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3) Assuming both firms behave as Bertrand duopolists, solve for p1 and p2. Show all work. Graph the reaction functions.
Demand for firm 1’s product: Q1 = 160 – p1 +(1/2)p2
Demand for firm 2’s product: Q2 = 160 – p2 + (1/2)p1
And TC1 = 20Q1; TC2 = 20Q2
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- 2) Demand for firm 1’s product: Q1 = 100 – p1 +(1/2)p2 Demand for firm 2’s product: Q2 = 100 – p2 + (1/2)p1 And TC1 = 10Q1; TC2 = 10Q2 Assuming both firms behave as Bertrand duopolists, solve for p1 and p2. Show all work. Graph the reaction functions.(Multi-Variable Unconstrained Optimization - pete in a market with inverse demand given by p = 10-2g1 - 292. Firm 1 faces cost function C = 2q1 and Firm 2 faces cost function C2 = 4q2. How much should each firm produce? What will be the market price? Two Cournot duopolists com- %3D %3DTwo Cournot competitors face inverse demand p = 50-Q, where Q = 9₁ +92 is the total output of firms 1 and 2. Both firms have marginal cost of 2. What are the equilibrium output levels q₁ and 92? 16 and 16 25 and 25 20 and 9 36 and 3
- 1. Consider two duopolists who each have a constant marginal cost c = e2 = 3 and face inverse demand P = 15 – Q,where Q = Q1 + Q2 is the total output of both firms. 1. Find the Cournot equilibrium quantity for each firm, the resulting market price, and the profits for each firm. 2. Find the Stackelberg equilibrium quantities for each firm, and the price, and the profits for each firm supposing that Firm 1 is the industry leader. 3. Suppose that Firm 2 figures out a way to lower its marginal cost to ez = 0 while firm 1 still has a marginal cost equal to 1: c = 3. How does this affect the Cournot equilibrium quantities, price, and profits? 4. How does this affect the Stackelberg equilibrium (with Firm 1 still as the leader) quantities, price, and profits?2. Stackelberg Firms 1, 2 and 3 compete in quantities. The inverse market demand is given by p = 400 (91 +92 +93), where 91, 92 and q3 are the quantities produced by firms 1, 2 and 3, respectively. The marginal cost for firm 1 is c₁ = 20, and the marginal cost for both firm 2 and firm 3 is 40. The order of play is as follows: Firm 1 first sets a quantity q₁. Then, firms 2 and 3 observe q₁ and simultaneously set q2 and 93. Each firm sets its quantity to maximize its own profits. (a) Let us first consider the optimal action of firm 2. Given a value q₁ initially set by firm 1 and a value of q3 set by firm 3, what is the value of q2 that maximizes the profits of firm 2? Hint: Your answer should provide q2 in terms of 91 and 93. (b) Notice that, after firm 1 sets q1, a subgame starts, in which firms 2 and 3 simultaneously set q2 and 93. Given 91, find the values of q2 and q3 that firms 2 and 3 must set in a Subgame Perfect Nash Equilibrium. Hint: Your answer should provide q2 and q3 in…6. Three oligopolists operate in a market with inverse demand given by P(Q) = a - Q, where Q = 9₁ +92 +93 and q; is the quantity produced by firm i. Each firm has a constant marginal cost of production, c, and no fixed cost. The firms choose their quantities as follows: (1) firm 1 chooses q₁ ≥ 0; (2) firms 2 and 3 observe q₁ and then simultaneously choose q2 and 93, respectively. What is the subgame-perfect outcome?
- Suppose a country's mobile phone industry is supplied by only two firms (i.e. an oligopoly). Explain how the presence of two firms affects the price elasticity of demand of each firm's output.Consider the following Stackelberg duopoly. Both firms produce a homogenous good. Firm 1 chooses how much to supply first. Firm 2 chooses how much to supply after observing the quantity supplied by firm 1. The market demand is Q= 100 – 4 P. For firm i, the total cost of production is TC(q) =5q,+2. What is the optimal quantity supplied by firm 12 10 20 30 40 QUESTION 6 Consider the following Stackelberg duopoly. Both produce a homogenous good. Firm 1 chooses how much to supply first. Firm 2 chooses how much to supply after observing the quantity supplied from firm 1. The market demand is Q= 100 - 4P. For firm i, the total cost of production is TC(q) =5q,+2. What is the market clearing price? O 10 O 15 20 O 25Help me please
- Gary's Gas and Frank's Fuel are the only two providers of gasoline in their town. Below is the demand schedule for the market of gasoline. Assume that the cost of producing gasoline is 3 per gallon (AC=3, FC-D0). Suppose that the two producers collude (split production and profits evenly), what are the joint profits of these two firms? Q demanded (in gallons) 10 12 4 Market price (in dollar) $22 $20 $18 $16 $14 $12 $10 $8 $6 $0 O $27 O None of these options is correct. $55 O $72 O $36 50 00 3)10. Suppose an industry has a duopoly structure. Duopolist 1 has a cost function given by: C₁(y₁) = (y₁)² for output y₁20. Duopolist 2 has a cost function given by: C2(y2) = 12y2 for output y2 20. Denoting total output produced in the industry by y = (y₁ + y₂) the inverse demand function for the good produced in the industry is given by: p = 100 - y (a) Find the reaction function of each duopolist. (b) Using (a), obtain the output levels that will be produced in a Cournot-Nash equilibrium, and the price level in such an equilibrium. Illustrate your solution in (b) above in a diagram.The inverse demand curve for a product is p = 20 - 0/5, where Q is the total volume brought to the market. At present two firms serve this market. Firm 1 has constant marginal costs of 5, while Firm 2 has constant marginal costs of 2. Both firms have fixed costs of 100. a) Assuming the fixed costs are sunk, calculate the equilibrium quantities, price and profits for the two firms. b) Now assuming the fixed costs are not sunk, calculate the equilibrium quantities, price and profits for the two firms. c) Discuss any competition issues raised by your answer in part b). d) Discuss the theoretical relevance of sunk costs to competition in markets.