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7.8: Problem Sets

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    47917
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    Problem Set 1. Profit Maximization for the Monopolist of Monopolistically Competitive Firm

    Exercise \(\PageIndex{1}\)

    Given the following:

    The inverse demand is P = 100-2Q.

    Marginal cost is 20.

    Average variable cost is 20.

    Assume a profit maximizing monopolist or monopolistically competitive firm.

    Find the quantity, price and profits above fixed costs (FC).

    Answer

    The quantity is 20 units.

    The price is 60 dollars.

    Profits above FC are 800 dollars.

    Exercise \(\PageIndex{2}\)

    Given the following:

    The inverse demand is P = 200-2.5Q.

    Marginal cost is 20.

    Average variable cost is 20.

    Assume a profit maximizing monopolist or monopolistically competitive firm.

    Find the quantity, price and profits above fixed costs (FC).

    Answer

    The quantity is 36 units.

    The price is 110 dollars.

    Profits above FC are 3240 dollars.

    Exercise \(\PageIndex{3}\)

    Given the following:

    The inverse demand is P = 300-3Q.

    Marginal cost is 30.

    Average variable cost is 30.

    Assume a profit maximizing monopolist or monopolistically competitive firm.

    Find the quantity, price and profits above fixed costs (FC).

    Answer

    The quantity is 45 units.

    The price is 165 dollars.

    Profits above FC are 6075 dollars.

    Exercise \(\PageIndex{4}\)

    Given the following:

    The inverse demand is P = 400-4Q.

    Marginal cost is 40.

    Average variable cost is 40.

    Assume a profit maximizing monopolist or monopolistically competitive firm.

    Find the quantity, price and profits above fixed costs (FC).

    Answer

    The quantity is 45 units.

    The price is 220 dollars.

    Profits above FC are 8100 dollars.

    Exercise \(\PageIndex{5}\)

    Given the following:

    The inverse demand is P = 460-5Q.

    Marginal cost is 50.

    Average variable cost is 50.

    Assume a profit maximizing monopolist or monopolistically competitive firm.

    Find the quantity, price and profits above fixed costs (FC).

    Answer

    The quantity is 41 units.

    The price is 255 dollars.

    Profits above FC are 8405 dollars.

    Exercise \(\PageIndex{6}\)

    Given the following:

    The inverse demand is P = 200-3Q.

    Marginal cost is 20.

    Average variable cost is 20.

    Assume a profit maximizing monopolist or monopolistically competitive firm.

    Find the quantity, price and profits above fixed costs (FC).

    Answer

    The quantity is 30 units.

    The price is 110 dollars.

    Profits above FC are 2700 dollars.

    Exercise \(\PageIndex{7}\)

    Given the following:

    The inverse demand is P = 288-3Q.

    Marginal cost is 30.

    Average variable cost is 30.

    Assume a profit maximizing monopolist or monopolistically competitive firm.

    Find the quantity, price and profits above fixed costs (FC).

    Answer

    The quantity is 43 units.

    The price is 159 dollars.

    Profits above FC are 5547 dollars.

    Exercise \(\PageIndex{8}\)

    Given the following:

    The inverse demand is P = 300-2.5Q.

    Marginal cost is 30.

    Average variable cost is 30.

    Assume a profit maximizing monopolist or monopolistically competitive firm.

    Find the quantity, price and profits above fixed costs (FC).

    Answer

    The quantity is 54 units.

    The price is 165 dollars.

    Profits above FC are 7290 dollars.

    Exercise \(\PageIndex{9}\)

    Given the following:

    The inverse demand is P = 400-4Q.

    Marginal cost is 80.

    Average variable cost is 80.

    Assume a profit maximizing monopolist or monopolistically competitive firm.

    Find the quantity, price and profits above fixed costs (FC).

    Answer

    The quantity is 40 units.

    The price is 240 dollars.

    Profits above FC are 6400 dollars.

    Exercise \(\PageIndex{10}\)

    Given the following:

    The inverse demand is P = 456-4.5Q.

    Marginal cost is 42.

    Average variable cost is 42.

    Assume a profit maximizing monopolist or monopolistically competitive firm.

    Find the quantity, price and profits above fixed costs (FC).

    Answer

    The quantity is 46 units.

    The price is 249 dollars.

    Profits above FC are 9522 dollars.

    Problem Set 2. Two-Firm Cournot Duopoly

    Exercise \(\PageIndex{1}\)

    Given the following:

    The inverse demand is P = 200-2Qa-2Qb.

    Marginal cost for each firm is 20.

    Average variable cost for each firm is 20.

    Qa and Qb are quantities Firms A and B place on the market, respectively.

    Find the Cournot Nash equilibrium quantity for each firm.

    Calculate the market price at this equilibrium.

    Calculate the resulting profits above fixed costs (FC) for each firm.

    Answer

    Each firm's quantity is 30 units.

    The market price is 80 dollars.

    Each firm's profits above FC are 1800 dollars.

    Exercise \(\PageIndex{2}\)

    Given the following:

    The inverse demand is P = 200-2.5Qa-2.5Qb.

    Marginal cost for each firm is 20.

    Average variable cost for each firm is 20.

    Qa and Qb are quantities Firms A and B place on the market, respectively.

    Find the Cournot Nash equilibrium quantity for each firm.

    Calculate the market price at this equilibrium.

    Calculate the resulting profits above fixed costs (FC) for each firm.

    Answer

    Each firm's quantity is 24 units.

    The market price is 80 dollars.

    Each firm's profits above FC are 1440 dollars.

    Exercise \(\PageIndex{3}\)

    Given the following:

    The inverse demand is P = 250-5Qa-5Qb.

    Marginal cost for each firm is 25.

    Average variable cost for each firm is 25.

    Qa and Qb are quantities Firms A and B place on the market, respectively.

    Find the Cournot Nash equilibrium quantity for each firm.

    Calculate the market price at this equilibrium.

    Calculate the resulting profits above fixed costs (FC) for each firm.

    Answer

    Each firm's quantity is 15 units.

    The market price is 100 dollars.

    Each firm's profits above FC are 1125 dollars.

    Exercise \(\PageIndex{4}\)

    Given the following:

    The inverse demand is P = 300-4Qa-4Qb.

    Marginal cost for each firm is 36.

    Average variable cost for each firm is 36.

    Qa and Qb are quantities Firms A and B place on the market, respectively.

    Find the Cournot Nash equilibrium quantity for each firm.

    Calculate the market price at this equilibrium.

    Calculate the resulting profits above fixed costs (FC) for each firm.

    Answer

    Each firm's quantity is 22 units.

    The market price is 124 dollars.

    Each firm's profits above FC are 1936 dollars.

    Exercise \(\PageIndex{5}\)

    Given the following:

    The inverse demand is P = 400-5Qa-5Qb.

    Marginal cost for each firm is 40.

    Average variable cost for each firm is 40.

    Qa and Qb are quantities Firms A and B place on the market, respectively.

    Find the Cournot Nash equilibrium quantity for each firm.

    Calculate the market price at this equilibrium.

    Calculate the resulting profits above fixed costs (FC) for each firm.

    Answer

    Each firm's quantity is 24 units.

    The market price is 160 dollars.

    Each firm's profits above FC are 2880 dollars.

    Exercise \(\PageIndex{6}\)

    Given the following:

    The inverse demand is P = 500-4Qa-4Qb.

    Marginal cost for each firm is 80.

    Average variable cost for each firm is 80.

    Qa and Qb are quantities Firms A and B place on the market, respectively.

    Find the Cournot Nash equilibrium quantity for each firm.

    Calculate the market price at this equilibrium.

    Calculate the resulting profits above fixed costs (FC) for each firm.

    Answer

    Each firm's quantity is 35 units.

    The market price is 220 dollars.

    Each firm's profits above FC are 4900 dollars.

    Exercise \(\PageIndex{7}\)

    Given the following:

    The inverse demand is P = 300-3Qa-3Qb.

    Marginal cost for each firm is 30.

    Average variable cost for each firm is 30.

    Qa and Qb are quantities Firms A and B place on the market, respectively.

    Find the Cournot Nash equilibrium quantity for each firm.

    Calculate the market price at this equilibrium.

    Calculate the resulting profits above fixed costs (FC) for each firm.

    Answer

    Each firm's quantity is 30 units.

    The market price is 120 dollars.

    Each firm's profits above FC are 2700 dollars.

    Exercise \(\PageIndex{8}\)

    Given the following:

    The inverse demand is P = 300-2.5Qa-2.5Qb.

    Marginal cost for each firm is 30.

    Average variable cost for each firm is 30.

    Qa and Qb are quantities Firms A and B place on the market, respectively.

    Find the Cournot Nash equilibrium quantity for each firm.

    Calculate the market price at this equilibrium.

    Calculate the resulting profits above fixed costs (FC) for each firm.

    Answer

    Each firm's quantity is 36 units.

    The market price is 120 dollars.

    Each firm's profits above FC are 3240 dollars.

    Exercise \(\PageIndex{9}\)

    Given the following:

    The inverse demand is P = 500-4Qa-4Qb.

    Marginal cost for each firm is 80.

    Average variable cost for each firm is 80.

    Qa and Qb are quantities Firms A and B place on the market, respectively.

    Find the Cournot Nash equilibrium quantity for each firm.

    Calculate the market price at this equilibrium.

    Calculate the resulting profits above fixed costs (FC) for each firm.

    Answer

    Each firm's quantity is 35 units.

    The market price is 220 dollars.

    Each firm's profits above FC are 4900 dollars.

    Exercise \(\PageIndex{10}\)

    Given the following:

    The inverse demand is P = 420-4.5Qa-4.5Qb.

    Marginal cost for each firm is 42.

    Average variable cost for each firm is 42.

    Qa and Qb are quantities Firms A and B place on the market, respectively.

    Find the Cournot Nash equilibrium quantity for each firm.

    Calculate the market price at this equilibrium.

    Calculate the resulting profits above fixed costs (FC) for each firm.

    Answer

    Each firm's quantity is 28 units.

    The market price is 168 dollars.

    Each firm's profits above FC are 3528 dollars.

    Problem Set 3. Find the Monopolist’s or Monopolistically Competitive Firm’s Price

    Exercise \(\PageIndex{1}\)

    Given the following:

    The elasticity of demand facing the firm is -1.5.

    The firm's marginal cost is 8.

    What price maximizes this firm's profits?

    Answer

    The profit maximizing price is 24.

    Exercise \(\PageIndex{2}\)

    Given the following:

    The elasticity of demand facing the firm is -2.5.

    The firm's marginal cost is 30.

    What price maximizes this firm's profits?

    Answer

    The profit maximizing price is 50.

    Exercise \(\PageIndex{3}\)

    Given the following:

    The elasticity of demand facing the firm is -2.

    The firm's marginal cost is 30.

    What price maximizes this firm's profits?

    Answer

    The profit maximizing price is 60.

    Exercise \(\PageIndex{4}\)

    Given the following:

    The elasticity of demand facing the firm is -3.

    The firm's marginal cost is 20.

    What price maximizes this firm's profits?

    Answer

    The profit maximizing price is 30.

    Exercise \(\PageIndex{5}\)

    Given the following:

    The elasticity of demand facing the firm is -2.

    The firm's marginal cost is 20.

    What price maximizes this firm's profits?

    Answer

    The profit maximizing price is 40.

    Exercise \(\PageIndex{6}\)

    Given the following:

    The elasticity of demand facing the firm is -1.5.

    The firm's marginal cost is 20.

    What price maximizes this firm's profits?

    Answer

    The profit maximizing price is 60.

    Exercise \(\PageIndex{7}\)

    Given the following:

    The elasticity of demand facing the firm is -2.5.

    The firm's marginal cost is 12.

    What price maximizes this firm's profits?

    Answer

    The profit maximizing price is 20.

    Exercise \(\PageIndex{8}\)

    Given the following:

    The elasticity of demand facing the firm is -2.

    The firm's marginal cost is 20.

    What price maximizes this firm's profits?

    Answer

    The profit maximizing price is 40.

    Exercise \(\PageIndex{9}\)

    Given the following:

    The elasticity of demand facing the firm is -3.

    The firm's marginal cost is 40.

    What price maximizes this firm's profits?

    Answer

    The profit maximizing price is 60.

    Exercise \(\PageIndex{10}\)

    Given the following:

    The elasticity of demand facing the firm is -2.

    The firm's marginal cost is 40.

    What price maximizes this firm's profits?

    Answer

    The profit maximizing price is 80.

    Problem Set 4. Multiple Choice

    Exercise \(\PageIndex{1}\)
    1. An industry with many sellers with differentiated products is classified as

    a) A monopoly

    b) An oligopoly

    c) Monopolistically competitive

    d) Perfectly competitive

    Answer

    c

    Exercise \(\PageIndex{2}\)
    1. The folk theorem is of primary interest in understanding competition in an industry that is

    a) A monopoly

    b) An oligopoly

    c) Monopolistically competitive

    d) Perfectly competitive

    Answer

    b

    Exercise \(\PageIndex{3}\)
    1. An industry where firms are price takers is

    a) A monopoly

    b) A monopsony

    c) Monopolistically competitive

    d) Perfectly competitive

    Answer

    d

    Exercise \(\PageIndex{4}\)
    1. An industry where firms face an infinitely negative own-price elasticity is

    a) A monopoly

    b) A monopsony

    c) Monopolistically competitive

    d) Perfectly competitive

    Answer

    d

    Exercise \(\PageIndex{5}\)
    1. In the Cournot model, competitors compete by choosing

    a) Prices

    b) Quantities

    c) Contracting methods

    d) Management styles

    Answer

    b

    Exercise \(\PageIndex{6}\)
    1. In the Bertrand model, competitors compete by choosing

    a) Prices

    b) Quantities

    c) Contracting methods

    d) Management styles

    Answer

    a

    Exercise \(\PageIndex{7}\)
    1. The Cournot or Bertrand Nash equilibrium is

    a) Analogous to the prisoner’s dilemma outcome because there is a feasible outcome that is better for the firms involved.

    b) Modeled using a hedonic pricing model

    c) Similar to 1st degree price discrimination

    d) Similar to 3rd degree price discrimination

    Answer

    a

    Exercise \(\PageIndex{8}\)
    1. Which is true of a price taking firm?

    a) It can sell all that it wants at the going price.

    b) Its actions have a negligible impact on the market price.

    c) It will maximize profits by producing where price is equal to marginal cost.

    d) All of the above.

    Answer

    d

    Exercise \(\PageIndex{9}\)
    1. A profit maximizing firm will set price = marginal cost (p = MC) in which market structure?

    a) Perfect competition

    b) Monopolistic competition

    c) Oligopoly

    d) Monopoly

    e) All of the above

    Answer

    a

    Exercise \(\PageIndex{10}\)
    1. A profit maximizing firm will set marginal revenue = marginal cost (MR = MC) in which market structure?

    a) Perfect competition

    b) Monopolistic competition

    c) Oligopoly

    d) Monopoly

    e) All of the above

    Answer

    e

    Exercise \(\PageIndex{11}\)
    1. In which market structure are strategic interactions among firms of primary interest?

    a) Perfect competition

    b) Monopolistic competition

    c) Oligopoly

    d) Monopoly

    Answer

    c

    Exercise \(\PageIndex{12}\)
    1. Which best describes a tit-for-tat response?

    a) The firm always prices lower than the competitor

    b) The firm always prices a bit higher than the competitor to protect its margin

    c) The firm cuts (raises) its price in response to a cut (raise) in price by its competitor

    d) The firm chooses its Nash equilibrium price

    Answer

    c

    Exercise \(\PageIndex{13}\)
    1. A firm that advertises, “We will match any competitors price”

    a) Could be warning its competitors that it follows a tit-for-tat pricing strategy

    b) Must have low costs

    c) Is more worried about market share than profits

    d) All of the above

    Answer

    a

    Exercise \(\PageIndex{14}\)
    1. Which factor makes it more likely that firms will be able to tacitly cooperate on a price above the Bertrand price?

    a) Discount rates are high

    b) It takes a long time for firms to respond to a price change by a competitor

    c) Firm’s know that the competitive interaction will last for only three periods

    d) Discount rates are low

    e) There are major differences among firms in terms of costs and quality

    Answer

    d

    Exercise \(\PageIndex{15}\)
    1. Which best describes a Nash equilibrium?

    a) Tacit coordination on the monopoly price

    b) A situation where MR < P

    c) A situation where each agent is choosing its best strategy given the strategies of all other agents.

    d) Cases where price is above the break-even point

    Answer

    c


    This page titled 7.8: Problem Sets is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Michael R. Thomsen via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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