Question

1. (Static Cournot Model) In Long Island there are two suppliers of distilled water, labeled firm...

1. (Static Cournot Model) In Long Island there are two suppliers of distilled water, labeled firm 1 and firm 2. Distilled water is considered to be a homogenous good. Let p denote the price per gallon, q1 quantity sold by firm 1, and q2 the quantity sold by firm 2. Firm 1 bears the production cost of c1 = 4, and firm 2 bears c2 = 2 per one gallon of water. Long Island’s inverse demand function for distilled water is given by P = 10 − 1/4Q where Q = q1 + q2 denotes the aggregate industry supply of distilled water in Long Island. Solve the following problems: (a) Suppose the firms compete in quantities (production levels). Compute each firm’s quantity best response function and conclude how much each firm produces in a Cournot-Nash equilibrium. (b) Compute the price and the profit of each firm in a Cournot-Nash equilibrium. 3 2. (Collusion) Now suppose firms face the same market demand as in Problem 1. But now there are three firms (firm 1, firm 2, and firm 3) where Q = q1 + q2 + q3. All of them bear the same production marginal cost of c1 = c2 = c3 = 4 per one gallon of water. Lastly, the game among these firms is repeated indefinitely in each period t = 1, 2, 3, ... . Let δ ∈ (0, 1) denote the firms’ common time discount factor. (a) Find the static (joint) monopolist’s quantity, price and profit when they collude. (b) Solve the static Cournot game. That is, find q1 * , q2 * , q3 * , p* , π1 * , π2 * , π3 * . (c) Now find the static profit of firm 1 when he solely deviates from collusion. 4 (d) Calculate the lifetime value of firm 1 when all of the firms maintain collusion forever (Vcol). Also find the lifetime value of firm 1 when he solely betrays at t = 1 and is detected by others at t = 2 (Vdev). (e) Compute the minimum threshold value of δ that would make collusion sustainable.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
(Static Cournot Model) In Long Island there are two suppliers of distilled water, labeled firm 1...
(Static Cournot Model) In Long Island there are two suppliers of distilled water, labeled firm 1 and firm 2. Distilled water is considered to be a homogenous good. Let p denote the price per gallon, q1 quantity sold by firm 1, and q2 the quantity sold by firm 2. Firm 1 bears the production cost of c1 = 4, and firm 2 bears c2 = 2 per one gallon of water. Long Island’s inverse demand function for distilled water is...
? = 10 − 1/4Q 4. (Collusion) Now suppose firms face the same market demand as...
? = 10 − 1/4Q 4. (Collusion) Now suppose firms face the same market demand as in Problem 3. But now there are three firms (firm 1, firm 2, and firm 3) where Q = q1 + q2 + q3. All of them bear the same production marginal cost of c1 = c2 = c3 = 4 per one gallon of water. Lastly, the game among these firms is repeated indefinitely in each period t = 1, 2, 3, ......
Q1. Consider a Cournot oligopoly in which the market demand curve is Q = 60 -...
Q1. Consider a Cournot oligopoly in which the market demand curve is Q = 60 - P. There are two firms in this market, so Q = q1 + q2. The firms in this market are not identical: Firm 1 faces cost function c1(q1) = 2q12, while firm 2's cost function is c2(q2) = 28q2. In the space below, write down a function for Firm 1's profit, in terms of q1 and q2. Q2. Refer back to the Cournot oligopoly...
Consider a duopoly with two firms with the cost functions: Firm 1: C1(q1)=5q1 Firm 2: C2(q2)=5q2...
Consider a duopoly with two firms with the cost functions: Firm 1: C1(q1)=5q1 Firm 2: C2(q2)=5q2 The firms compete in a market with inverse demand p = 300 - 8Q where Q=q1+q2. The firms compete in a Cournot fashion by choosing output simultaneously.   What is the Nash-Cournot equilibrium output of firm 1? Round to nearest .1
Consider a Cournot model with two firms, firm 1 and firm 2, producing quantities q1 and...
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)...
Consider an asymmetric Cournot duopoly game, where the two firms have different costs of production. Firm...
Consider an asymmetric Cournot duopoly game, where the two firms have different costs of production. Firm 1 selects quantity q1 and pays the production cost of 2q1 . Firm 2 selects quantity q2 and pays the production cost 4q2 . The market price is given by p = 12 − q1 − q2 . Thus, the payoff functions are u1 (q1,q2) = (12 − q1 − q2 ) q1 − 2q1 and u2 ( q1 , q2 ) = (12...
Consider a market with two identical firms. The market demand is P = 26 – 2Q,...
Consider a market with two identical firms. The market demand is P = 26 – 2Q, where Q = q1 + q2. MC1 = MC2 = 2. 1. Solve for output and price with collusion. 2. Solve for the Cournot-Nash equilibrium. 3. Now assume this market has a Stackelberg leader, Firm 1. Solve for the quantity, price, and profit for each firm. 4. Assume there is no product differentiation and the firms follow a Bertrand pricing model. Solve for the...
There is a Cournot game consisting of two different firms that produce the same goods. Quantity...
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...
There is Cournot competition between Joel (Firm 1) and Daniel (Firm 2). The inverse demand for...
There is Cournot competition between Joel (Firm 1) and Daniel (Firm 2). The inverse demand for their goods is: P(q1 +q2) = 30?2(q1 +q2), and the cost functions are: c1(q1) = 12q1, c2(q2) = 6q2. Revert to assuming that there is no capacity constraint. But now the gov- ernment imposes a price ceiling, p ? = 14, which is higher than marginal cost. As it is now illegal to sell for more than $14 per unit, the price will now...
There is a Cournot duopoly competition between Firm 1 and Firm 2. The inverse demand function...
There is a Cournot duopoly competition between Firm 1 and Firm 2. The inverse demand function is given by P(Q)=100-q, where Q=q1+q2 and qi denotes the quantity produced by firm i for all iÎ {1, 2} and the cost function is given by ci(qi)=10qi. Describe this problem as a normal-form game. Find pure-strategy Nash Equilibria for both firms.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT