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Exam 11: Imperfect Competition

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Question 51

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The market inverse demand curve for thrust bearings is P = 15 - 1.5Q, where Q is measured in hundreds of bearings per day and P is the price per bearing. The marginal cost is $3. Suppose two firms, which are Bertrand competitors, produce identical thrust bearings for this market. In this case, the market price is $____.

A) 9
B) 7
C) 5
D) 3

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Question 52

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Consider two firms engaged in Bertrand competition with differentiated goods and zero marginal costs. Firm A's demand curve is q_A = 60 - 0.50P_A + 0.40P_B. Firm B's demand curve is q_B = 72 - 0.50P_B + 0.40P_A. In a Nash equilibrium, approximately how much profit does Firm A earn?

A) $4,800
B) $3,210
C) $6,040
D) $5,588

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Question 53

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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, each firm produces ____.

Crush and Frenzy both produce motorized bicycles, which are identical in all aspects. The total demand in this market is for Q motorized bicycles. The price of Crush's bicycle is P_C and the price of Frenzy's bicycle is P_F. If the firms are engaged in Bertrand competition, which of the following statements is TRUE? I. If P_C > P_P, Crush sells Q bicycles. II. If P_C = P_F, Crush sells 0.50Q bicycles. III. If P_C < P_F, Crush sells zero bicycles.

Suppose two colas compete in a Bertrand market structure with differentiated products. Demand for the first cola is given by where p₁ is price for cola 1 and p₂ is the price for cola 2. Demand for the second cola is The costs of providing the colas are C₁ = q₁ and C₂ = q_2, respectively. The second cola firm will charge $____ for its cola.

(Figure: Market for Two-Firm Industry III) According to the figure, which of the following statements is TRUE? I. If Firm B expects Firm A to charge $3, Firm B should charge $5.50. II) If Firm A expects Firm B to charge $6, Firm A should charge $7. III) The Nash equilibrium is for each firm to charge the same price.

The output of firms is determined simultaneously in _____ competition but sequentially in _____ competition.

An industry faces the demand curve Q = 400 - 4P, where each firm produces an identical good at a constant marginal cost of $10. The Bertrand equilibrium price is $____ for each firm.

Majestic Manicures operates in a monopolistically competitive market. Its inverse demand curve is P = 85 - 4Q, where Q is the number of daily manicures and P is the price per manicure. The total cost of providing manicures is TC = 13Q and marginal cost is $13. a. What is Majestic Manicures' profit-maximizing output level and price? b. What is Majestic Manicures' profit? c. What will happen to Majestic Manicures' demand curve in the long run? d. What is the expected long-run equilibrium price for manicures?

In a Bertrand competition, with differentiated goods in a market structure of two firms, firm A's first-order condition can be expressed as:

(Figure: Cartel I) If two firms selling identical products act as a cartel and split the market evenly, each firm will earn profits of _____. Why is quantity collusion not considered a Nash equilibrium?

The fudge makers compete in a Bertrand market structure with differentiated products. The demand curve for Fudge Factory is given by where p_F is the price for fudge at Fudge Factory and p_C is the price at Chocolate Corner. The demand curve for Chocolate Corner is given by Fudge Factory's cost is C_F = 5q_F and Chocolate Corner's cost is C_C = 5q_C. Use calculus for the following. a. Identify Fudge Factory's profit function and its reaction function. b. Identify Chocolate Corner's profit function and its reaction function. c. Identify the equilibrium prices at the two fudge makers.

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. Gotcha's profit-maximizing quantity is ____.

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. a. Calculate each firm's reaction function. b. How much output does each firm produce? c. What is the market price? d. How much profit does each firm 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 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 = 0.75q₂ respectively. The equilibrium price for style 2 is $____.

In a Cournot market structure with two firms, firm A's second-order condition sufficient for maximization is:

The inverse market demand curve is P = 170 - 4Q. Two firms in this market are evenly splitting the output. Each firm produces the product at a constant marginal cost of $10. Which of the following statements is TRUE? I. If one firm produces 2 more units of output, its profits will rise to $864. II. If neither firm cheats, each firm will earn a profit of $800. III. If one firm produces 3 more units of output, the other firm's profits will fall to $680.

In a Cournot market structure with two firms, firm A's reaction function gives:

The Nash equilibrium in Bertrand competition with identical goods:

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. Shop 1 produces ____ to maximize profit.