You are given the market demand function Q = 1500-1000p, and that each duopoly firm's marginal cost is $0.20 per unit, which implies the cost function: C(qi) = 0.20qi, assuming no fixed costs for i = 1, 2. The cooperative Cournot quantities are q₁ = and q₂ = (enter your responses as whole numbers). The cooperative Cournot price is $ (round to the nearest penny). Calculate the cooperative Cournot profits: firm 1 $ and firm 2 $ (round both responses to the nearest cent).
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- The market demand in a homogeneous-product Cournot duopoly is P = 100 - 2Q, where Q=Q1+Q2 (Firm 1 and Firm 2), and the costs functions for each firms are: TC1 = 12Q1 and TC2 = 20Q2. Instructions: Use no decimals. Use the average cost to calculate monopoly profits. Do not round if values are used to complete other calculations. Complete the following table. Q1 Q2 P Profits F1 Profits F2 Duopoly competition CollusionThe market demand in a homogeneous-product Cournot duopoly is P = 100 - 2Q, where Q = Q1 + Q2 (Firm 1 and Firm 2), and the costs functions for each firms are: TC1 = 12Q1 and TC2 = 20Q2. Instructions: Use no decimals. Use the average cost to calculate monopoly profits. Do not round if values are used to complete other calculations. Complete the following table. Q1 Q2 P Profits F1 Profits F2 F1 colludes, F2 cheats w/ QDC F1 colludes, F2 cheats w/ QBRFThe market demand in a homogeneous-product Cournot duopoly is P = 100 - 2Q, where Q = Q1 + Q2 (Firm 1 and Firm 2), and the costs functions for each firms are: TC1 = 12Q1 and TC2 = 20Q2. Instructions: Use no decimals. Use the average cost to calculate monopoly profits. Do not round if values are used to complete other calculations. Complete the following table. Q1 Q2 P Profits F1 Profits F2 F1 cheats w/ QDC, F2 colludes F1 cheats w/ QBRF, F2 2 colludes
- In a homogeneous products duopoly, each firm has a marginal cost curve MC= 10, i= 1,2. The market inverse demand curve is P= 50−Q, where Q = Q1+Q2. a) What would be the equilibrium price in this market if firms acted as price-taking firms? b) What would be the equilibrium price in this market if the two firms acted as a profit-maximizing cartel? Obtain the Lerner index c) What would be the Cournot equilibrium quantities, price and profit in this market? Obtain the Lerner index of each firm and compare it to b)Consider a Bertrand duopoly. Both firms produce an identical good at the same constant marginal cost of $0.80. Demand is given by Q=100−P. If the two firms charge the same price, they share market demand equally. The firms are located in Singapore, where the smallest currency denomination is $0.05. The firms thus can only choose prices in increments of $0.05. a) Suppose that both firms choose the same price, P. What is the profit of a firm as a function of P? b) Now suppose that one firm unilaterally deviates from the arrangement in (a) by charging a price $0.05 lower than P. What is that firm’s profit as a function of P? c) A Nash equilibrium occurs when no firm has an incentive to deviate by lowering its price. Using your answers in (a) and (b), set up an inequality that characterizes the Nash equilibrium. Then solve for the Nash equilibria in this game. (Hint: there are three equilibria)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 by TCi = 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?
- Consider an industry that consists of 4 firms, all competing over the same market, given by the following demand equation: P=80-3Q All firms have the same Total Cost Function, given by: TC₁=10q,+2q Suppose the firms decide to collude and voluntarily restrict output and raise price, in order to increase profits. a) What price will be charged by the members of the cartel? Assume the head of the cartel is fair and distributes output q, equally among the 4 firms (since they have identical costs). b)What is the output of each individual firm? c) What is each individual firm's profit? We know that there is a built-in incentive for cartel members to cheat on the cartel. If, as a result, the cartel breaks down: d) What price will be charged in the market? e) Assuming each firm captures an equal share of the market, what now is each firm's output, q? f) What now is individual firm profit? g) Illustrate your answerAnswer the given question with a proper explanation and step-by-step solution. Two firms compete in a market to sell a homogeneous product with inverse demand function P = 400 – 2Q. Each firm produces at a constant marginal cost of $50 and has no fixed costs -- both firms have a cost function C(Q) = 50Q. If this market is defined as a Stackelberg Oligopoly, what is the optimal amount for the leader (firm 1) to produce? (Round to one decimal place) If this market is defined as a Stackelberg Oligopoly, what is the optimal amount for the follower (firm 2) to produce? (Round to one decimal place) What is the market price? (Round to the nearest whole number) What are the leader's (firm 1's) profits? (Round to the nearest whole number) What are the follower's (firm 2's) profits? (Round to the nearest whole number)Q. Three firms operate in a market with a Demand function p = 169 - 2Q. All three firms have identical Cost functions: TC = 1200 - 95q + 2q2.i) Given that the firms are able to collude, what is the equilibrium market price and output?ii) If all of the firms cheat and each increases output by two units, what would be the new equilibrium price and the impact on an individual firm’s profits?
- Consider a duopoly where firms compete in prices and firms do not have any capacity constraints. Market demand is P(Q)=45-4Q, and each firm faces a marginal cost of $9 per unit. How much is each firm's total variable cost if firms equally divide the market at Nash equilibrium?Suppose we have a duopoly with Firm 1 and Firm 2 and the following inverse demand function:P = 100 – 5(Q1 + Q2)Total Cost and Marginal Cost values for firms 1 and 2 are:TC1 = 20Q1TC2 = 30Q2MC1 = 20MC2 = 30Assuming a Cournot Duopoly, the following response functions are derived:Firm 1: Q1 = 8 – 0.5Q2Firm 2: Q2 = 7 – 0.5Q1Using this information, calculate the quantity produced for each firm, the price, and profits foreach firm and the market as a whole.Two firms - firm 1 and firm 2 - share a market for a specific product. Both have zero marginal cost. They compete in the manner of Bertrand and the market demand for the product is given by: q = 20 − min{p1, p2}. 1. What are the equilibrium prices and profits? 2. Suppose the two firms have signed a collusion contract, that is, they agree to set the same price and share the market equally. What is the price they would set and what would be their profits? For the following parts, suppose the Bertrand game is played for infinitely many times with discount factor for both firms δ ∈ [0, 1). 3. Let both players adopt the following strategy: start with collusion; maintain the collusive price as long as no one has ever deviated before; otherwise set the Bertrand price. What is the minimum value of δ for which this is a SPNE. 4. Suppose the policy maker has imposed a price floor p = 4, that is, neither firm is allowed to set a price below $4. How does your answer to part 3 change? Is it now…