrium prices, quantities and profits for both firms.

(10pts) Assume the two firms collude and form a cartel. That is, they maximize their total profits by setting prices. What will be the new equilibrium prices, quantities, and profits?

(5pts) Assume two firms agree to set prices at the collusion equilibrium level given in (b), but one of the firm unilaterally deviates its price to the Cournot equilibrium level given in (a), what will be the quantities and profits for both firms in this case? Is this deviation profitable for this firm?

(5pts) Based on the information given in (a),(b),(c), draw out the payoff matrix for two firms which have two potential strategies: Collude or Deviate. Explain why this game is a prisoner dillema. (Hint: the strategy is what price the firm chooses; the payoff is the corresponding profit)

Answer #1

11. Suppose two firms (1 and 2) sell differentiated products and
compete by setting prices. The demand functions are q1 = 7 − P1 +
(P2/2) and q2 = 7 − P2 + (P1/2).
Firms have a zero cost of production.
(a) Find the Nash equilibrium in the simultaneous-move game.
Also find the quantities sold by each firm. [5 marks]
(b) Find the subgame-perfect equilibrium if 1 moves before 2.
Also find the quantities sold by each firm. [5 marks]...

2. Question 2
Consider two firms (A and B) engaging in Cournot Competition.
Both firms face an inverse market demand curve P(Q)=700-5Q, where
Q=qA+qB. The marginal revenue curve for firm A is MRA=700-10qA-5qB
and the marginal revenue curve for firm B is MRB=700-10qB-5qA. The
firms have identical cost functions, with constant marginal cost
MC=20.
A) Determine the profit function for firm A and firm B.
B) Solve for the best-response functions of both firms.
C) Determine the equilibrium quantities both...

Consider the following market: Two firms compete in quantities,
i.e., they are Cournot competitors. The firms produce at constant
marginal costs equal to 20. The inverse demand curve in the market
is given by P(q) = 260 − q.
a. Find the equilibrium quantities under Cournot competition as
well as the quantity that a monopolist would produce. Calculate the
equilibrium profits in Cournot duopoly and the monopoly
profits.
Suppose that the firms compete in this market for an infinite
number...

Suppose that 2 firms
are competing against each other in Cournot (output) competition
and that the market demand curve is given by P = 60 – Q or Q = 60 –
P. In addition, assume the marginal cost for each firm is equal to
0 as we did in class.
a. Solve for firm 1’s
total revenue. Note that this should not require any calculus.
b. If you take the
derivative of firm 1’s total revenue, you should find...

There is a Cournot game consisting of two different firms that
produce the same goods.
Quantity produced by firm one = q
Quantity produced by firm two = q2
The marginal cost for firm one equals average cost, which is
3.
The marginal cost for firm two equals average cost, which is
4.
The formula for the inverse demand curve of the market is P = 70
- (q1 +q2).
Answer the following questions with work:
1. What is the...

Consider two firms, Firm A and Firm B, who compete as
duopolists. Each firm produces an identical product. The total
inverse demand curve for the industry is ? = 250 − (?? + ?? ). Firm
A has a total cost curve ?? (?? ) = 100 + ?? 2 . Firm B has a total
cost curve ?? (?? ) = 100 + 2??.
a. Suppose for now, only Firm A exists (?? = 0). What is the
Monopoly...

Consider a Cournot model with two firms, firm 1 and firm 2,
producing quantities q1 and q2, respectively. Suppose the inverse
market demand function is: P = 450 – Q where Q denotes the total
quantity supplied on the market. Also, each firm i = 1,2 has a
total cost function c(qi) = 30qi. a) What is the Nash equilibrium
of this Cournot game ? What is the market prices ? Compute each
firm’s profit and the industry profit. b)...

Cournot Competition The market demand for a good is represented
by P = 400 ? 20Q. Firms are symmetric with cost functions C = 30q.
Assume the firms compete in a Cournot Oligopoly (i.e., simultaneous
choices of quantity). (d) Compute prices quantities, and consumer
surplus under perfect competition in which each firm in the market
takes price as a given. (e) Now, think of a case where there are N
firms. What are equilibrium prices and quantities, and how do...

Two firms compete by choosing price. Their demand functions are
Q1 = 20 - P1 + P2 and Q2 = 20 +P1 -P2 where P1 and P2 are the
prices charged by each firm, respectively, and Q1 and Q2 are the
resulting demands. Note that the demand for each good depends only
on the difference in prices; if the two firms colluded and set the
same price, they could make that price as high as they wanted, and
earn infinite...

The market demand function is Q=10,000-1,000p.
Each firm has a marginal cost of m=$0.16. Firm 1, the leader,
acts before Firm 2, the follower. Solve for the Stackelberg-Nash
equilibrium quantities, prices, and profits. Compare your solution
to the Cournot-Nash equilibrium.
The Stackelberg-Nash equilibrium quantities are:
q1=___________ units
and q2=____________units
The Stackelberg-Nash equilibrium price is:
p=$_____________
Profits for the firms are
profit1=$_______________
and profit2=$_______________
The Cournot-Nash equilibrium quantities are:
q1=______________units
and q2=______________units
The Cournot-Nash equilibrium price is:
p=$______________
Profits for the...

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