Consider a duopoly where firms compete for market share by setting prices. The firms produce differentiated products and face the following demand functions where q is output and P is the price in dollars.               q1 = 100 – 2P1 + 2P2           Demand Function for Firm 1               q2 = 120 – 4P2 + P1             Demand Function for Firm 2 Suppose that firm 1 is able to produce output at a constant marginal cost of $30 and that firm 2 is able to produce output at a constant marginal cost of $20. Both firms operate with no fixed costs. Derive the best response function for firm 1. Derive the best response function for firm 2.

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?

Two firms compete on price every year. The inverse demand function each firm faces depends on which firm has chosen the lowest price that year. The one that did captures the entire market. If, on the other hand, both prices are the same then they split the market evenly. Consumers round up prices to the nearest integer. For the firm with the lowest price p, demand is given by: q = 24-2p: Marginal costs are constant and equal to $4 for both firms. a. Define the Normal form of the stage game and determine the Nash Equilibria, the Cooperative Equilibrium and the Optimal Deviation from cooperation. b. For the once repeated (2 stages) game, determine if a Nash Equilibrium exists that improves on simply playing the (better) Nash Equilibrium of the stage game twice c. For the infinitely repeated game, determine what the interest rate would have to be to prevent the firms from cooperating. d*. Determine the relation between the interest rate and the number of punishment periods in a…

In the Cournot equilibirum, what is the market price and units produced by firm 1 and firm 2?

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 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.

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.