For a Cournot oligopoly model with n firms facing constant marginal costs c, and market demand P = 1 - Q. where Q is the total quantity demanded in the market, the equilibrium quantity for each firm will be O (1-c)/(n+1) O (1+c)/(n+1) O (1+cn)/(n+1) O (1-cn)/(n+1)
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How does it go from qi = (1 - q1 - q2 - ... - qn - c)/2 to q = (1 - cq)/(n + 1) via the substitution in the last step?
- In a Cournot duopoly model, the market demand curve is given by P 100 - yI - y2- !! where y, is the amount of output firm 1 produces and y2 is firm 2's level of output. The cost function of firm 1 is c(y1) 75 +8y1. The cost function of firm 2 is c(y2) = 100 +12y2. %3D The reaction function of firm 1 is y1 = -0.5y2- The reaction function of firm 2 is y2 = -0.5y1- In the Cournot equilibrium, firm 2 produces units of output and makes a producer surplus of $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?Two competing firms produce homogenous products. They also have the iden- tical total cost function: if a firm i produces quantity q, then its total cost is C, (4.) = 2q«- If the two firms compete in quantities (Cournot model of duopoly), then the market demand is P (g1, 2) = 60 – q1 - 2. If the two firms compete in prices (Bertrand model of duopoly) and firm i chooses price then the demand for firm i is P.. 60-P if p, is lower than the competitor's price if p, is higher than the competitor's price if p, is equal to the competitor's price Now consider two scenarios: A. The two firms are two law firms. One unit of product = one hour of labour. B. The two firms are two avocado farms. One unit of product = one ton of avocados. For each of these two scenarios, answer the following questions: (a) Should we use the Cournot model or the Bertrand model to study the firms' compe- tition? (b) Use your model of choice to predict each firm's profit level in equilibrium. (c) If the two firms…
- If firm 1 and firm 2 are the oligopolistic firms in bottled spring water production in Nomansland. The market demand is given by ? = 5000 −20?, Qd is the number of kilolitres demanded per month while P is the price of kilolitres of bottled water. The marginal cost of a kilolitre of bottled water is R10.How do I Find the Cournot equilibrium quantities and price? and how do I Find the Cournot profits and the monopolist profits?For a Cournot oligopoly model with n firms facing constant marginal costs c, and market demand P = 1 - Q, where Q is the total quantity demanded in the market. If the n firms collude successfully, then the equilibrium quantity for each firm will be O (1-c)/2n O (1-c)/n O (1+c)/2n O (1+c)/nSuppose oil production in the Gulf of Mexico was a symmetric horizontal oligopoly in Cournot competition. Assume there are two producers, each with a constant marginal cost of production of $50 per barrel. Let the demand function for oil in the region be D(p) = 12000 – 20p, where demand is measured in barrels per day. (You will need to calculate inverse demand from demand before moving on). What would the perfectly competitive equilibrium price and quantity be? What would be the consumer surplus and producer surplus? Draw each firm’s residual inverse demand curve. Calculate the Cournot-Nash equilibrium price and quantity. What is the total consumer surplus, total producer surplus across the two firms, and deadweight loss?
- 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.)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 e2(q2) = 2q2. The inverse market demand function is given by P = 100 – 5(q1 +92). (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?You are given the market demand function Q= 2200 – 1000p, and that each duopoly firm's marginal cost is $0.07 per unit, which implies the cost function: C(at) = 0.07i, assuming no fixed costs for i = 1, 2. The Cournot equilibrium quantities are q1 = and q2 = (enter your responses as whole numbers). The Cournot equilibrium price is $ (round to the nearest penny). Calculate the Cournot profits: firm 1 $ and firm 2 $ (round both responses to the nearest cent).
- Walmart (firm 1) and Amazon (firm 2) are a duopoly in the grocery market. They are faced with an inverse demand of P(Q1, Q2) = 16−2 (Q1+Q2) and total costs of TC(Qi) = 2Q2i, i= 1,2. Note that the marginal cost is not constant! 1. Obtain the Cournot equilibrium quantities and profits. 2. Obtain the Stackelberg equilibrium in which Walmart moves first. Compare with the Cournotequilibrium. 3. Obtain the cartel outcome (= shared monopoly). Compare with Stackelberg and Cournot.QUESTION 12 Consider an industry with two identical firms (denoted firm 1 and 2) producing a homogenous good. Firms compete in quantities and have a constant marginal cost of 30. Demand in the industry is given by D(p) = 195 - p/2. Let q1 and q2 denote the quantities of firm 1 and 2, respectively. Derive the best resonse functions and the Nash equilibrium in quantities. Which of the following statements are correct? [There may be more than one correct statement.] The Nash equilibrium quantity for each firm is 40. O The Nash equilibrium quantity for each firm is 60. The reaction function of firm 1 is given by q1 = 60 - (92)/2. The reaction function of firm 1 is given by q1 = 45 - (92)/2. The reaction function of firm 1 is given by q1 = 90 - (92)/2. O The Nash equilibrium quantity for each firm is 30. None of the above. 000Suppose 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.