Consider a local market where there are two local firms, A and B with the following cost functions producing homogenous good: CA=q₁² +50q4-98² CB=2q8² +70qB+0.25q² where q and qв represent the production levels of firm A and firm B, respectively. The market price of the good produced by two firms is equal to 150. Furthermore, suppose that the two firms act as price-takers (because firms from other locations also serve it). a) Briefly describe the relationship between the two firms (Hint: study the cost structure). b) Find the production levels and the profits of the two firms, assuming that they operate independently.

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,…

1. Consider a market where there are only two firms that produce a homogeneous product. The two firms face the direct market demand curve given Q = 15-p, where Q = 9₁ +92 and 9₁ and q2 are the quantities of firm 1 and firm 2, respectively. Suppose firm 1's total cost is C₁ = 9₁ and firm 2's total cost function is C₂ = 2q2. Suppose that the two firms act independently and choose their outputs simultaneously as in the Cournot model. Show the basis and briefly explain what is going on as you answer each of the following questions. Your mark will depend upon the correctness of your basis and explanation. 1. What is the equation of the demand curve faced by firm 1? What is the equation of the demand curve faced by firm 2? Find the output reaction function of each firm. 2. 3. Find the Nash-Cournot equilibrium quantity that each firm will produce. 4. At the Nash-Cournot equilibrium, at what price does each firm sell its output? 5. Find the consumer surplus, producer surplus at the…

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…