There are two firms in a homogenous product market described by the demand function P(q1,q2)%3D131-(1/5)(q1+q2), and both firms have marginal costs of 50. Firms choose once and simultaneously quantities. How much does firm 1 produce in equilibrium?
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- please help me with the last question. Thank you1. 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…
- 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?In this question you will work out a model of price competition (Bertrand competition) with differentiated products, i.e., when the two firms that compete produce slightly different products. Consider two price-setting firms, 1 and 2, each with marginal cost c, that produce goods, 1 and 2, that are imperfect substitutes. Some customers are loyal to a particular variety of the good so both firms can still have positive sales when they set different prices. Demand for firm 1's output, q1, as a function of the prices of both products, p1 and p2 , is given by q1 = 2 – 3p1 + 3p2. And the demand for firm 2's output, q2, is given by q2 = 6 – 2p2 + P1. a. How can we tell, by looking at the demand functions above, that in the preferences of consumers the two products are substitutes? Explain your answer.. b. Write this strategic situation as a simultaneous game between the two firms, specifying the set of players, the set of alternatives and the preferences of each firm. Write down the profit…Answer 1, 2 and 3, see the question properly.
- Economics: Industrial Economics Question: In a market that operates under quantity competition there are 2 firms (Cournot duopoly). The inverse demand function is P = A - B Q. The cost structure of firm 1 is given by C1(q1) = F1 + c1 q1 and that of firm 2 is given by C2(q2) = F2 + c2 q2. Prior to competing, the two firms can engage in research at levels (x1, x2) respectively in order to lower their marginal costs. As a result, marginal costs are c1 = c - x1 - β2x2 and c2= C - x2 - β1 X1. where β1 = β2 > ½. Finally, the research costs are F1 = a1 (x1)^2 /2 and F2 = a2 (x2)^2 /2, where a1 > 0 and a2> 0. 1. The Nash Equilibrium research levels are Choices: A. Higher than the cooperative research levels for both firms. B. Higher than cooperative research levels for firm 1 but lower for... C. Lower than the cooperative research levels for both firms. D. Higher than cooperative research levels for firm 2 but lower for... 2. An increase in the value of a2 would Choices: A.…Compute the equilibrium prices, quantities, and profits for both firms. Consider now the first stage.2
- 5. N - Σ Consider a Cournot model in which N firms compete with each other by setting quantities. The market inverse demand function is P = a i=1 qi, where a > 0 and q; is the quantity of firm i. Firm i's cost function is quadratic: q, where c₂ > 0. (a) Suppose N 2. Find the Nash equilibrium. Show which firm produces more in the equilibrium and explain your result. (b) = Suppose N≥ 2 and ci = c for all i. Find the Nash equilibrium. Show whether the firms produce more or less than the constant marginal cost case where the cost function is cqi, with a>c>0.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?)COURSE: MICROECONOMICS - Cournot Model:In the market for a given good there are only 2 firms satisfying the demand, and their respective total cost functions respond to the form: CTi = 10Qi + 5 and the demand is estimated to be: P = 31 - QIf the decision variable for both firms is that the quantity they will produce and realize will be decided simultaneously it is asked to:(a) calculate the profit and reaction function of each firmb) graph market equilibriumc) calculate the profits that both companies will obtain in equilibrium