Two identical firms compete as a Cournot duopoly. The inverse market demand they face is P-128 - 4Q. The total cost function for each firm is TC(Q;)=8Q; where i is firm 1 or firm 2. Based on this information firm 1 and 2's best response functions are Q₁16-0.25Q₂ and Q2-16-0.25Q1. Q₁16-0.5Q₂ and Q2-16-0.5Q₁- Q1-15-0.25Q2 and Q2=15-0.25Q1. Q₁15-0.5Q2 and Q2 = 15-0.5Q₁.
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- 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 $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?Two firms in a Cournat oligpoly each have the best response function, such that the optimal quantity for each individual firm to produce must satisfy the equation: Q-27-Q/2 What quantity Q will each firm produce in the market? Type your answer...
- A duopoly faces a market demand of p= 120 - Q. Firm 1 has a constant marginal cost of MC' =S10. Firm 2's constant marginal cost is MC = S20. Calculate the output of each firm, market output, and price if there is (a) a collusive equilibrium or (b) a Cournot equilibrium. The collusive equilibrium occurs where q, equals and q, equals (Enter numeric responses using real numbers rounded to two decimal places) Market output is The collusive equilibrium price is S The Cournot-Nash equilibrium occurs where q, equals and q2 equals Market output is Furthermore, the Cournot equilibrium price is SConsider 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…
- The firms in a duopoly produce differentiated products. The inverse demand for Firm 1 is The inverse demand for Firm 2 is and P₁ = 52-9₁-0.592. Each firm has a marginal cost of m= $1 per unit. Solve for the Nash-Cournot equilibrium quantities. The Cournot equilibrium quantities are (Enter your responses rounded to two decimal places.) P₂ = 100-92-0.5q1₁. 91 = units 92 units. =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?1 Consider a duopoly with firm 1 and firm 2. Their cost functions are 2q₁ and cq2, respectively, where 2 < c < 10. The market demand function is p=10-Q, where Q=q₁+9₂. (a) Assume that the two firms play the Bertrand price game. Find the firms' price choices in the Bertrand equilibrium. (b) Assume that the two firms play the Cournot quantity game. Find the firms' quantity choices in the Cournot equilibrium.
- Consider a Cournot oligopoly with three firms i = 1,2, 3. All firms have the same constant marginal cost c = 1. The inverse demand function of the market is given by P = 9-Q, where P is the market price, and Q = E1 9i is the aggregate output. 3 (a) Solve for the Nash equilibrium of the game including firm out- puts, market price, aggregate output, and firm profits (Hint: the NE is symmetric). (b) Now suppose these three firms play a 2-stage game. In stage 1, they produce capacities q1, 72 and 73, which are equal to the Nash equilibrium quantities of the Cournot game characterised by part (a). In stage 2, they simultaneously decide on their prices p1, p2 and p3. The marginal cost for each firm to sell up to capacity is 0. It is impossible to sell more than capacity. The residual demand for firm i is 9 – Pi - Eiti āj if pi > P; for all j # i if p; = Pj for all j # i if p; < P; for all j #i | 9-pi D; (pi, p-i) = 3 9 – p; (Note, here we assume that the efficient/parallel rationing ap-…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.)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.