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Consider a Cournot Duopoly model. The inverse demand for their products is given by
P = 200 − 6Q, where Q is the total quantity supplied in the market (that is, Q = Q1 + Q2). Each firm has an identical cost function, given by
TCi = 2Qi, for i = 1, 2.
(a) In the Cournot model, what does each firm choose?
(b) What is the timing of each firm’s decision?
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could you show the work for solving (1) and (2) in part A at the end?
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- OLIGOPOLY 1.- Each of two firms, firms 1 and 2, has a cost function C(q) = 30q; the inverse demand function for the firms' output is p = 120-Q, where Q is the total output. Firms simultaneously choose their output and the market price is that at which demand exactly absorbs the total output (Cournot model).(a) Obtain the reaction function of a firm.(b) Map the function obtained in (a), and graphically represent the Cournot equilibrium in this market.(c) Repeat (b), this time analytically.(d) Now suppose that firm 1's cost function is C(q) = 45q instead, but firm 2's cost is unchanged. Analyze the new solution in the market.(e) Obtain the total surplus, consumer surplus, and industry profits in both cases, and compare. What is the effect of the worsening in firm 1's cost?Consider a Duopoly model, in which two firms decide a quantity sequentially. For the convenience, let's say Firm 1 is a dominant firm and Firm 2 is a follower. The market demand is given by P=110 - 5Q, where Q is the total output (i.e., Q=Q1+Q2). Each firm has an identical cost function, TCi=7Qi, i=1, 2. Each firm maximizes its profit by choosing the quantity. In this Stackelberg equilibrium, Firm 1 will sell __________ units.Consider a Duopoly model, in which two firms decide a quantity sequentially. For the convenience, let's say Firm 1 is a dominant firm and Firm 2 is a follower. The market demand is given by P=110 - 5Q, where Q is the total output (i.e., Q=Q1+Q2). Each firm has an identical cost function, TCi=7Qi, i=1, 2. Each firm maximizes its profit by choosing the quantity. In this Stackelberg equilibrium, Firm 1 will sell how many units.
- Q2. Consider a two-firms Cournot model with constant returns to scale. Assume also that the inverse demand function is P = 100 – 2Q, with marginal cost equal to 20for both firms, where Q = q1 + q2 . c) Calculate Stackleberg equilibrium. Draw a picture of this outcome using best-response functions and isoprofit contours.Consider a Duopoly model, in which two firms decide a quantity simultaneously. The market demand is given by P=50 - Q, where Q is the total output (Q=Q1+Q2). Each firm has an identical cost function, TCi=6Qi, i=1, 2. If Firm 1 believes Q2=10, Firm 1 should sell Q1= ____ units in order to maximize its profit.Consider a homogeneous good industry (such as an agricultural product) with just two firms and a total market demand Q = 400−P, so the inverse demand is P = 400 − Q. Suppose both firms have a constant marginal cost equal to $100 per unit of output and a fixed cost equal to $10,000. One simple way to depict rivalry in a duopoly (2 firms) is the Cournot model. This model is reasonable in agricultural markets where firms choose production (plantings) in advance and the market price is determined later after the crop is harvested. In the Cournot model we imagine that the two firms simultaneously choose their production or quantity, and that demand (market clearing) determines the price given each firms’ quantity. (a) Suppose (hypothetically) that the second firm produces 0 units, and the first firm anticipates this, so the first firm is the only seller. How much will the first firm produce (in this case the first firm acts like a monopolist and sets output where MR = MC)? Hint: The first…
- Consider a homogeneous good industry (such as an agricultural product) with just two firms and a total market demand Q = 400−P, so the inverse demand is P = 400 − Q. Suppose both firms have a constant marginal cost equal to $100 per unit of output and a fixed cost equal to $10,000. One simple way to depict rivalry in a duopoly (2 firms) is the Cournot model. This model is reasonable in agricultural markets where firms choose production (plantings) in advance and the market price is determined later after the crop is harvested. In the Cournot model, we imagine that the two firms simultaneously choose their production or quantity and that demand (market clearing) determines the price given each firms’ quantity. (a) Suppose (hypothetically) that the second firm produces 0 units, and the first firm anticipates this, so the first firm is the only seller. How much will the first firm produce (in this case the first firm acts as a monopolist and sets output where MR = MC)? Hint: The first…Consider a Cournot Oligopoly. One firm has costs C1(Q1) = 12Q1 while the other firm’s cost function is C2(Q2) = 10Q2. The demand for both firms’ products Q=Q1 +Q2 isQD(P)=200−2P. (a) Determine the equilibrium price P, the market shares s1, s2, and the quantities Q1, Q2 produced by both firms. (b) Suppose more firms with the lower cost technology, i.e., with cost function Ci(Qi) = 10Qi enter the market. How many firms with this technology must be in the market such that firm 1’s profit becomes negative. In other words, suppose there is one firm with the high costs, and n firms with the low costs. At what level n will profits of the high-cost firm be negative?Suppose that two Japanese companies, Hitachi and Toshiba, are the sole producers (i.e., duopolists) of a microprocessor chip used in a number of different brands of personal computers. Assume that total demand for the chips is fixed and that each firm charges the same price for the chips. Each firm’s market share and profits are a function of the magnitude of the promotional campaign used to promote its version of the chip. Also assume that only two strategies are available to each firm: a limited promotional campaign (budget) and an extensive promotional campaign (budget). If the two firms engage in a limited promotional campaign, each firm will earn a quarterly profit of $14 million. If the two firms undertake an extensive promotional campaign, each firm will earn a quarterly profit of $11 million. With this strategy combination, market share and total sales will be the same as for a limited promotional campaign, but promotional costs will be higher and hence profits will be lower.…
- Consider a standard Cournot oligopoly with n = 2k identical firms (with k ≥ 1), an inverse demand P(X), and a cost function C(x) with no fixed costs. Consider only two possible cases: C(x) convex and C(x) concave. Assume that there is always a unique symmetric equilibrium with per firm output xk and profit pk. Assume that there are k two-firm mergers. a. List all conditions on the primitives of the model such that each firm is better o¤ after these mergers. Explain your answer (no proof needed). b. Can such a set of mergers be expected to take place without regulatory intervention? Explain. c. Under what conditions can such a set of mergers increase social welfare?Consider a Duopoly model, in which two firms decide a quantity simultaneously. The market demand is given by P=120 - 3Q, where Q is the total output (i.e., Q=Q1+Q2). Each firm has an identical cost function, TCi=12Qi, i=1, 2. If Firm 1 believes Q2=12, Firm 1 should sell Q1= _____ units in order to maximize its profit.Consider duopoly model with firm 1 and firm 2. Firms have constant marginal costs, c_1 = c_2 = 10. Demand functions are given by equations: Q_1= (7*100) - 2*P_1 + P_2 Q_2 = (7*100) + P_1 - 2*P_ 2 Note that * signifies the multiplication sign. Firms play a simultaneous moves game where each store chooses its own price. Find each firms’ best response functions. Draw the best response functions of each firm. Label the graph properly. Is this a game of strategic substitutes or strategic complements? Why? Find the pure-strategy Nash equilibrium of the game. Find the profits each firm receives.
