Consider two identical firms (firm 1 and firm 2) that face a linear market demand curve. Each firm has a marginal cost of zero and the two firms together face demand: P = 150 - 0.25Q, where Q = Q1 + Q2. Find the Cournot equilibrium quantity and market price for each firm.

Firm 1 and firm 2 compete with each other by choosing quantities. The market demand is given by P(Q) = ( 300 − Q, if Q < 300) (0, otherwise), where Q = q1 + q2. Firm 1 has a cost function C1(q1) = 40q1, and firm 2 has a cost function C2(q2) = 50q2. Answer the following questions. 1. Assume the game lasts only one period. Compute the equilibrium price, quantities and profits for both firms. 2. If firm 1 becomes the monopolist on this market, what quantities will firm 1 choose to produce? Denote this quantity as QM. 3. One possible strategy is that each firm produces QM 2 . Would the resulting outcome be better for both firms (Pareto improvement)? Explain why this is not the equilibrium in the one period game. 4. Assume this game is infinitely repeated and the interest rate in this economy is r. For what values of r the strategy in (3) is sustainable by using a “Grim Trigger” strategy?

Consider a duopoly with homogenous goods where Firm 1 has the following production function:  Q1 = F1(L,K) = L1/2 K1/2, where Q and K are measured in units and L in hours. Firm 2 uses labour and capital as well but has a different production function, given by Q2 = F2(L,K) = L1/3 K2/3. You may assume that the market for labour and capital is perfectly competitive and the current wage rate is £40 and the rental rate on capital is £10. Both firms sell their products on the same market with inverse demand function       P = 52 – (Q1 + Q2), where P is measured in pound sterling. Which production function(s) exhibit(s) decreasing returns to scale?  Suppose Firm 1 wishes to produce 6 units. What is the cost minimising input mix for Firm 1?  Suppose Firm 2 wishes to produce 4 units. What is the cost minimising input mix for Firm 2?  Assume both firms now have the option to produce either 4 units or 6 units. We will consider the situation where both firms simultaneously, but independently,…

Question 3:Suppose the inverse demand for a good is given by P = 50 – 4Q, where Q is the totalquantity supplied by all firms in the market. Suppose each firm in the market has a constantmarginal cost of 18.Q3 a) Assume the market consists of two firms that set their quantities simultaneously.Calculate the duopoly levels of production and the equilibrium price. Q3 b) Now assume firm 1 chooses its production level before firm 2 does. What will be theequilibrium quantities, price and profits in this case?Q3 c) Now instead suppose that the two firms compete over prices rather than quantities.What will be the equilibrium price and profits of firms 1 and 2 in this case? Finally, if firm 1manages to lower its marginal cost to 14, what will be the new equilibrium price, quantitiesand profits?

Suppose Giocattolo of Italy and American Toy Company of the United States are the only two firms producing toys for sale in the U.S. market. Each firm realizes constant long-term costs so that the average total cost (ATC) equals the marginal cost (MC) at each level of output. Thus, MCo = ATCO is the long-term market supply schedule for toys. Suppose Giocattolo and American Toy Company operate as competitors, and the cost schedules of each company are MCo = ATCO = $10. On the following graph, use the grey point (star symbol) to identify the competitive market equilibrium. Then, use the green triangle (triangle symbols) to identify consumer surplus in this case. Note: Select and drag the point from the palette to the graph. Dashed drop lines will automatically extend to both axes. Then select and drag the shaded region from the palette to the graph. To resize the shaded region, select one of the points and move to the desired position. ? PRICE (Dollars per toy) 20 18 16 14 10 00 6 4 2 0…

There are two identical firms in an industry, 1 and 2, each with cost function , i = 1,2. The industry demand curve is P = 100 − 5X where industry output, X, is the sum of the two firms’ outputs (X1 + X2). (a) If each firm makes its output decisions on the assumption that the other will not react to its choices (the Cournot assumption), what is the equilibrium output for each firm? What is the equilibrium price? (b) Suppose that each firm takes it in turn to choose its level of output, on the assumption that the other’s output level is fixed. Would the process of adjustment be stable? (c) Suppose that firm 1 introduces a cost-saving innovation, so that its cost curve becomes C1 = 8X1. Firm 2’s cost curve and the industry demand curve are unchanged. What happens to the equilibrium quantity produced by each firm and to market price?  

Suppose the inverse market demand for manufactures is P(Q) = A – Q, where P and Q denote price and total goods produced and the parameter A denotes the size of the domestic market. Suppose any firm has a cost function, c(q) = cq, where A > c. Suppose there are two firm in the market which produce q1 and q2, where Q = q1 + q 2                                                                                                                                                    a. Solve for the Cournot equilibrium levels of output (Q*), price (P*) and markups.                                                                                       b. What is the impact of an increase in market size, A, on Q*, P* and markups when there are two firms? Provide some intuition for these predictions.                                                                                                                                                                                                   c.…

Consider an industry comprised of three identical firms faced with a linear cost function given by: C(qi) = cqi; for i = 1; 2; 3. Let inverse market demand be given by: P(Q) = a - bQ; where Q = q1 + q2 + q3.a. Compute the Cournot equilibrium; that is, find prices, quantities, and profits.b. Suppose that firms 1 and 2 merge, converting the market into a duopoly consisting of the “superfirm” and firm 3. Compute the new Cournot equilibrium. Once again find prices, quantities, and profits.c. Suppose that all three firms merge. Compute quantities, prices, and profits for the cartel solution.d. Suppose that firm 1 and 2 represent two members of OPEC – Saudi Arabia and Venezuela, say – while firm 3 is a non-OPEC oil exporting country – Russia, say. Describe the dynamics of OPEC. (Hint: re-interpret the solution to part 2, as 1 firm deviating from the fully cartelized solution. Is it convenient to have a partial cartel?)

Consider an industry with two identical firms (denoted firm 1 and 2) producing a homogenous good. Firms compete in quantities. Firm 1 has a constant marginal cost of 20. Firm 2 has a constant marginal cost of 80. Demand in the industry is given by D(p) = 380 - p. Let q1 and 92 denote the quantities of firm 1 and 2, respectively. Derive the Nash equilibrium in quantities. What is the total production in this industry?

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.