let the market demand be given by Q = 120- Assume for simplicity that each firm operate total cost. Find each firm's Cournot Nash equilibrium output. 91=30, 92=30 91=32, 92=32 O 91=40, 92=40
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- 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).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 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…What is the duopoly Nash-Cournot equilibrium if the market demand function is Q = 500 - 10p and each firm’s marginal cost is 5¢ per unit?
- 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).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.
- Little Kona is a small coffee company that is considering entering a market dominated by Big Brew. Each company's profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price: True or False: Only Little Kona has a dominant strategy in this game. True or False Which of the following outcomes represent a Nash equilibrium in this case? Check all that apply. Big Brew maintains a high price and Little Kona enters. a.Big Brew maintains a low price and Little Kona enters. b.Big Brew maintains a high price and Little Kona does not enter. c.Big Brew maintains a low price and Little Kona does not enter. Big Brew threatens Little Kona by saying, “If you enter, we're going to set a low price, so you had better stay out.” True or False: Little Kona should not believe the threat. True or False If the two firms could collude and agree on how to split the total profits, what outcome would they…How do I determine values for Y that have dominant strategy? What is the Nash equilibirum? If the Market demand for two companies is P=120-Q and marginal cost is 20. How will the payoff matrix with strategies for each that show cournot equilibirum quantity/half of the monopoly quantity look? How do i solve for the nash equilibrium?Firms A and B operate in a market with inverse demand given by p = 160 - (q_{A} + q_{B}) Their total cost functions are C_{A}(q_{A}) = q_{A} ^ 2 / 2 and C_{B}(q_{B}) = q_{B} ^ 2 / 2 , respectively. The firms compete in quantities (Cournot competition). Denote by q_{A} ^ C and q_{B} ^ C the Nash equilibrium quantities in this game. What are q_{A} ^ C and q_{B} ^ C Hint: Again, note that I gave you the total cost function for each firm, not the marginal costs. (a) q_{A} ^ C = 24 q_{B} ^ C = 24 (b) q_{A} ^ C = 60 q_{B} ^ C = 30 (c) q_{A} ^ C = 40 q_{B} ^ C = 40 (d) q_{A} ^ C = 20 q_{B} ^ C = 20 (e) q_{A} ^ C = 30 q_{B} ^ C = 30
- Consider two firms that compete according to the Cournot model. Inverse demand is P (Q) = 16 − Q. Their cost functions are C (q1) = 2q1 and C (q2) = 6q2 (a) Solve for Nash equilibrium quantities of each firm (b) Suppose firm 2 becomes more inefficient and its cost function changes to C (q2) = xq2 where x > 6. How large must x be to cause firm 2 to not want to produce anything in equilibrium?Consider a situation where two firms, 1 and 2, compete by choosing prices simultaneously. They can either compete (charge a low price) or cooperate (collude, charging a high price). The firms play this competition game repeatedly and indefinitely, using a grim trigger strategy to incentivize cooperation. They use the same interest rate, i , to discount future payoffs. Payoffs are $4,050 when both firms cooperate and $3,600 when they compete. If one firm charge a low price while the other charges a high price, the firm charging the low price gets $7,200, and the other gets zero. Which of the following statements is correct?(a) For any i < 1/7 the firms will cooperate(b) For any i > 1/8 the firms will cooperate(c) For i = 1/9 the firms will be indifferent between cooperating or competing(d) There is no way to sustain cooperation in this scenarioHow would the Cournot equilibrium change in the airline example if American's marginal cost were $90 and United's were $180? The demand the duopoly quantity-setting firms face is Q=339−p with an inverse demand function of p=339−1qA −1qU where qA is the quantity produced by American and qU is the quantity produced by United. The Cournot-Nash equilibrium occurs where qA equals ? enter your response here and qU equals? enter your response here. (enter numeric responses using integers) Furthermore, the equilibrium occurs at a price of ? (round your answer to the nearest penny)
