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- Calculate every step please!!!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 pleaseA 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 ?
- If the inverse demand for bean sprouts were given by P(Y) = 430 − 2Y and the total cost of producing Y units for any firm were TC(Y) = 10Y and if the industry consisted of two Cournot duopolists, then in equilibrium each firm's production would beProblem 3 Consider the infinitely repeated game with the discount factor & € (0, 1) of the following Cournot duopoly model with inverse demand function P(Q) = a Q if Q≤ a 0 if Q > a where Q = 91 +92 and cost functions Ci(qi) = cqi, i = 1,2. The profit function of firm i is given by Ti (91, 92) = qiP(9₁ +92) - cqi. Consider the following grim-trigger strategy. Produce half the monopoly output in the first period and as long as everybody has produced that amount so far. Otherwise produce the Cournot output. Verify that this is a subgame perfect equilibrium.You are given the market demand function Q= 3400 – 1000p, and that each duopoly firm's marginal cost is $0.28 per unit, which implies the cost function: C(4:) = 0.28qi, assuming no fixed costs for i = 1, 2. The Cournot equilibrium quantities are q, and 92 (enter your responses as whole numbers).
- Suppose there are just two firms, 1 and 2, in the oil market and the inverse demand for oil is given by P = 60 – Q. The marginal cost for each firm is €30. What price should Firm 2 charge at the Cournot equilibriumConsider 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?Consider the following oligopolistic market. In the first stage, Firm 1 chooses quantity q1₁. Firms 2 and 3 observe Firm 1's choice, and then proceed to simultaneously choose 92 and 93, respectively. Market demand is given by p(Q) = 100 – · Q, and Q = 9₁ +92 +93. Firm 1's costs are c₁ (9₁) = 591, firm 2's costs are c₂ (92) = 492 and firm 3's costs are C3 (93) = 493. C2 Starting from the end of the game, you can express Firm 2's best response function in terms of 9₁ and 93, and you can similarly express Firm 3's best response function in terms of 9₁ and 92. Using these, answer the following questions. If rounding is needed, write your answers to 3 decimal places. a) If Firm 1 chooses q₁ = 3, what quantity will Firm 2 choose? b) If Firm 1 chooses 9₁ = 100, what quantity will Firm 2 choose? c) In the subgame perfect Nash equilibrium of this game, firm 1 produces what quantity? d) In the subgame perfect Nash equilibrium of this game, firm 2 and firm 3 each produce what quantity?
