2. Consider a standard Cournot triopoly model, i.e., inverse demand p(Q) = a - bQ, where Q = -1 9₁ and a, b>0, output cost function ci(qi) = cqi for i = 1, 2, 3, c> 0. qi (a) Find the symmetric equilibrium output (q*), price (p*), and profit levels (*). (b) Suppose that firms 1 and 3 merge horizontally, i.e., form a single larger firm, call it firm 1, and compete against firm 2 as in a Cournot duopoly. The newly formed firm 1 and firm 2 have identical cost functions, which are the ci(qi) discussed above, and face the same inverse market demand p(Q). Assume that firm 1 and firm 3 split equilibrium profits. Find for i = 1, 2, 3 and compare with part (a). Are firm 1 and firm 3 better-off after the merge?

2. Consider a standard Cournot triopoly model, i.e., inverse demand p(Q) = a - bQ, where Q = -1 9₁ and a, b>0, output cost function ci(qi) = cqi for i = 1, 2, 3, c> 0. qi (a) Find the symmetric equilibrium output (q), price (p), and profit levels (*). (b) Suppose that firms 1 and 3 merge horizontally, i.e., form a single larger firm, call it firm 1, and compete against firm 2 as in a Cournot duopoly. The newly formed firm 1 and firm 2 have identical cost functions, which are the ci(qi) discussed above, and face the same inverse market demand p(Q). Assume that firm 1 and firm 3 split equilibrium profits. Find for i = 1, 2, 3 and compare with part (a). Are firm 1 and firm 3 better-off after the merge?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Suppose the inverse market demand for manufactures is P(Q) = A – Q, where P and Q denote price and total goods produced and the parameter A denotes the size of the domestic market. Suppose any firm has a cost function, c(q) = cq, where A > c. Suppose there are two firm in the market which produce q1 and q2, where Q = q1 + q 2 a. Solve for the Cournot equilibrium levels of output (Q*), price (P*) and markups. b. What is the impact of an increase in market size, A, on Q*, P* and markups when there are two firms? Provide some intuition for these predictions. c.…
Consider the Bertrand model and answer the question below related to the content. Assume that each firm in the Bertrand Duopoly model can only choose non-negative integer quantities: 0, 1, 2, ... . Assume the demand is Q(P)=10-P and the marginal cost is 0 for each firm. Given this information, which of the following is FALSE? [Hint: Check values of profit functions.] A. If firm 2 sets price equal to 1, then the best response of firm 1 to this price is 1 B. If firm 2 sets price equal to 4, then the best response of firm 1 to this price is 4 C. If firm 2 sets price equal to 2, then the best response of firm 1 to this price is 1
Consider a Cournot Duopoly model. The inverse demand for their products is given byP = 200 − 6Q, where Q is the total quantity supplied in the market (that is, Q = Q1 + Q2). Each firm has an identical cost function, given byT Ci = 2Qi, for i = 1, 2.(a) In the Cournot model, what does each firm choose?(b) What is the timing of each firm’s decision?(c) Find the Nash equilibrium quantities (Q∗1, Q∗2)?(d) What is the equilibrium price? Just help with c and d here please
Answering all questions compulsory....
A duopoly faces an inverse market demand of P(Q) = 150−Q.Firm 1 has a constant marginal cost of MC1 (q1) = $30.Firm 2's constant marginal cost is MC2 (q2) = $60.Assume fixed costs are negligible for both firms. Calculate the output of each firm, market output, and price if there is (A) a collusive equilibrium or (B) a Cournot equilibrium. (A) Collusive equilibrium (Enter your responses rounded to two decimal places) The collusive equilibrium occurs where q1 equals ?and q2 equals ? Market output is ? The collusive equilibrium price is ? (B) Cournot equilibrium (Enter your responses using rounded to two decimal places) The Nash-Cournot equilibrium occurs where q1 equals ? and q2 equals ? Market output is ? The equilibrium occurs at a price of ?
Firm 1 and Firm 2 are Stackelberg competitors. Firm 1 is the leader and Firm 2 is the follower. They have the same cost functions: Firm 1: C₁(Q1) = 4Q1 Firm 2: C2(Q2) = 4Q2 The market demand is QD = 42 -0.5P Compute the SPE of this game. In equilibrium, Firm 1 produces Q₁= and the price is P= v, Firm 2 produces Q2=
Two firms are engaged in Cournot (simultaneous quantity) competition. Market-level inverse demand is given by P = 160 − 4Q Firm 1 has constant marginal costs of MC1 = 8, while Firm 2 has constant marginal costs of MC2 = 24. 1) Does there exist a low enough positive marginal cost for firm 1 such that firm 1 acts like a monopoly in this market, if so what is the MC if not why?
Suppose the inverse market demand for manufactures is P(Q) = A – Q, where P and Q denote price and total goods produced and the parameter A denotes the size of the domestic market. Suppose any firm has a cost function, c(q) = cq, where A > c. Suppose there are two firm in the market which produce q1 and q2, where Q = q1 + q 2 a. Solve for the Cournot equilibrium levels of output (Q*), price (P*) and markups. b. What is the impact of an increase in market size, A, on Q*, P* and markups when there are two firms? Provide some intuition for these predictions. c.…
Consider a duopoly market, where two firms sell differentiated products, which are imperfect substitutes. The market can be modelled as a static price competition game, similar to a linear city model. The two firms choose prices p, and p2 simultaneously. The derived demand functions for the two firms are: D1 (P1, P2) = SG+P1)and D2 (P1, P2)= S(;+-P2), where S > 0 and the parameter t > 0 measures the 2t 2t degree of product differentiation. Both firms have constant marginal cost c> 0 for production. (a) Derive the Nash equilibrium of this game, including the prices, outputs and profit of the two firms. (b) From the demand functions, qi= D¡ (p; , p¡ )= SG+P), derive the residual inverse demand functions: p; = P; (qi , p¡) (work out: P; (qi , P;)). Show that for t > 0, P;(qi , P;) is downward 2t aPi (qi ,Pj) . sloping, i.e., c, i.e., firm į has market power. %3D (c) Calculate the limits of the equilibrium prices and profit as t → 0 ? What is P; (qi , p;) as t → 0? Is it downward sloping?…
The inverse demand for a homogeneous product Stackelberg duopoly is P = 14000 – 20. The cost functions for the leader and follower are C(Q) = 2000Q, and C;(QF) = 4000Q, respectively. a) What is the follower's revenue function? Note that MRF = 14,000-2Q1-4QF and MCF = 4,000. b) What is the follower's reaction curve? c) Determine the equilibrium output level for both the leader and the follower. [Note that for a quadratic revenue function R(Q)=aQ²+bQ+c, it holds that MR(Q)=2aQ+b.] d) Determine the equilibrium market price. e) Determine the profits of the leader and the follower.
Suppose the iceberg lettuce industry is a Cournot duopoly with two firms: Xtra Leafy (a) and Yummy Farms (y). Xtra Leafy produces q units of output and Yummy Farms produces qy units of output. Aggregate market output is Q = x + y. The (inverse) market demand schedule is: p = 176 - 2Q Both firms have identical cost structures: MC = MC₁ = ATC₂ = ATC₁ = $12 Find Xtra Leafy's Cournot reaction function of the form: 9x = a + bay Where "a" is the reaction function's intercept and "b" is its slope. Note: Please review the formatting instructions above. If any value is negative, be sure to include its negative sign. a. a= b. b = Hint: One of your answers will be negative. Think about why.
(4) Firm l's cost function is C1(q1) = q1 and firm 2's cost function is C2(q2) = 2q2. Consider a duopoly selling in a market with inverse demand function p = 12 q. (a) Assume firms choose output simultaneously (Cournot model). Compute the equilibrium quantities and the market price in a Nash equilibrium. (b) Now assume that firm 1 is a leader and chooses its output q1 first. Then, firm 2 chooses its output q2 after observing q1 (Stackelberg model). Find a subgame-perfect Nash equilibrium of this game. Carefully specify the strategies for firm 1 and firm 2. What quantities are produced in equilibrium and what is the market price in equilibrium?