An industry contains two firms and the inverse demand function for the firms output is P-180-30, where is the total oups ose that firm I's cost and marginal cost functions are C(q)- 30q; and MC(q)-30, while firm 2's cost and marginal cost functions -q² and MC(q)-2q2 Determine each firm's Nash equilibrium output. Determine each firm's profit at the Nash equilibrium output.
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- 3. The (market) inverse demand function for a good is as follows: 12- 2q if q = [0,6], if q> 6. Pp(q) = { 12 There are two firms: N = {1,2}. Each firm's cost function is such that producing a units of the good incurs cost 2r. We consider the Cournot competition of the two firms. That is, they simultaneously choose their quantities. The firms are profit-maximizers. (1) Find a Nash equilibrium. (2) What is the size of the deadweight loss incurred by the Duopoly, compared to the competitive equilibrium allocation?an Problem 5. Consider following price competition between 2 firms. Both firms choose their prices (p, and p2) simultaneously and the market demand function given by q 10-min{p₁, P2}. Assume production costs are 0 for both firms. Thus, the payoff (profit) function for firm i is: u.(Pi. Pj) (10-P.)Pi (10-pi)Pi 2 Notice that this function is not continuous in pi 1 if Pi Pj7. 2 firms are engaged in Bertrand competition. They each face the following cost curve C(Q) = 3Q² +3. Market demand is representated by D(P) = 50 - P. What is the Bertrand Nash equilibrium? Why is this a Nash Equilibrium?
- The behaviour of a firm depends on the features of the market in which it sells its product(s) and on its production costs. The following diagrams illustrate the possible short-run equilibrium positions of two firms. Firm A MC AC Po AR=MR Quantity Both firms employ the marginal approach to determine profit in the short-run. However, differ with regards to certain market structure criteria: The number of firms in the market The nature of the good or service sold Ease of entry for new competitors into the market Control that the firm has over price In scenario 7, the possible short-run equilibrium positions of two firms are given. With reference to "Firm A", answer the following question. 9.1 Identify the market structure of Firm A. 9.2 Using the marginal approach to determine profit, is Firm A making a short-run profit or loss? Explain your answer with reference to the provided diagram. OFocus Unil revenue and cost5. N - Σ Consider a Cournot model in which N firms compete with each other by setting quantities. The market inverse demand function is P = a i=1 qi, where a > 0 and q; is the quantity of firm i. Firm i's cost function is quadratic: q, where c₂ > 0. (a) Suppose N 2. Find the Nash equilibrium. Show which firm produces more in the equilibrium and explain your result. (b) = Suppose N≥ 2 and ci = c for all i. Find the Nash equilibrium. Show whether the firms produce more or less than the constant marginal cost case where the cost function is cqi, with a>c>0.7. A honey farm is located next to an apple orchard and each acts as a competitive firm. Let the number of apples produced be measured by A and the amount of honey produced by H. The cost functions of the two firms are CH (H) = H²/100 and C₁(A)=4-H. The price of honey is £2 and the price of apples is £3. 100 a. If the firms operate independently, what is the equilibrium number of apples and amount of honey produced? Are these amounts the Pareto-efficient? Explain. b. Suppose the two firms merge. What is the profit maximising amount of apples and honey that the merged firm produce? Explain. c. What is the socially optimum amount of honey and apples? Discuss methods to induce the independent firms to produce the socially optimal number of apples and amount of honey. Explain.
- 2) Assume that there are 2 firms producing an identical product. Both firms have the same total cost function TC(q) =q2. The inverse demand function for the firms' output is p=120 Q, where Q is the total output and p is price. 1. What are the equilibrium price, output and profits of each firm if they are competing with each other? (Hint: Consider the equilibrium in a Cournot game.) 2. What happens if they form a cartel? Calculate the equilibrium price, output, and profits for the cartel? 3. If a single firm cheated, what would its output and profits be, assuming the other firm maintains the cartel price? Calculate the new outputs and profits for bath firms: 4. Discuss why it is hard to enforce a cartel. Explain using words. DO NOT do any calculations. DO NOT draw any graphs. 5. What can the cartel members do to enforce the cartel agreement? Propose a method. Describe the method using words. DO NOT do any calculations. DO NOT draw any graphs.There are only two driveway paving companies in a small town, Asphalt, Inc. and Blacktop Bros. The inverse demand curve for paving services is ?= 2040 ―20? where quantity is measured in pave jobs per month and price is measured in dollars per job. Assume Asphalt, Inc. has a marginal cost of $100 per driveway and Blacktop Bros. has a marginal cost of $150. Answer the following questions: Determine each firm’s reaction curve and graph it. How many paving jobs will each firm produce in Cournot equilibrium? What will the market price of a pave job be? How much profit does each firm earn?a) Suppose that the two firms engage in Cournot competition. Find the equilibrium price PNE in the industry, the equilibrium outputs QANE and QBNE, as well as the profits πANE and πBNE, for each firm. b) Suppose the marginal cost for firm B increases from $20 to $140, while everything else remains unchanged. Find the new equilibrium price PNE in the industry, the new equilibrium outputs QANE and QBNE, as well as the new profits πANE and πBNE for each firm. c) Suppose that, in addition to the marginal cost increase from $20 to $140 from sub question b), firm B also has a fixed cost of $2500, out of which $2100 may be recouped if it shuts down; everything else remains unchanged. In this case, what will firm B’s optimal output be? (Justify your answer.) What will firm A’s profit be?
- Two firms facing a demand curve are P = 50 -5Qwhere Q = Q1 + Q2. The cost functions of the two firms are:C1(Q1) = 20 + 10Q1C2(C2) = 10 + 12Q2Based on this information:a. Suppose both companies have entered the industry, then what is the price?and the profit-maximizing amount for the two firms under conditionsperfectly competitive market?b. What is the quantity, price and profit of the two firms ifcompanies collude in pricing?c. What are the quantities, prices, and profits of the two firms if theydo the Cournot strategy, and draw the reaction curves of the twothe company?d. What are the quantity, price, and profit of the two firms if theycarry out the stakeberg strategy.Here is a market with three firms: 1, 2, and 3. The demand curve is P=100-Q. There is no fixed cost but the marginal cost 10 for all firms. Firm 1 is a leader firm so that it decides the quantity Q1 first. Then two firms respectively decide their quantities Q2 and Q3 simultaneously. 1) At an equilibrium (SPE), Q1 is Q2=Q3= 2) At the equilibrium, (the market quantity) Q= and (the market price) P= 3) The profit of firm 1 is while the profit of firm 2 and 3 respectively iswo firms A and B produce an identical product (Note: Industry Output = Q). The firms have to decide how much output qA and qB (Note: qA = Firm A Output; qB = Firm B Output) they must produce since they are the only two firms in the industry that manufacture this product. Their marginal cost (MC) is equal to their average cost (AC) and it is constant at MC = AC = X, for both firms. Market demand is given as Q = Y – 2P (where P = price and Q = quantity). Select any value for X between [21 – 69] and any value for Y between [501 – 999]. Using this information, calculate the Industry Price, Industry Output, Industry Profit, Consumer Surplus and Deadweight Loss under each of the following models: (a) Cournot Model error_outlineHomework solutions you need when you need them. Subscribe now.arrow_forward Question Two firms A and B produce an identical product (Note: Industry Output = Q). The firms have to decide how much output qA and qB (Note: qA =…