Exam 11: Imperfect Competition

The inverse demand for tacos is given by P = 10 - 0.02Q, where P is the price per taco and Q is the total number of tacos brought to market. There are two taco shops in the local market. Shop 1's cost function is given by C₁ = 0.01q₁², where q₁ is the number of tacos it brings to market. Shop 2's cost function is given by C₂ = 0.01q₂², where q₂ is the number of tacos it brings to market. Assume the two shops compete by setting output (Cournot). Let Q = q₁ + q₂. In equilibrium, the market output is ____.

Dagger and Jackson offer different types of kayak tours, competing on price. Dagger faces q_D = 1,000 - 20p_D + 5p_J and constant marginal costs of $30. Jackson faces q_J = 1,000 - 20p_J + 5p_D and constant marginal costs of $45. Graph the reaction function for each firm and indicate the Nash equilibrium.

A Nash equilibrium occurs when:

In monopolistic competition, the long-run equilibrium price _____ marginal cost because _____.

Answer the following questions. a. What are the assumptions of Bertrand competition with identical goods? b. Suppose that two firms are engaged in Bertrand competition with identical goods and each firm has a marginal cost of $33. What is the Nash equilibrium? c. In Bertrand competition with identical goods, Firm A charges $50 and Firm B charges $40. What are the firms' market shares?

(Table: Car Dealerships I) Payoffs: Anastasia's Monthly Profit, Dasha's Monthly Profit If state law prevented car dealerships from opening on Sunday, Anastasia's Hyundai would earn _____, and Dasha's Nissan would earn _____.

Suppose that Etsy (an e-commerce site focused on handmade or vintage items) necklace vendors compete in a Bertrand market structure with differentiated products. Demand for style 1, produced by vendor 1, is given by where p₁ is the price of style 1 and p₂ is the price of style 2, produced by vendor 2. Demand for style 2 is The costs of providing these necklaces are C₁ = q₁ and C₂ = 0.75q_2, respectively. a. Identify vendor 1's profit function. b. Identify vendor 2's profit function. c. Identify vendor 1's reaction function. d. Identify vendor 2's reaction function. e. Identify the equilibrium price for each necklace.

An industry faces the demand curve Q = 400 - 4P, where each firm produces an identical good at a constant marginal cost of $10. What are the Bertrand equilibrium price and quantity?

Suppose that Mystic Energy and E-Storm are the only two producers of hydrogen fuel cells. The market inverse demand curve for hydrogen fuel cells is P = 1,300 - 0.08Q, where Q is the number of fuels cells per month and P is the price per fuel cell. The marginal cost is constant at $500. Acting as a cartel, the owners of Mystic Energy and E-Storm agree to evenly split the market output. In this case, E-Storm produces ____.

Suppose that Mystic Energy and E-Storm are the only two producers of hydrogen fuel cells. The market inverse demand curve for hydrogen fuel cells is P = 1,300 - 0.08Q, where Q is the number of fuels cells per month and P is the price per fuel cell. The marginal cost is constant at $500. Acting as a cartel, the owners of Mystic Energy and E-Storm agree to evenly split the market output. In this case, E-Storm earns a profit of $ ____.

Two firms are in Bertrand competition with differentiated goods. Firm A faces the demand curve q_A = 40 - P_A + 0.50P_B. What is Firm A's total revenue?

Gotcha, the only seller of stun guns, faces the inverse market demand curve P = 400 - 12Q, where Q measures the number of stun guns per day and P is the price per stun gun. The marginal cost is constant at $64. Suppose a new firm, Ouchy, enters the stun gun market. Ouchy's marginal cost is also constant at $64. Gotcha and Ouchy agree to form a cartel and evenly split the market output. The market price in this case is $____.

Two firms that are engaged in Stackelberg competition face the market inverse demand curve P = 100 - 2Q, where Q is the total market output comprising Firm 1's output, q₁, and Firm 2's output, q₂. Each firm produces the product at a constant marginal cost of $22. If Firm 2's reaction function is q₂ = 22 - 0.5q₁, what is Firm 1's (the first-mover's) inverse demand curve?

Ney Inc. and ARN Parts are the only two producers of bulldozer bucket teeth. The owners of the two firms conspire to charge a monopoly price, with each firm serving half the market. The market inverse demand curve is P = 1,000 - 10Q, where Q measures the daily number of sets of bulldozer bucket teeth and P is the price per set. The marginal cost of production for either firm is constant at $200, and fixed costs are zero. Suppose Ney Inc. cheats on the cartel agreement by producing an additional 10 sets of bucket teeth per day (while ARN Parts adheres to the cartel agreement). In this case, Ney Inc. will earn a profit of $_____.

Consider a two-firm oligopoly facing a market inverse demand curve of P = 100 - 2(q₁ + q₂), where q₁ is the output of Firm 1 and q₂ is the output of Firm 2. Firm 1's marginal cost is constant at $12, while Firm 2's marginal cost is constant at $20. In Cournot equilibrium, how much output does each firm produce?

Ney Inc. and ARN Parts are the only two producers of bulldozer bucket teeth. The owners of the two firms conspire to charge a monopoly price, with each firm serving half the market. The market inverse demand curve is P = 1,000 - 10Q, where Q measures the daily number of sets of bulldozer bucket teeth and P is the price per set. The marginal cost of production for either firm is constant at $200, and fixed costs are zero. Suppose Ney Inc. cheats on the cartel agreement by producing an additional 10 sets of bucket teeth per day (while ARN Parts adheres to the cartel agreement). In this case, ARN Parts will earn a profit of $_____.

In Bertrand competition with differentiated goods, the demand curve for bags of Wilson tennis balls is q_W = 80 - 4P_W + 2P_D , and the demand curve for bags of Dunlop tennis balls is q_D = 80 - 2P_D + P_W. The two firms both have zero marginal costs. How many bags of tennis balls does each firm produce?

The inverse demand for shampoo is given by P = 30 - 0.03Q, where P is the price per bottle in dollars and Q is bottles brought to market in hundreds. There are two manufacturers in the local market. Firm 1's cost function is given by C₁ = 0.05q₁², where q₁ is the number of bottles it brings to market. Firm 2's cost function is given by C₂ = 0.03q₂², where q₂ is the number of bottles it brings to market. The two firms are Cournot competitors who set output so that Q = q₁ + q₂. Use calculus for the following. a. Write firm 1's profit function and identify firm 1's reaction function to firm 2's output. b. Write firm 2's profit function and identify firm 2's reaction function to firm 1's output. c. Identify the equilibrium price and output of each firm.

Which of the following statements is TRUE? I. The gain in profit from cheating on a cartel agreement is greater if there are more firms in the cartel. II. In a cartel, compliant firms will earn rising profits as cheating firms lower prices by expanding output. III. If a firm cheats on a cartel agreement, the loss in profit to the compliant firm will be smaller in a two-firm cartel than a four-firm cartel.

Two firms are producing identical goods in a market characterized by the inverse demand curve P = 60 - 2Q, where Q is the sum of Firm 1 and Firm 2's output, q₁ + q₂. Each firm's marginal cost is constant at $12, and fixed costs are zero. Answer the following questions, assuming that the firms are Cournot competitors. In this case, the market price is $____.