In a duopoly market, two firms produce the identical products, the cost function of firm 1 is: C, = 20q1, the cost function of firm 2 is: C, 2Q, here Q = qı + 92. 2092, the market demand function is: P = 500 In a Bertrand model, the two firms set their price simultaneously, assume both firms do not have production capacity limits, and there is no collusion. What is the market equilibrium price and quantity? If the two firms decide to form a Cartel, i.e. they want to maximize the profit of the whole industry, and then split the production and profit evenly. What is the market price? What is the
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- 1. Consider a market where there are only two firms that produce a homogeneous product. The two firms face the direct market demand curve given Q = 15-p, where Q = 9₁ +92 and 9₁ and q2 are the quantities of firm 1 and firm 2, respectively. Suppose firm 1's total cost is C₁ = 9₁ and firm 2's total cost function is C₂ = 2q2. Suppose that the two firms act independently and choose their outputs simultaneously as in the Cournot model. Show the basis and briefly explain what is going on as you answer each of the following questions. Your mark will depend upon the correctness of your basis and explanation. 1. What is the equation of the demand curve faced by firm 1? What is the equation of the demand curve faced by firm 2? Find the output reaction function of each firm. 2. 3. Find the Nash-Cournot equilibrium quantity that each firm will produce. 4. At the Nash-Cournot equilibrium, at what price does each firm sell its output? 5. Find the consumer surplus, producer surplus at the…The inverse market demand curve for salmon is given by P(Y) = 100 – 2Y, and the total cost function for any firm in the industry is given by TC(y) = 4y. a. Suppose that two Cournot firms operated in the market. What would be the reaction function for Firm 1 and the reaction function of Firm 2? (Notes: The marginal cost is not zero). If the firms were operating at the Cournot equilibrium point, what would the industry output and price be? b. For the Cournot case, draw the two reaction curves and indicate the equilibrium point on the graph. The market for widgets consists of two firms that produce identical products. Competition in the market is such that each of the firms independently produces a quantity of output, and these quantities are then sold in the market at a price that is determined by the total amount produced by the two firms. Firm 2 is known to have a cost advantage over firm 1. A recent study found that the (inverse) market demand curve faced by the two firms is P = 280 – 2(Q1 + Q2), and costs are C1(Q1) = 3Q1 and C2(Q2) = 2Q2. a. Determine the marginal revenue for each firm. b. Determine the reaction function for each firm.
- Suppose we have two identical firms A and B, selling identical products. They are the only firms in the market and compete by choosing quantities at the same time. The Market demand curve is given by P=477-Q. The only cost is a constant marginal cost of $16. Suppose Firm A produces a quantity of 66 and Firm B produces a quantity of 49. If Firm A decides to increase its quantity by 1 unit while Firm B continues to produce the same 49 units, what is the Marginal Revenue for Firm A from this extra unit? Enter a number only, no $ sign. Don't forget to include the negative sign if revenue decreases.Two firms sells an identical product. The demand function for each firm is given: Q = 20 - P, where Q = q1 + q2 is the market demand and P is the price. The cost function for reach firm is given: TCi = 10 + 2qi for i = 1, 2. a) If these two firms collude and they want to maximize their combined profit, how much are the market equilibrium quantity and price? b) If these two firms decide their production simultaneously, how much does each firm produce? What is the market equilibrium price? c) If Firm 1 is a leader who decides the production level first and Firm 2 is a follower, how much does each firm produce? What is the market equilibrium price?Two firms compete in selling identical widgets. They choose their output levels Q1 and Q2 simultaneously and face the demand curve P = 30 - Q where Q = Q1 + Q2. Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm 2’s marginal cost to $15. Firm 1’s marginal cost remains constant at zero. TRUE-FALSE: Is the following statement true of false? ”As a result, the market price will rise to the monopoly level.” Solve for the Cournot equilibrium and write a convincing explanation of your answer.
- 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…In a market there are five firms, all have a total cost curve equal to CT = 2q. The market demand is Q = 500 - 5P. How much profit would each firm get if they collude and share the market equitably? What is the profit to each firm if they agree to collude, but one firm misleads the others charging a slightly lower price? What is the profit if all firms do not collude and compete via price?Two firms compete in selling homogeneous goods. They choose their output levels q1 and q2 simultaneously and face demand curve P=80-6Q, where Q=q1+q2. The total cost function of firm 1 is C1=8q1 and the total cost function of firm 2 is C2=32q2+2/3. a) Find and draw the reaction curves of the two firms. b) Compute equilibrium quantities, price and profits. Suppose now that firm 2, thanks to a technological innovation, becomes more efficient. The new total cost function of firm 2 is C2=8q2 c) Compute the new equilibrium quantities, price and profits.
- Two firms sell substitutable products; the market price is: P = 90-Q, where Q Q₁ + Q2 is the total market quantity, which consists of Q1₁ (the quantity produced by Firm 1) and Q2 (the quantity produced by Firm 2). The firms choose their quantities simultaneously. Firm 1's costs are C₁ 6Q₁ + Q². Firm 2's costs are C₂ = Q². = O Which is the payoff function for Firm 2? O π₂ = 90Q₂ - 2 Which is the best response function for Firm 1? O π₂ = 90Q₂ - Q²². πT2 π₂ = 45 - Q² Q₁ Q₂₁ 2 O π₂ = 45 - 1²/20₁². Q₁ Q₁ 3 = 16. ²/Q²-Q₁2. = 32- 2- 1/1/202₂. 3 Q₁ = 45. Q1 = 40 + ²/Q₂₁ 2.2. = 10- -Firm 1 and firm 2 are Bertrand duopoloists. Firm 1 has a marginal cost of $6.00 per unit, and firm 2 has a marginal cost of $8.01 per unit. The demand for their product is p=23.00−Q, where Q is the total quantity demanded. How much does each firm sell in equilibrium? Assume that prices can only be set to the nearest cent, firms split the market if they set the same price, and there are no fixed costs. Firm 1 production:______ Firm 2 production:______ What are the profits for each firm in equilibrium? Firm 1 profit: $______ Firm 2 profit: $______There are two firms that are producing identical goods in a market characterized by the inverse demand curve P = 60 - 2Q, where Q is the sum of Firm 1's and Firm 2's output, q₁+q2. Each firm's marginal cost is constant at 12, and fixed cost are 0. Answer the following question, assuming that the firms are Cournot competitors. a. Calculate each firm's reaction function and illustrate them graphically (15 points) b. How much output does each firm produce? (12.5 points) c. What is the market price? (7.5 points) d. How much profit does each firm earn? What is the industry profit? (10 points)