4. Duopoly quantity-setting firms face the market demand p = 150 – q1 – 92. Each firm has a marginal cost of $60 per unit a) What is the NE? b) What is the Stackelberg equilibrium when Firm 1 moves first?
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![4. Duopoly quantity-setting firms face the market demand p = 150 – q1 – 42. Each firm
has a marginal cost of $60 per unit
a) What is the NE?
b) What is the Stackelberg equilibrium when Firm 1 moves first?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6871a655-6df9-491d-9e6a-d916a0d3d66e%2Facd278b8-be3e-4111-b9cb-2d43cc9ffef9%2Fhapl1cf_processed.jpeg&w=3840&q=75)
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- 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)a) Suppose that the two firms engage in Cournot competition. Find the equilibrium price PNE in the industry, the equilibrium outputs QANE and QBNE, as well as the profits πANE and πBNE, for each firm. b) Suppose the marginal cost for firm B increases from $20 to $140, while everything else remains unchanged. Find the new equilibrium price PNE in the industry, the new equilibrium outputs QANE and QBNE, as well as the new profits πANE and πBNE for each firm. c) Suppose that, in addition to the marginal cost increase from $20 to $140 from sub question b), firm B also has a fixed cost of $2500, out of which $2100 may be recouped if it shuts down; everything else remains unchanged. In this case, what will firm B’s optimal output be? (Justify your answer.) What will firm A’s profit be?2) Assume that there are 2 firms producing an identical product. Both firms have the same total cost function TC(q) =q2. The inverse demand function for the firms' output is p=120 Q, where Q is the total output and p is price. 1. What are the equilibrium price, output and profits of each firm if they are competing with each other? (Hint: Consider the equilibrium in a Cournot game.) 2. What happens if they form a cartel? Calculate the equilibrium price, output, and profits for the cartel? 3. If a single firm cheated, what would its output and profits be, assuming the other firm maintains the cartel price? Calculate the new outputs and profits for bath firms: 4. Discuss why it is hard to enforce a cartel. Explain using words. DO NOT do any calculations. DO NOT draw any graphs. 5. What can the cartel members do to enforce the cartel agreement? Propose a method. Describe the method using words. DO NOT do any calculations. DO NOT draw any graphs.
- 1. marginal costs e, = c, = c, = 20. The inverse demand function is given by P = 100 - Q. where Q = q, + 4: + 93- Consider a market with three firms (i - 1, 2, 3). which have identical a) Identify the reaction functions for each firm and compute the Cournot equilibrium, i.e., the market price and quantity. b) What happens to the market price if all three firms merge compared to part (a)?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.QUESTION 1A) Two cournot competitors face inverse demand P = 50 - Q. Where, Q = q1+q2, is the total output of firms 1 and 2. What are the equilibrium output levels for q1 and q2, If firm 1 marginal cost is 1, and firm 2's marginal cost is 12? QUESTION 1B. Continuing with the inverse demand, P = 50 - Q, if each firm has a marginal cost of 0, what is the difference between the equilibrium price under Cournot competition and under Bertrand competition? b. C. d. a. The Cournot price is higher than the Bertrand price by 50. The Cournot price is lower than the Bertrand price by 25. The Cournot price is higher than the Bertrand price by 50/3. Equilibrium prices under Cournot and Bertrand are the same, so the difference is zero.
- 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 25Gary'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 zero per gallon (AC-D0, FC-0). Suppose that the two producers collude (split production and profits evenly), what are the profits of each firm? Q demanded (in gallons) 4 6 7 8. 10 Market price (in dollar) $22 $20 $18 $16 $14 $12 $10 $8 $6 $0 $70 $72 O $36 O $76 $64 3. 2. 1,Here is a market with three firms: 1, 2, and 3. The demand curve is P=100-Q. There is no fixed cost but the marginal cost 10 for all firms. Firm 1 is a leader firm so that it decides the quantity Q1 first. Then two firms respectively decide their quantities Q2 and Q3 simultaneously. 1) At an equilibrium (SPE), Q1 is Q2=Q3= 2) At the equilibrium, (the market quantity) Q= and (the market price) P= 3) The profit of firm 1 is while the profit of firm 2 and 3 respectively is
- 5. Consider a market where there are two mers with inverse demand func- consu tions p(q1) = 10 -91 and p(q2) = 5-92. (a) Suppose there is a single firm with inverse supply function p(q) = }q. Find the competitive equilibrium. (b) Find the elasticity of demand and supply at the equilibrium. (c) Suppose instead that there are three firms with the identical inverse sup- ply function given in part (a). Find the competitive equilibrium.Two firms face the same inverse demand curve: P= 370– q, – 92 . Both firms have the same constant marginal cost: MC = 10. (a) %3D if both firms choose their output levels simultaneously, how much profits and consumer surplus will be earned in equilibrium? (b) Firm 1 is offered the following deal: by paying Z it can either (i) acquire a new technology that lowers its marginal cost to zero or (ii) have to opportunity to produce output before firm 2. Which option would it take and what is the maximum Z it would be willing to pay?Q3. There are two firms selling differentiated products. Firm A faces the following demand for his product: e, = 20 – -P, + -P, 2. Firm B faces the following demand: 1 P. +-P, 2. 0, = 220- Assume that the marginal cost is zero both for firm A and firm B. What are the equilibrium prices of a simultaneous price competition? What would the equilibrium prices be if A is the leader and B is the follower?
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