Two firms compete by choosing price. Their demand functions are Q, = 20 - P, + P2 and Q2 = 20 + P1 - P2. where P, and P2 are the prices charged by each firm, respectively, and Q, and Q2 are the resulting demands. Note that the demand for each good depends only on he difference in prices; if the two firms colluded and set the same price, they could make that price as high as they wanted, and earn infinite profits. Marginal costs are zero. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.) Each firm will charge a price of $. (Enter a numeric response rounded to two decimal places.) Each firm will produceunits of output. n turn, each firm will earn profit of $ Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will each sell, and what will be profits?

Consider two firms, referred to as firms 1 and 2, who compete in a market by choosing quantities produced and face the following inverse demand: P(Q) 10-20 Each firm has a marginal cost of production of $4.00. Suppose these firms collude by agreeing to produce quantities to maximize their joint profits. Firm 1 sticks to the agreement, but firm 2 does not. If firm 2 can secretly change its produced quantity, how much would it produce?

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Two firms sell substitutable products; the market price is: P = 90-Q, where Q Q₁ + Q2 is the total market quantity, which consists of Q1₁ (the quantity produced by Firm 1) and Q2 (the quantity produced by Firm 2). The firms choose their quantities simultaneously. Firm 1's costs are C₁ 6Q₁ + Q². Firm 2's costs are C₂ = Q². = O Which is the payoff function for Firm 2? O π₂ = 90Q₂ - 2 Which is the best response function for Firm 1? O π₂ = 90Q₂ - Q²². πT2 π₂ = 45 - Q² Q₁ Q₂₁ 2 O π₂ = 45 - 1²/20₁². Q₁ Q₁ 3 = 16. ²/Q²-Q₁2. = 32- 2- 1/1/202₂. 3 Q₁ = 45. Q1 = 40 + ²/Q₂₁ 2.2. = 10- -

Suppose the airline industry consisted of only two firms: American and Texas Air Corp. Let the two firms have identical cost functions, C(q) = 28q. Assume that the demand curve for the industry is given by P = 100 - Q and that each firm expects the other to behave as a Cournot competitor. Calculate the Cournot-Nash equilibrium for each firm, assuming that each chooses the output level that maximizes its profits when taking its rival's output as given. What are the profits of each firm? (Round all quantities and dollar amounts to two decimal places.) When competing, each firm will produce units of output.

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,…

Consider two oligopolists, each choosing between a “high” and a “low” level of production. Given their choices of how much to produce, their profits will be as follows: Explain how firm B will reason that it makes sense to produce the high amount, regardless of what firm A chooses. Then explain how firm A will reason that it makes sense to produce the high amount, regardless of what firm B chooses. How might collusion assist the two firms in this case?  

A homogenous-good duopoly faces an inverse market demand function of p = 150 − Q. Assume that both firms face the same constant marginal cost, MC1 = MC2 = 30. Calculate the output of each firm, the market output, and the market price in a Nash-Cournot equilibrium Re-solve part (a) assuming that the marginal cost of firm 1 falls to MC1 =20 Explain what will happen to each firm’s output, the market output, and the market price if the two firms can collude (e.g., form a cartel)

Consider a duopoly where firms compete in prices and firms do not have any capacity constraints. Market demand is P(Q)=45-4Q, and each firm faces a marginal cost of $9 per unit. How much is each firm's total variable cost if firms equally divide the market at Nash equilibrium?

Suppose two firms, A and B, have a cost function of ?(??) = 30??, for ? = ?, ?. The inverse demand for the market is given by ? = 120 − ?, where Q represents the total quantity in the market, ? = ?? + ??. 1. Solve for the firms’ outputs in a Nash Equilibrium of the Cournot Model. 2. Let Firm A be the first mover, and Firm B be the second mover. Solve for the firms’ outputs in a SPNE of the Stackelberg Model.