The inverse demand for a homogeneous-product Stackelberg duopoly is P= 24,000 -5Q. The cost structures for the leader and the follower, respectively, are CL(QL) = 3,000QL and CF(QA = 4,000G a. What is the follower's reaction function? 0.5 QL o. Determine the equilibrium output level for both the leader and the follower. Leader output | Follower output: |
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- Consider two firms competing à la Bertrand with homogeneous product. Suppose a third firm enters the market. Market power, measured by the Lerner Index, of the two firms already in the market: O (a) Always decreases for both firms O (b) Always decreases for the firm with higher marginal cost O (c) Decreases for both firms only if the new entrant has a lower marginal cost than the two firms already in the market O (d) None of the abovea)Consider a homogeneous goods industry where two firms operate and the linear demand is given by p(y1 + y2 ) = a - b(y1 + y2 ), where p is the market price, and y1 (y2) is the output produced by firm 1 (2). There are no costs for firm 1 or firm 2. Derive the best responses (reaction curve) for firm 1 and firm 2. Explain the term best response (reaction curve). Illustrate the best responses in a diagram. b) For the case in (a) determine the Cournot equilibrium (Nash equilibrium in quantities) when firm 1 and firm 2 compete simultaneously in quantities. How large are firm 1’s and firm 2’s profits? What is the industry output? c) Suppose the inverse demand curve in a market is D(p) =a-bp, where D(p) is the quantity demanded and p is the market price. Firm 1 is the leader and has a cost function c1(y1)=cy1 while firm 2 is the follower with a cost function c2(y2 )=. Firm 1 sets its price to maximise its profit. Firm 1 correctly forecasts that the follower takes the price leader’s…There are two identical firms in an industry, 1 and 2, each with cost function , i = 1,2. The industry demand curve is P = 100 − 5X where industry output, X, is the sum of the two firms’ outputs (X1 + X2). (a) If each firm makes its output decisions on the assumption that the other will not react to its choices (the Cournot assumption), what is the equilibrium output for each firm? What is the equilibrium price? (b) Suppose that each firm takes it in turn to choose its level of output, on the assumption that the other’s output level is fixed. Would the process of adjustment be stable? (c) Suppose that firm 1 introduces a cost-saving innovation, so that its cost curve becomes C1 = 8X1. Firm 2’s cost curve and the industry demand curve are unchanged. What happens to the equilibrium quantity produced by each firm and to market price?
- An industry has a demand function of QP(p) = 500 – 250p. Suppose now that each firm has a constant marginal cost equal to 1. a. If there are n identical firms, what would be the profit of each under Cournot competition? 5. What would be the profit of each if they collude? c. If the firms face that demand function each period, what discount factor is required to support collusion? d. What happens to the required discount factor as n grows?Consider the following model of Cournot competition with fixed cost. There are two identical firms, and the inverse demand function is given by 5. P(q1, 42) 19 – (q1 + 92). Firms have constant marginal cost, but any firm operating in this market (that is, q; > 0) must pay a license fee F. In particular, firm i's cost function is if qi = 0 c:(4;) = { F+4 if qi > 0. (a) Derive the firms' best response functions. (b) For what values of F, if any, will there be a symmetric (pure) Nash equilibrium in which firms produce a positive quantity? What is the Nash equilibrium in that case? (c) For what values of F, if any, will both firms shutting down be the Sy anmetric (pure) Nash equilibrium?5. N - Σ Consider a Cournot model in which N firms compete with each other by setting quantities. The market inverse demand function is P = a i=1 qi, where a > 0 and q; is the quantity of firm i. Firm i's cost function is quadratic: q, where c₂ > 0. (a) Suppose N 2. Find the Nash equilibrium. Show which firm produces more in the equilibrium and explain your result. (b) = Suppose N≥ 2 and ci = c for all i. Find the Nash equilibrium. Show whether the firms produce more or less than the constant marginal cost case where the cost function is cqi, with a>c>0.
- Consider an industry with N firms that compete by setting the quantities of an identical product simultaneously. The resulting market price is given by: p = 1000 − 4Q. The total cost function of each firm is C(qi) = 50 + 20qi . (a) Derive the output reaction of firm i to the belief that its rivals are jointly producing a total output of Q-i . Assuming that every firm produces the same quantity in equilibrium, use your answer to compute that quantity. (b) Suppose firms would enter (exit) this industry if the existing firms were making a profit (loss). Write down a mathematical equation, the solution to which would give you the equilibrium number of firms in this industry. You don’t have to solve this equation.An upstream firm (U) sells an input to a downstream firm (D) which resells it to consumers. The marginal cost of U is 4. Each unit is sold by U to D at a transfer price r. Requirement final is p = 12 - y. a) Suppose U and D are separate firms. Find r, y and p. b) Suppose U and D are one integrated firm. Find p and y. c) Suppose the firms are not integrated, but firm U uses a two-part tariff: it requires payment of r for each unit sold to D; in addition, it requires payment lump sum of T. Find the value of r that U will choose. Find the minimum and maximum values by T. d) Suppose the firms are not integrated, but U imposes a resale price control on firm D. Find the value of r that U will choose, and the constraint that it will impose on the price final pAn upstream firm (U) sells an input to a downstream firm (D) which resells it to consumers. The marginal cost of U is 4. Each unit is sold by U to D at a transfer price r. Requirement final is p = 12 - y. a) Suppose U and D are separate firms. Find r, y and p. b) Suppose U and D are one integrated firm. Find p and y. c) Suppose the firms are not integrated, but firm U uses a two-part tariff: it requires payment of r for each unit sold to D; in addition, it requires payment lump sum of T. Find the value of r that U will choose. Find the minimum and maximum values by T. d) Suppose the firms are not integrated, but U imposes a resale price control on firm D. Find the value of r that U will choose, and the constraint that it will impose on the price final p Plzz give the answer of all questions.
- Demand is assumed to be unit-elastic: X(p) = 1/p. There are m ≥ b2 firms operating in the market with constant marginal cost levels c1 ≤ c2 ≤ ……. ≤ cm. They engage in Cournot competition. a. Show that the equilibrium price implies Lerner indexes Where si is the market share of firm i. b. Using the equilibrium price, show that the profit of firm i is equal to (si)2. c. Show that the industry profit is equal to the Herfindahl index H = Σi(si)2. d. What is the effect of a specific taxt on equilibrium price? How does this tax affect the industry profit and the Herfindahl index?6. Two identical firms that have the cost function C(q) = 4qj, where j = {1,2} are competing in a homogenous good market. The two firms make simultaneous decisions on price, and they face industry demand Q(P) = 20-p. What is the Bertrand-Nash equilibrium profit of each firm? Hints for (b) and (c): Solve for each firm j's output (q;) and use the fact that Ij = p;qj - Cj(qj). b. Now, suppose the two firms are deciding whether to set a collusive market price of $6 (this means that they would both charge $6). Solve for their profits under this pricing scheme. a. C. If one of the firms decides to deviate from the collusive scheme and undercut its rival's price by $1, how much profit would it earn?(Preferably answered digitally as I have a hard time understanding paper hand writing.)