4. Consider a Cournot Oligopoly with two firms, where firm 1 is twice as efficient as firm 2. In particular, firm l's cost function is c1(q1) = q1, while firm 2's cost function is c2(q2) = 2q2. The inverse market demand function is given by P= 100 – 5(q1+q2). (a) Find the firms' reaction (best response) functions. (b) Find the firms' equilibrium output levels and their profits. Does firm 1 make twice the profit of firm 2?

4. Consider a Cournot Oligopoly with two firms, where firm 1 is twice as efficient as firm 2. In particular, firm l's cost function is c1(q1) = q1, while firm 2's cost function is c2(q2) = 2q2. The inverse market demand function is given by P= 100 – 5(q1+q2). (a) Find the firms' reaction (best response) functions. (b) Find the firms' equilibrium output levels and their profits. Does firm 1 make twice the profit of firm 2?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.3P

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Consider a Cournot oligopoly with n = 2 firms. Firm 1 cost function is TC₁ (9₁) = 20 + 12q₁ + q², while firm 2 cost function is TC₂ (9₂) = 50 +8q2 + q2 . The total market demand is P(Q) = 50 — 2Q, where Q is the total quantity produced by all (active) firms in the industry. a- Compute the Cournot equilibrium total quantity, price, quantity for each firm, and profit for each firm. Which firm is making higher profits? b- Consider the situation in which a third firm (firm 3) enters the market. What is the total equilibrium quantity, price, quantity and profit for each firm if TC3 = TC₁? [hint: q₁ and q3 will be the same, since 1 and 3 are identical] c- How would your answer at point b change if instead TC3 = TC₂? Would consumers prefer firm 3 to enter with the total cost of firm 1 or firm 2? d- What would be the highest one-time cost that firm 3 would be willing to pay to enter the market and then compete in a Cournot game with total cost equal to firm 1?
1. Best responses in a Cournot Oligopoly Firm A and Firm B sell identical goods Total market demand for the good is: The inverse demand function is therefore 1 P(QM) = 780 -Q=780 -0.02222QM 45 QM is total market production (i.e., combined production of firm's A and B. That is: Q(P) = 35, 100- 45P 2M = A +QB As a result, the inverse demand curve for each firm is: P(QA, QB) = 780- -1/32₁-752 45 Unlike the example in class, the two firms have different costs. = 4000A TCA (QA) TCB (QB) = 260QB = 780 -0.022220A -0.02222QB a. Using the demand function and the cost functions above, what is firm A's profit function. b. Using the profit function above and assuming that firm B produces Qg, calculate what firm A's best response is to firm B’s decision to produce QB- Note: Firm A's best response should be a function of B
1 Consider a duopoly with firm 1 and firm 2. Their cost functions are 2q₁ and cq2, respectively, where 2 < c < 10. The market demand function is p=10-Q, where Q=q₁+9₂. (a) Assume that the two firms play the Bertrand price game. Find the firms' price choices in the Bertrand equilibrium. (b) Assume that the two firms play the Cournot quantity game. Find the firms' quantity choices in the Cournot equilibrium.
There are two firms that are producing identical goods in a market characterized by the inverse demand curve P = 60 - 2Q, where Q is the sum of Firm 1's and Firm 2's output, q₁+q2. Each firm's marginal cost is constant at 12, and fixed cost are 0. Answer the following question, assuming that the firms are Cournot competitors. a. Calculate each firm's reaction function and illustrate them graphically (15 points) b. How much output does each firm produce? (12.5 points) c. What is the market price? (7.5 points) d. How much profit does each firm earn? What is the industry profit? (10 points)
2. An industry contains two firms that have identical cost functions C(q)=10+2q. The inverse demand function for the market is P=50-2Q where Q is the total industry output. Assuming the firms compete in quantities: Find the firms' best response functions. b. Solve for the Cournot Nash Equilibrium of the game. What is the total industry output in equilibrium? What is the equilibrium price? с. i. If both firms could collude, what would the industry output and price be? Suppose they decide that each firm produces half of the industry output found in part (i). Is this agreement self-enforcing? Explain. ii. a.
= Consider two firms, firm 1 and firm 2, facing the demand curve P = 24 - 2Q, where Q = Q₁ + Q₂. The firms' cost functions are C₁(Q₁) = Q² and C₂(Q₂) = 2Q². Derive the reaction functions if the firms behave non-cooperatively. a. b. C. d. e. What is each firm's Cournot-Nash-Equilibrium output and profit if they behave non-cooperatively? Draw the firms' reaction functions and show the equilibrium. Suppose that both firms have entered the industry as a cartel. What is the joint profit-maximising level of output? How much will each firm produce? How much is the profit of each firm? Compare and explain graphically each firm's Cournot-Nash-Equilibrium output with their new output where firm 2 chooses its output first. Put firm 1's output on the horizontal axis and firm 2's on the vertical axis. (Note: No calculation is required.)
c and d
1. Two firms (A and B) play a competition game (i.e. Cournot) in which they can choose any Qi from 0 to ¥. The firms have the same cost functions C(Qi) = 10Qi + 0.5Qi2, and thus MCi = 10 + Qi. They face a market demand curve of P = 220 – (QA + QB). Now assume firm A chooses quantity first. Firm B observes this choice and then chooses its own quantity. d)Firm A has MRA = 150 – 4QA/3. What are the equilibrium QA and QB selected in this game? e)What is the equilibrium price, and how much profit does each firm collect?
1. In class, we showed that in a Cournot duopoly with demand p: ab(91 +92) and marginal costs of c₁ for firm 1 and c2 for firm two, the firms' best response functions were as follows: a C1 92 2b 91 a-c2 92 - 2b 91 822 and (a) Find equilibrium expressions for q₁ and q in terms of a, b, C1, and C2 only. (b) Show that the equilibrium price will be p": = a + c1 + €2 3
a and b
What is the homogeneous-good duopoly Cournot equilibrium if the market demand function is Q= 1,800 - 1,000p. and each firm's marginal cost is $0.28 per unit? The Cournot-Nash equilibrium occurs where q, equals and 92 equals (Enter numenic responses using real numbers rounded to two decimai places.) Furthermore, the equilibrium occurs at a price of $ (Round your answer to the nearest penny.)