Consider the differentiated goods Bertrand price competition model where firms A and B produce similar goods and sell them at pA and pB. The demand for each firm’s product is given by qA =60−2pA +pB andqB =60–2pB +pA ,and there are NO costs of producing either good (all costs are 0). (a)Calculate the (Bertrand) equilibrium prices and the net profits of each firm (b) Now suppose that -instead of competing to maximize their own individual profits- the firms decide to “collude” and set prices pA and pB to maximize their joint profits (sum of their profits). What would be each firm’s optimal price and net profits? Compare these prices and profits with what you found in (a) (greater/smaller/the same?).

Consider an industry with 2 firms engaging in quantity competition and facing the market demand function as Q = 200 – 4P. Suppose each firm bears the same cost production as C(q) = 100 + 0.25q? when producing q units. a. Derive Firm 1's best response function, q1(q2), against Firm 2's output level choice, q2. b. Find the equilibrium output level of Firm 1 at the N.E. equilibrium. c. Find the deadweight loss caused by the duopoly. d. Find again the equilibrium output level of Firm 1 if it acts as the leader while Firm 2 as the follower.

A large number of firms enter the Swedish market for the game Padel. For simplicity assume that they all act as price takers and let the cost function for each of them be given by C(q)=1000+0.4*q² where q is the number of customers served. a) In the long run free entry should drive profit to zero. At this point p=MC=ATC. Intuitively why is this the case?   b) The condition in c) implies that in a free entry equilibrium with firms that have the same cost function each firm's production will be given by the lowest point in the average total cost curve. How much does each firm produce in the free entry equilibrium? What is price in this equilibrium? (Hint: You can either differentiate the expression for average cost to determine its minimum or you can look for the minimum point using your graph in b).   c) Assume that overall demand is given by Q-1200-2*P. How many firms will there be in equilibrium?

Two firms, A and B, sell the same good X in a market with total demand Q = 100 – P. The two firms compete on quantities and decides how much to produce simultaneously. Firm A cost function is C(qA) = 40qA. Firm B cost function is C(qB) = 60qB. 1. Find the best reply functions of both firms and represent them in a graph. 2. Find the quantity produced by each firm in a Nash equilibrium. 3. Find the firms and consumers surplus. 4. Compare the surplus of firms found above with the surplus arising when both firm cooperate to sustain a monopoly outcome. 5. Assume now that A and B compete as in a Stackelberg model. A chooses first and B chooses after observing the choice of A. Find equilibrium quantities produced by each firm and the market equilibrium price.

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Consider an industry with N firms that compete by setting the quantities of an identical product simultaneously. The resulting market price is given by: p = 1000 − 4Q. The total cost function of each firm is C(qi) = 50 + 20qi  . (a) Derive the output reaction of firm i to the belief that its rivals are jointly producing a total output of Q-i . Assuming that every firm produces the same quantity in equilibrium, use your answer to compute that quantity. (b) Suppose firms would enter (exit) this industry if the existing firms were making a profit (loss). Write down a mathematical equation, the solution to which would give you the equilibrium number of firms in this industry. You don’t have to solve this equation.

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?

Q2: Firms A and B are two firms supplying products in two separate differentiated goods markets. Equations (1) and (2) give the total cost functions of the two firms: - Firm A: TC - 2Q -(1) - Firm B TC - 10 + 2Q - -(2) Each firm has the ability to produce a maximum quantity of 80,000 units in ten bateches of 8,000. Use the information given about firms A and B and appropriate diagrams/figures to explain how the equilibrium for both firms will change if a rival company increases its prices.

Suppose that the market consists of 6 identical firms , that the market demand curve is P=200-2Q and that each firm's marginal cost is 32. The cournot equilibrium quantity per firm is q=_____________________ and the equilibrium quantity in the market is Q=______________________. The market price is P=$______________ per unit.

wo 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 =…