Suppose two firms compete as Cournot Oligopolists. The profit functions of these two firms are IT = (150 – 91 - 92)91 – 20q1 T2 = (150 – 91 – 92)92 – 2292 Which generate the following best response functions. 150 – 20 1 91 = 2 150 – 20 1 92 = 2 a. Plot these reaction functions in a graph with q, on the horizontal axis and q, on the vertical axis. b. Derive, I want to see your work, the Nash equilibrium outcome of this game. c. How does the Nash equilibrium change if the demand curve shifts out, a bigger intercept on the demand equation.
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- Two firms in a duopolistic industry produce outputs 91 and q₂ at a constant and equal marginal cost of 2. The inverse market demand curve is given by p = 14 - (q_{1} + q_{2}) for price per unit p. Consider the Stackelberg duopolistic game where firm 1 is an incumbent monopoly acting as a leader and firm 2 is a potential entrant that faces a fixed cost F = 16 if it enters and competes in the market. What is the outcome of the Stackelberg leader-follower game in this case? 92 =Consider an oligopolistic industry with N competing firms. Suppose that these firms have no fixed costs and that they all have the same marginal costs. Each firm must choose what quantity to produce independently of each other, and all firms must choose at the same time. If we increase the number of firms in this industry (to for example N+1), the market price a.increases b.decreases c.remains unchanged d.becomes nil e.none of the aboveJoe and Rebecca are small-town ready-mix concrete duopolists. The market demand function is Qd = 10,000 – 100P, where P is the price of a cubic yard of concrete and Qd is the number of cubic yards demanded per year. Marginal cost is $25 per cubic yard. Suppose that Joe and Rebecca compete in quantities and competition in this market is described by Cournot model. What are Joe and Rebecca’s Nash equilibrium outputs? What is the resulting price? What do they each earn as profit? How does the price compare to the marginal cost? Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand function is Qd = 10,000 – 100P, where P is the price of a cubic yard of concrete and Qd is the number of cubic yards demanded per year. Marginal cost is $25 per cubic yard. Suppose that Joe and Rebecca compete in quantities and competition in this market is described by Cournot model. What are Joe and Rebecca’s Nash equilibrium outputs? What is the resulting price? What do they each…
- 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 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?Three firms produce identical products and compete in a market where the inverse demand function is P(q1, q2, q3) = 78 − q1− q2− q3. Each has a per-unit cost of 14 and zero fixed cost. They simultaneously choose quantities. In scenario (a), find the Nash equilibrium of this game and let A = firm 2's profit in the Nash equilibrium. In scenario (b), assume that the firms form a cartel, i.e., they act as a monopoly and split the profit evenly. If the total quantity produced by the cartel is Q, then the inverse demand is P(Q) = 78 - Q. Let B = firm 2's profit in the cartel. Calculate the value of A - B and enter your answer in the box below. Please round your answer to 3 decimal places (e.g., write 4/3 as 1.333).
- Several firms collude in an oligopoly where the Industry Supply is given by QS = 6 - 5P and Industry Demand is given by, QD = 5P – 5. If the probability that this collusion will continue is given by (1/P*), what is the minimum number of firms required to break the tacit collusion?Three oligopolistic firms ("1", "2" and "3") conduct quantity competition in a certain market. The interactions between them take place as follows: firm 1 defines its production quantity, which is immediately observed by firms 2 and 3; then, firm 2 makes its decision on how much it will produce, and only after observing the decisions of firms 1 and 2 does firm 3 finally make its respective choice. Furthermore, the total costs of firms 1, 2 and 3 correspond respectively to c₁(q₁) = 10q₁, c₂(q₂) = 8q₂ and c₃(q₃) = 2q₃, and the firms face a (inverse) demand given by p(Q) = 110 - Q (where Q = q₁ + q₂ + q₃). Based on this information, determine what will be the total amount produced by the firms in the (single) ENPS for that game. (Note: the correct answer is an integer.)Assume that you are a Cournot duopolist in a market where the aggregate demand curve is P = 600 − 4Q. Your production cost is $15 per unit. Your opponent decides to produce and sell 100 units. What is your best response?
- 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.Dan Murphy's (DM) and BWS are the only two liquor chains in Australia that hold the rights to sell a popular new beer named Victoria Sweeter (VS). Both Dan Murphy's and BWS are contemplating between charging a high price ($60 per case) or a low price ($40 per case). The payoff matrix below shows all possible scenarios and outcomes for the two firms. BWS Charge $60 per case Charge $40 per case Dan Murphy's (DM) Charge $60 per case DM: $30,000 profitBWS: $25,000 profit DM: $13,000 profitBWS: $38,000 profit Charge $40 per case DM: $45,000 profitBWS: $12,000 profit DM: $19,000 profitBWS: $20,000 profit * Profits reported in the above table are monthly figures on the Victoria Sweeter (VS) beer only. Required: (a) Identify the dominant strategy for Dan Murphy's in this game. Show a detailed analysis to prove why it is the dominant strategy (b) Identify the non-cooperative* Nash equilibrium for this game. (* Non-cooperative means that each firm makes their…Suppose that two firms produce mountain spring water and the market demand for mountain spring water is given as follows: P= 254 - 91 - 92 Firm 1 and Firm 2 have a MC = 50 a) Find the Cournot-Nash equilibrium price and quantity of each firm. b) Assume now that firm 1 becomes the Stackelberg leader. What will be the market price, output by each firm? Compared to part a, who gains? c) If Firm 1 chooses a quantity, then Firm 2 chooses a quantity (having observed Firm 1's quantity), then Firm 1 has an opportunity to revise its quantity (having observed Firm 2's quantity), then payoffs are determined, does either firm stand to gain relative to the case of simultaneous quantity choice? Why or why not? (hint: there is no need to do any calculation here).