3. Consider the Bertrand competition with differentiated products. Firm A's demand is qA = 124PA + 4PB and firm B's demand is qв = 18 - 6pB + 4PA. The marginal cost of firm A is 4 while the marginal cost of firm B is 3. What are the prices the firms will charge?
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- Given the level of demand below, what is the marginal revenue of the first unit of production? Price Quantity 25 1 22 2 18 3 15 4 12 5 Group of answer choices $12 $10 $6 $252.- Each of two firms, firms 1 and 2, has a cost function C(q) = 1 2 q; the demand function for the firms' output is Q = 1.5-p, where Q is the total output. Firms compete in prices. That is, firms choose simultaneously what price they charge. Consumers will buy from the firm offering the lowest price. In case of tying, firms split equally the demand at the (common) price. The firm that charges the higher price sells nothing. (Bertrand model.) (a) Formally argue that there could be no equilibrium in prices other than p1 = p2 = 1 2. (b) Solve the same problem, but this time assuming that firms compete in quantities.Now, suppose that firm 1 has a capacity constraint of 1/3. That is, no matter what demand it gets, it can serve at most 1/3 units. Suppose that these units are served to the consumers who are willing to pay the most. Thus, even if it sets a price above that of firm 1, firm 2 may be able to sell some output. (c) Obtain the (residual) demand of firm 2 (as a function of its own…2.- Each of two firms, firms 1 and 2, has a cost function C(q) = 0.5q; the demand function for the firms' output is Q = 1.5 - p, where Q is the total output. Firms compete in prices. That is, firms choose simultaneously what price they charge. Consumers will buy from the firm offering the lowest price. In case of tying, firms split equally the demand at the (common) price. The firm that charges the higher price sells nothing. (Bertrand model.) (a) Formally argue that there could be no equilibrium in prices other than p1 = p2 = 0.5 (b) Solve the same problem, but this time assuming that firms compete in quantities.Now, suppose that firm 1 has a capacity constraint of 1/3. That is, no matter what demand it gets, it can serve at most 1/3 units. Suppose that these units are served to the consumers who are willing to pay the most. Thus, even if it sets a price above that of firm 1, firm 2 may be able to sell some output. (c) Obtain the (residual) demand of firm 2 (as a function of its own…
- Price Quantity Total Cost $25.00 0 $130 $24.00 10 $275 $23.00 20 $435 $22.50 30 $610 $22.00 40 $800 $21.60 50 $1,005 $21.20 60 $1,225 Sharon's Day Spa began to offer a relaxing aromatherapy treatment. The firm asks you how much to charge to maximize profits. The demand curve for the treatment is given by the first two columns in the table above. The total costs are provided in the third column. For each level of output, calculate total revenue, marginal revenue, average cost, and marginal cost. What is the profit-maximizing level of output for the treatments and how much will the firm earn in profits?Type out the correct answer ASAP with proper explanation 1.Assume inverse demand of P = 20 - 0.2Q where P is the market price and Q is the market demand. Also assume that there are 2 firms who both have a marginal cost of 2. (a) In a Cournot context, what is the equilibrium price, market quantity, and profit for each firm? (b) In a Bertrand context, what is the equilibrium price, market quantity, and profit for each firm?Answer the given question with a proper explanation and step-by-step solution. Suppose inverse demand is given by the following: P = 40 - 0.5Q There are two firms each with the same marginal cost. Marginal Cost is 10. Under Cournot competition, what is the output for firm one? 10 20 25 30
- Suppose you are the marketing manager for Fruit of the Loom. An individual's inverse demand for Fruit of the Loom women's underwear is estimated to be P = 25 − 3Q (in cents). If the cost to Fruit of the Loom to produce an item of women's underwear is C(Q) = 1 + 4Q (in cents), compute the profit Fruit of the Loom will earn by charging the optimal block price. a. $108.50 b. $0.73 c. $1.37 d. $136.50There are two sellers who compete by choosing quantity (Cournot). The inverse demand is P = 120 − Q. Each firm’s cost is 30Q. There are no fixed costs. In this market, firms decide how much to produce, and then the price is determined by the market (think of fishing boats, for example). Suppose that Firm 2 produces 30. Then the inverse demand facing Firm 1 is P = 120 − 30 − Q1 = 90 − Q1. This implies that Firm 1’s marginal revenue is 90 −2Q1. How much will Firm 1 produce to maximize its profits? Suppose that Firm 1 produces 30. Then the inverse demand facing Firm 2 is P = 120 − 30 − Q2 = 90 − Q2. This implies that Firm 2’s marginal revenue is 90 −2Q2. How much will Firm 2 produce to maximize its profits? If both firms produce 30, what are both firms’ profits? Suppose the buyers in this market proposed that the firms compete in a price game rather than a quantity game. For example, they might suggest that sellers compete in a price auction before production takes place. The winner…Suppose the firm faces a demand curve for its product P=32-2Q, and the firm's costs of production and marketing are C(Q)=2Q^2. Find the following; a. The formula for profit piein terms of Q b. The first order condition(FOC) and the second order condition(SOC) for maximum total revenue c. The price and quantity that maximizes total revenue, and the corresponding value of the total revenue. d.The FOC and SOC for maximum profit e. The price and quantity that maximize profit and the corresponding value of profit. f. What would the competitive price and quantity be, assuming C(Q)=2Q^2 represented the industry cost function
- Consider an industry with the market demand Q=130-P. Firms' marginal cost and average cost are the same, MC=AC=10. What is the competitive equilibrium quantity Qc, the competitive equilibrium price Pc, and the competitive equilibrium profit cUnder perfect competition, each firm is a price taker. Suppose a single seller in the wheat market. The company produces and markets wheats at a Price = $38 per container. The firm’s total costs are given as: TC = 10 +2Q + 3Q2 A. Find the Firm’s marginal cost? Show your steps, including graphs. Review additional resources? Hint: See the rules for differentiation B. is the firm’s demand curve? Show it on a graph and label the axes showing P and Q C. What level of output should the firm produce? Hint: Set P = MC and solve for Q. Use a graph to show your answers as well D. What is the firm Fixed Cost? Why? Also, use a graph to support your answer. E. What price should the firm charge? Why?Consider a differentiated products market with two Bertrand competitors. Firm’s 1 demand curve is given by Q1= 20 - P1 +P2 and firm’s 2 demand curve is given by Q2= 20 – P2 +P1. Firm 1’s marginal cost is £2 and firm 2’s marginal cost is £20. What is the equilibrium price of firm 1? a. 28 b. 14 c. 11 d. 34