Two companies produce similar items for the same market. Company 1 produces q₁ items and Company 2 produces q2 items. The costs C₁ and C₂ incurred by Company 1 and Company 2, respectively, are given by C₁ = 79₁ and C₂ = 1092, and the market price P is given by P = 100 q1 q2. Let ₁ and 2 den ote the profits made by Company 1 and Company 2, respectively. Each company wants to choose its production strategy in order to maximize its profit. (a) Find expressions for ₁ and ₂ in terms of q₁ and 92. (b) Find the solution of this problem, using the Cournot model.
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- Two firms sell an identical product in a market by setting prices simultaneously. Consumers buy from the firm that offers the lower price; if the prices are identical, the firms split the demand. If ? is the lowest price (in dollars), aggregate demand is ? = 250 − ?. Suppose prices can only be set in increments of 1 cent. (a) Suppose Firm 1 and Firm 2 have limited production capacities of 40 units each. The marginal cost of firm 1 is $35 and the marginal cost of firm 2 is $25. If Firm 1 believes that Firm 2 will set a price of $30, what price should Firm 1 set? Show your work. (Assume efficient rationing while calculating firm’s residual demand.) (b) Ignore the information in part (a). Suppose each firm has unlimited capacity, but that the marginal costs of Firm 1 and Firm 2 are $40 and $150 respectively. Do ?1 = 149.99 and ?2 = 150 satisfy the requirements of a Nash equilibrium? Explain why. You must explain why a strategy is a best response or not to the other strategy.A company sells two goods (1 and 2) to two consumers (A and B). The consumers have reservation prices for the two goods given in the table below. Each consumer will purchase one unit of a good as long as its price is less than or equal to the consumer's reservation price for that good. The marginal cost of producing each good is $35 per unit. Consumer A Consumer B Good 1 $80 $60 Good 2 $40 $70 If the company plans to sell the goods separately, it should charge a price of $ 60 for good 1 and 5 70 for good 2. (Enter your responses as integers) If the company wants to use pure bundling by packaging the goods together and selling them only as a bundle, it should charge $ 120 for the bundle containing one unit of good 1 and one unit of good 2. (Enter your response as an integer) If the company wants to practice mixed bundling, it should charge a price of $ 80 for good 1, a price above $40 for good 2, and a price of $ 100 for the bundle containing one unit of each good (Enter your responses…Suppose the outputs of beauty shops and pet-grooming salons are complementary, providing one-stop shopping for personal and pet maintenance. Betty Beehive is thinking about moving her beauty shop from an isolated location to a vacant building next to Peter’s pet grooming shop.In making her decision, she makes the following assumptions: If Betty moves, she will keep all her current customers (20 people per week) and attract 25% of Peter’s current customers. Peter currently has 60 customers per week. 3. Excluding rent, Betty’s profit per beauty treatment is $10. 4.The weekly rent at the new location is $200 higher than Betty’s current rent. Question = If Betty moves her beauty shop, will her profits increase or decrease? By how much? Question =Suppose that if Betty makes the move, 50 percent of her original customerswill switch from George’s grooming salon to Peter’s. If Peter’s profit pertreatment is $8, how much would he be willing to pay Betty to make themove? Will the…
- Two firms, Firm 1 and Firm 2, compete by simultaneously choosing prices. Both firms sell an identical product for which each of 100 consumers has a maximum willingness to pay of $40. Each consumer will buy at most 1 unit, and will buy it from whichever firm charges the lowest price. If both firms set the same price, they share the market equally. Costs are given by C; (qi) = 16q¡ . Because of government regulation, firms can only choose prices which are integer numbers, and they cannot price above $40. Could you help me with these questions? a) If Firm 1 chooses Pi price? = 32, Firm 2's best response is to set what b) If Firm 2 chooses the price determined in the previous question, Firm 1's best response is to choose what price? c) If Firm 1 chooses p₁ = 9, Firm 2's best response is a range of prices. What is the lowest price in this range?C2) Company A is the only supplier of glass in Big Apple City used for tall buildings’ exteriors. Its marginal cost of production is cA=1, and it has no other production costs. The demand for such glass in Big Apple city is QD=2-P. Company B in Jersey City produces the same glass and is considering whether to expand to Big Apple city. If it enters, it needs to get a permit to allow it to be a supplier in the Big-Apple city at a cost of L=0.5, which does not vary with quantity of output, and its marginal cost of production is cB=0.5. If it expands to the Big-Apple city, companies A and B both supply to the market, and the market price P satisfies QA+QB=2-P, where QA is company A’s production level and QB is company B’s. a) If company B expands to the Big-Apple city, what is the resulting price in a Nash equilibrium? b) Company B hires a consulting company to advise whether it should expand to the Big-Apple city. If you’re running the consulting company, what is your advice? Explain…= Q.3 Two firms produce homogeneous products. The inverse demand function is given by: p(x₁, x₂) = 80x₁-x2, where x₁ is the quantity chosen by firm 1 and x₂ the quantity chosen simultaneously by firm 2. The cost function of firm 2 is C₂ (x₂) = 20x₂. The cost function of firm 1 is C₁ (x₁) = ₁x₁. Nature chooses C₁ = C₁ = 15 with probability 0.5 and c₁ = CH = 25 with probability 0.5. While firm 1 observes nature's choice, firm 2 cannot observe that choice. Identify the static Bayesian Nash equilibrium.
- C2) Company A is the only supplier of glass in Big Apple City used for tall buildings’ exteriors. Its marginal cost of production is cA=1, and it has no other production costs. The demand for such glass in Big Apple city is QD=2-P. Company B in Jersey City produces the same glass and is considering whether to expand to Big Apple city. If it enters, it needs to get a permit to allow it to be a supplier in the Big-Apple city at a cost of L=0.5, which does not vary with quantity of output, and its marginal cost of production is cB=0.5. If it expands to the Big-Apple city, companies A and B both supply to the market, and the market price P satisfies QA+QB=2-P, where QA is company A’s production level and QB is company B’s. a) If company B expands to the Big-Apple city, what is the resulting price in a Nash equilibrium? b) Company B hires a consulting company to advise whether it should expand to the Big-Apple city. If you’re running the consulting company, what is your advice? Explain…Firm 1 is the leader and Firm 2 the follower in the model of price leadership. Thus, Firms 1 and 2 are the only two producers of a certain good; Firm 1 chooses the price p it will commit to maintain in the market; after having observed Firm 1's decision p, Firm 2 chooses the quantity yz it will produce. Here, the firms cost functions are as follows: c(y;)=3y, +y,?/2 and c2(Y2)= y2?/4. The inverse demand curve is p(Y)=70-Y. What is true about the quantity Firm 2 will produce at the equilibrium of this model? O a. It is between 40 and 42. O b. None of the other answers. It is between 44 and 45. O d. It is between 38 and 39. Oe. It is between 43 and 43.5.The market for widgets is characterized by many buyers but only two producers, A and B. The market demand for widgets is given by: P = 500 − 10QD where QD = total demand for widgets Both producers face the same production cost, which is $120 in fixed cost and a constant variable cost of $20 per widget. Determine the profit-maximizing levels of output by producers A and B if they both choose the quantity of widgets produced simultaneously. What is the profit for each producer? If both producers collude, what is the equilibrium price and quantity? What is the profit for each producer? (You can assume the firms will share the market equally). Compare your answers to parts (a) and (b). Which outcome (collusive or non-collusive) would the producers prefer? Explain. Which outcome (collusive or non-collusive) is a more stable outcome? Explain. Note: Be sure to show your work.
- An industrial firm makes two products, A and B. These products require water resources where they are very scarce. The products they make are unique, and hence they can set the unit price of each product at any value they want to. However, experience tells them that the higher the unit price for a product, the less amount of that product they will sell. The relationship between the unit price and quantity that can be sold is given by the following two demand functions: Assume for simplicity that the unit price for product A is (16 - A) and for product B is (18-2.5B). Suppose the total amount of A and B could not exceed the total amount of Tmax. Where Tmax = 10. Please use "Lagrange Multiplier" method to determine what are the amounts of A and B, and their unit prices, that maximize total revenue (Set the marginal increments at 1).Suppose you are one of two producers of aluminium. You (firm 1) and your competitor (firm 2) announce simultaneously the quantities Q1 and Q2 (in tonnes) and earn the profits Q1*P(Q) and Q2*P(Q), respectively, where P(Q) = 50 – Q is the market price per tonne of aluminium and Q = Q1 + Q2 is the total output. Assume, for simplicity, that there are no production costs. a) Can the collusive agreement to produce Q1 = Q2 = 12 tons of aluminium be sustained in a Nash equilibrium of the one-shot game? Explain your answer. c) Find all pure strategy Nash equilibria when both firms simultaneously announce prices from the set {0,1,…,10} instead of quantities and only the firm with the lowest price p sells 50 - p tonnes (half of this amount when both firms…Two firms, Firm 1 and Firm 2, compete by simultaneously choosing prices. Both firms sell an identical product for which each of 100 consumers has a maximum willingness to pay of $40. Each consumer will buy at most 1 unit, and will buy it from whichever firm charges the lowest price. If both firms set the same price, they share the market equally. Costs are given by c; (q) = 16q;. Because of government regulation, firms can only choose prices which are integer numbers, and they cannot price above $40. Answer the following: a) If Firm 1 chooses pi = 32, Firm 2's best response is to set what price? b) If Firm 2 chooses the price determined in the previous question, Firm 1's best response is to choose what price? c) If Firm 1 chooses pi = 9, Firm 2's best response is a range of prices. What is the lowest price in this range? d) Now suppose both firms are capacity-constrained: Firm 1 can produce at most 42 units, and Firm 2 can produce at most 44 units. If firms set different prices,…