Suppose that two duopolists are producing given differentiated products (like Hyundai and GM cars in the...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Suppose that two duopolists are producing given differentiated products (like Hyundai and GM cars in the automobile industry). The market demands for each firm's products are given by ₁ = 12 - 2p₁ + P₂ and Y₂ = 12 - 2p₂ + P₁, respectively. Assume, for simplicity, that each firm does not pay any cost to produce any positive quantity of output. (1) Suppose two firms compete in the Bertrand way. That is, two firms choose their prices simultaneously and independently. Write down the normal form of the game. (2) Find the Nash equilibrium for the game. (3) Now suppose firm 1 is the price leader of the industry. Find the subgame perfect equilibrium of the price leadership game. (4) Suppose that two firms compete in Cournot fashion. That is, two firms choose their quantities simultaneously and independently. Write down the normal form of the new game. (5) Find the Nash equilibrium for the new game. (6) Now suppose two firms compete in Stackelberg fashion and firm 1 is the leader of the industry. Find the subgame perfect equilibrium of the quantity leadership game. (7) Now suppose two firms decide to collude and form a cartel. Find the joint-profit maximizing price-quantity combination for the cartel. (8) What is the market equilibrium in this industry if two firms behave like firms in the competitive market? (9) Compare all the equilibria you found above. Is it always better for a firm to be an industry leader than to be a follower? (10) Now suppose two firms have to play the Bertrand duopoly game in part (1) for ten periods without discounting. What is the subgame perfect equilibrium outcome in the new game? How many subgame perfect equilibria are there in this game? (11) Now suppose two firms have to play the Bertrand game repeatedly infinitely many times. Can they support the monopoly allocation found in (7) by choosing an appropriate subgame perfect equilibrium? If so, write down a trigger strategy equilibrium which supports it. What is the minimal discount factor (6) in this case? (12) Answer question (11) again when firms play the repeated Cournot game. Suppose that two duopolists are producing given differentiated products (like Hyundai and GM cars in the automobile industry). The market demands for each firm's products are given by ₁ = 12 - 2p₁ + P₂ and Y₂ = 12 - 2p₂ + P₁, respectively. Assume, for simplicity, that each firm does not pay any cost to produce any positive quantity of output. (1) Suppose two firms compete in the Bertrand way. That is, two firms choose their prices simultaneously and independently. Write down the normal form of the game. (2) Find the Nash equilibrium for the game. (3) Now suppose firm 1 is the price leader of the industry. Find the subgame perfect equilibrium of the price leadership game. (4) Suppose that two firms compete in Cournot fashion. That is, two firms choose their quantities simultaneously and independently. Write down the normal form of the new game. (5) Find the Nash equilibrium for the new game. (6) Now suppose two firms compete in Stackelberg fashion and firm 1 is the leader of the industry. Find the subgame perfect equilibrium of the quantity leadership game. (7) Now suppose two firms decide to collude and form a cartel. Find the joint-profit maximizing price-quantity combination for the cartel. (8) What is the market equilibrium in this industry if two firms behave like firms in the competitive market? (9) Compare all the equilibria you found above. Is it always better for a firm to be an industry leader than to be a follower? (10) Now suppose two firms have to play the Bertrand duopoly game in part (1) for ten periods without discounting. What is the subgame perfect equilibrium outcome in the new game? How many subgame perfect equilibria are there in this game? (11) Now suppose two firms have to play the Bertrand game repeatedly infinitely many times. Can they support the monopoly allocation found in (7) by choosing an appropriate subgame perfect equilibrium? If so, write down a trigger strategy equilibrium which supports it. What is the minimal discount factor (6) in this case? (12) Answer question (11) again when firms play the repeated Cournot game.
Expert Answer:
Answer rating: 100% (QA)
1 The normal form of the game can be written as Firm 1 Price P1 0 P2 P3 Quantity Q1 Q2 Q3 Q4 Firm 2 Price P1 P2 P3 0 Quantity Q1 Q2 Q3 Q4 2 The Nash equilibrium for this game is where both firms set t... View the full answer
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
Mop and Broom Manufacturing has tracked the number of units sold of their most popular mop over the past 24 months. This is shown. (a) Develop a linear trend line for the data. (b) Compute a...
-
Mop and Broom Manufacturing has tracked the number of units sold of their most popular mop over the past twenty-four months. This is shown. Develop a linear trend line for the data. (Round your...
-
Generate forecasts for months 7 24 using a six period and a three period moving average Use MAD to compare the forecasts Month Sales Forecast 6 month Mooving Average Forecast 3 month Mooving Average...
-
A semicircular plate of radius r, oriented as in the figure, is submerged in fluid of density 68 lb/ft 3 so that its diameter is located at a depth of m feet. Calculate the force on one side of the...
-
Starting in 2005, a chain of events, including the war in Iraq, Hurricane Katrina, and the expanding economies in India and China, lead to a sharp increase in fuel costs. As a result, the U.S....
-
Determine the forces in all bars of the trusses. Indicate tension or compression. 22.5'- E 60 kips 36 kips B D +7.5 15 15- 36 kips 20'
-
Identify at least three grounds a party may have for objecting to interrogatories.
-
Jones Group has been generating stable after-tax return on equity (ROE) despite declining operating income. Explain how it might be able to maintain its stable after-tax ROE.
-
Prof provided the answer key but REQUIRES showing the solution/analysis using Excel functions/formulas STEP-BY-STEP. Thank you. Answer Key : PJ% = .2974, or 29.74% PK% = .2333, or 23.33% Question :...
-
Andrew Miller recently opened a new doughnut shop near Cornwall, England. He sells doughnuts in packets of four each. The average price of a doughnut box is $4.00 and each box costs Andrew an average...
-
"Angle of elevation" refers to an angle formed by a horizontal line and a line joining an observer's eye to an object above the horizontal line. A person is standing 15 meters away from a building...
-
9. A hiker travels 1.50 km in a direction 34.0 east of north. She then changes direction to go 6.50 km at 62.0 south of east. What is her displacement from start to finish? /5 ** Explain the steps...
-
DEERE & COMPANY STATEMENTS OF CONSOLIDATED INCOME For the Years Ended October 30, 2022, October 31, 2021, and November 1, 2020 (In millions of dollars and shares except per share amounts) Net Sales...
-
Cherokee Incorporated is a merchandiser that provided the following information: Amount Number of units sold 13,000 Selling price per unit $ 18 Variable selling expense per unit $ 2 Variable...
-
Ramirez Company installs a computerized manufacturing machine in its factory at the beginning of the year at a cost of $45,300. The machine's useful life is estimated at 10 years, or 403,000 units of...
-
For each entry below make a correcting entry if necessary. If the entry given is correct, then state "No entry required". (Credit account titles are automatically indented when the amount is entered....
-
y" y = 0; y(t) = et ; y2(t) = cosht
-
An investor sells a European call on a share for $4. The stock price is $47 and the strike price is $50. Under what circumstances does the investor make a profit? Under what circumstances will the...
-
WAI, the company in Problem 8, has received the following additional customer orders shown here. You must determine which of the orders the company can accept. If the company must reject any orders,...
-
Business continues to grow at Clean Machine. Melanie has decided to use a second car washing bay, staffed with another identical two-person team. Clean Machine will now use a single-line,...
-
Explain why companies do capacity requirements planning.
-
The rotor shown in Fig. 9.44 (a) is balanced temporarily in a balancing machine by adding the masses \(m_{1}=m_{2}=90 \mathrm{~g}\) in the plane \(A\) and \(m_{3}=m_{4}=90 \mathrm{~g}\) in the plane...
-
A turbine rotor is run at the natural frequency of the system. A stroboscope indicates that the maximum displacement of the rotor occurs at an angle \(229^{\circ}\) in the direction of rotation. At...
-
The cylinders of a four-cylinder in-line engine are placed at intervals of \(300 \mathrm{~mm}\) in the axial direction. The cranks have the same length, \(100 \mathrm{~mm}\), and their angular...
Study smarter with the SolutionInn App