Question 5
Demand in a market dominated by two firms (a Cournot duopoly) is determined according to: P = 200 – 2(Q1 + Q2), where P is the market price, Q1 is the quantity demanded by Firm 1, and Q2 is the quantity demanded by Firm 2. The marginal cost and average cost for each firm is constant; AC=MC = $60.
The cournot-duopoly equilibrium profit for each firm is _____.
Hint: Write your answer to two decimal places.
QUESTION 6
The following matrix shows the pricing strategies and resultant profits for two profit-maximizing firms. The profit's are written (Z,Y) where Z is the profit that Firm A (the firm that chooses which row) receives and Y is the profit Firm B (the firm that chooses the column) receives.
Strategies | High | Low |
High | X,X | 4,11.5 |
Low | 11.5,4 | 10,10 |
What is the lowest value of X such that High, High is a Nash Equilibrium in this scenario.
Hint: Write your answer to two decimal places.
Hint two: X=35 would make High, High a Nash Equilibrium since neither firm would benefit from deviating. However, I want to know the smallest value of X such that High, High is the Nash Equilibrium.
10 points
QUESTION 7
Demand in a market dominated by two firms (a Cournot duopoly) is determined according to: P = 200 – 2(Q1 + Q2), where P is the market price, Q1 is the quantity demanded by Firm 1, and Q2 is the quantity demanded by Firm 2. The marginal cost and average cost for each firm is constant; AC=MC = $64.
The cournot-duopoly equilibrium quantity produced by each firm is _____.
Hint: Write your answer to two decimal places.
Question 5:
Each firm maximizes profit according to the rule: MR = MC.
P = 200 - 2(Q1 + Q2) = 200 - 2Q1 - 2Q2
Firm 1: Total Revenue, TR1 = P*Q1 = (200 - 2Q1 - 2Q2)*Q1 = 200Q1 -
2Q12 - 2Q1Q2
Marginal Revenue, MR1 =
So, MR1 = MC gives,
200 - 4Q1 - 2Q2 = 60
So, 4Q1 = 200 - 60 - 2Q2 = 140 - 2Q2
So, Q1 = (140/4) - (2Q2/4)
So, Q1 = 35 - 0.5Q2
This is the best response function of firm 1, BR1.
As demand function and MC are same for both firms, so best response
function of firm 2 is:
Q2 = 35 - 0.5Q1
Now, substituting BR1 in BR2, we get,
Q2 = 35 - 0.5(35 - 0.5Q2) = 35 - 17.5 + 0.25Q2
So, Q2 - 0.25Q2 = 17.5
So, 0.75Q2 = 17.5
So, Q2 = 17.5/0.75 = 23.33
So, Q1 = 35 - 0.5Q2 = 35 - 0.5(23.33) = 35 - 11.67 = 23.33
So, P = 200 – 2(Q1 + Q2) = 200 – 2(23.33 +
23.33) = 200 - 93.32 = 106.68
So, equilibrium profit for each firm = Total revenue for each
firm - Total cost of each firm = P*Q1 - AC*Q1 = (P - AC)*Q1
= (106.68 - 60)*23.33 = $1,089.04
(Note: Post one question at a time.)
Question 5 Demand in a market dominated by two firms (a Cournot duopoly) is determined according...
Demand in a market dominated by two firms (a Cournot duopoly) is determined according to: P = 300 – 4(Q1 + Q2), where P is the market price, Q1 is the quantity demanded by Firm 1, and Q2 is the quantity demanded by Firm 2. The marginal cost and average cost for each firm is constant; AC=MC = $74. The cournot-duopoly equilibrium profit for each firm is
Demand in a market dominated by two firms (a Cournot duopoly) is determined according to: P = 200 – 2(Q1 + Q2), where P is the market price, Q1 is the quantity demanded by Firm 1, and Q2 is the quantity demanded by Firm 2. The marginal cost and average cost for each firm is constant; AC=MC = $75. The cournot-duopoly equilibrium quantity produced by each firm is _____. Hint: Write your answer to two decimal places.
In a market with a duopoly, if market demand is find the Cournot Reaction curves and the Cournot quantity solutions then deduce the price in the case where Marginal cost curves for either of the duopoly firms is and . Compare your results to the case where a Monopolist that has a replaces the duopoly. What are the monopoly quantity and price? Which quantities are bigger, Cournot or Monopoly? What is the consumer Surplus in both cases? Set up the...
Now consider a typical Cournot duopoly situation such that the market is being served by two firms (Firm 1 and Firm 2) that simultaneously decide on the level of output to sell in the market, while producing an identical product. The total output of the industry is Q = q1 + q2, where q1 and q2 are the output of Firm 1 and 2, respectively. Each firm has a symmetric cost function: C(q1) = 12 q1 and C(q2) = 12...
Two identical firms compete as a Cournot duopoly. The inverse market demand they face is P = 120-2Q. The total cost function for each firm is TC1(Q) = 4Q1. The total cost function for firm 2 is TC2(Q) = 2Q2. What is the output of each firm? Find: Q1 = ? Q2 = ?
Duopoly quantity-setting firms face the market demand p=210-Q. Each firm has a marginal cost of $15 per unit. What is the Cournot equilibrium? The Cournot Equilibrium quantities for Firm 1 (q1) and Firm 2 (q2) are: q1= __ units and q2 =__ units . (Enter numeric responses using real numbers rounded to two decimal places.) The Cournot equilibrium price is p=$__ (two decimal places)
2. (Cournot Model) Consider a Cournot duopoly. The market demand is p=160 - q2. Firm 1's marginal cost is 10, and firm 2's marginal cost is also 10. There are no fixed costs. A. Derive each firm's best response function B. What is the Nash equilibrium of this model? Find the equilibrium market price. C. Find the equilibrium profit for each firm D. Find the equilibrium consumer surplus in this market. 3. (Bertrand Model) Consider a Bertrand duopoly. The market...
can someone help me solve/explain step by step 3) Suppose that there are only two firms in the industry for printers, HP and Xerox, making the industry a Cournot duopoly. The demand for printers is given by the equation, P = 300-4Q1-402, where P is the market price, Q1 is the quantity demanded from HP, and Q2 is the quantity demanded from Xerox. The marginal cost for each firm is constant at $60. a) Derive the equation for HP's revenue....
1. Consider the following asymmetric version of the Cournot duopoly model. Two firms compete by simultaneously choosing the quantities (q, and q2) they produce. Their products are homogeneous, and market demand is given by p- 260-2Q, where Q-q +q2. Firm 1 has a cost advantage; Firm 1 produces at zero cost, while Firm 2 produces at a constant average cost of 40. (The difference in costs is what makes this an asymmetric game.) a. Derive both firms' profit functions, as...
Consider the Cournot duopoly model in which two firms, 1 and 2, simul- taneously choose the quantities they supply, q1 and q2. The price each will face is determined by the market demand function (q1, q2) = a − b(q1 + q2). Each firm has a probability μ of having a marginal unit cost of cL, and a probability 1 − μ of having a marginal unit cost of cH, cH > cL. These probabilities are common knowledge, but the...