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    transfer price

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    Please answer the questions below and give full explanations so I can follow and learn how to apply myelf.

    1. You are the manager of a firm that sells its product in a competitive market at a price
    of $60. Your firm's cost function is C(Q) = 30 + 3Q2.
    a. What is the profit-maximizing output for your firm?
    b. What is the maximum profit for your firm?

    2. You are the manager of a monopoly that faces a demand curve described by
    P = 85 - 5Q. Your costs are C(Q) = 20 + 5Q.
    a. What is the profit-maximizing output?
    b. What is the profit-maximizing price?)
    c. What is the maximum profit? (

    3. A monopoly has two production plants with cost functions C1(Q1) = 50 + 0.1 Q12 and
    C2(Q2) = 30 + 0.05 Q22. The demand it faces is Q = 500 - 10 P.
    a. What is the profit-maximizing level of output? ;

    b. What is the profit-maximizing price? (
    c. What is the maximum profit? (Answer: Not given)

    4. Consider the following pay-off table for a one-shot game:

    Firm A
    `
    Firm B

    Low Price

    High Price

    Low Price

    (2, 2)
    (10, -8)

    High Price

    (-8, 10)
    (15, 15)

    a. What are the dominant strategies for Firm A and Firm B, respectively?
    (Answer: .)
    b. What are the Nash equilibrium strategies for this game?
    [Answer:
    5. You are the manager of a Mom and Pop store that can buy milk from a supplier at
    $3.00 per gallon. Suppose the elasticity of demand for milk by customers at your store
    is -4.
    a. What is the profit-maximizing price for the milk you sell?

    6. During spring break, students have an elasticity of demand for a trip to Cancun
    Mexico of -4. Assume the general public has an elasticity of -2.
    a. How much should an airline charge students for a ticket if the price it charges
    the general public is $420?

    7. The average consumer at a firm with market power has an inverse demand function of
    P = 10 - Q. The firm's cost function is C(Q) = 2Q. If the firm engages in two part
    pricing,
    a. what is the optimal fixed fee to charge each consumer?
    b. what is the optimal price to charge a consumer for each unit purchased?
    ()

    8. A firm with market power has an individual consumer demand of Q = 4 - 0.25P and
    costs of C(Q) = 8Q.
    a. What is optimal price to charge for a block of 2 units?

    9. Suppose two types of consumers buy pants and shirts. Consumers of type A will pay
    $70 for pants and $20 for a shirt. Consumers of type B will pay $60 for pants and $25
    for a shirt. The firm selling suits faces no competition and has a marginal cost of zero
    and cannot price discriminate between the consumers.
    a. What is the optimal commodity bundling strategy? (

    10. A firm has a division that produces X, whose total costs are C(Q) = 10 + 5Q2 (where
    Q is the quantity of X). The marketing division adds its own total costs of 5 + 3Q.
    There is no external market price of X.
    a. What should be the transfer price of X?)

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    Solution Preview

    1. You are the manager of a firm that sells its product in a competitive market at a price of $60. Your firm's cost function is C(Q) = 30 + 3Q2.
    a. What is the profit-maximizing output for your firm?

    The marginal cost is MC = dC/dQ = 6Q
    By first order condition, the firm will max profit by setting MC = MR = P in a competitive market, i.e.,
    6Q = 60
    Q = 60/6 = 10
    So the profit-maximizing output is 10.

    b. What is the maximum profit for your firm?

    max Profit = P*Q - C
    = 60*10 - (30 + 3*10^2) = $270

    2. You are the manager of a monopoly that faces a demand curve described by
    P = 85 - 5Q. Your costs are C(Q) = 20 + 5Q.

    a. What is the profit-maximizing output?

    The firm's total revenue is TR = P*Q= (85 - 5Q)*Q = 85Q - 5Q^2
    so it's marginal revenue is MR = dTR / dQ = 85 - 10Q
    Also, the firm's marginal cost is MC = dC/dQ = 5
    The monopolist will max profit by setting MC = MR, i.e.,
    85 - 10Q = 5
    80 = 10Q
    Q = 8

    b. What is the profit-maximizing price?)
    from the demand curve:
    P = 85 - 5Q = 85 - 5*8 = $45

    c. What is the maximum profit?

    max Profit = P*Q - C
    = 45*8 - (20 + 5*8) = $300

    3. A monopoly has two production plants with cost functions C1(Q1) = 50 + 0.1 Q1^2 and C2(Q2) = 30 + 0.05 Q2^2. The demand it faces is Q = 500 - 10 P.

    a. What is the profit-maximizing level of output? ;

    MC1 = dC1/dQ1 = 0.2 Q1
    MC2 = dC2/dQ2 = 0.1 Q2
    From demand curve, we rewrite it into: P = 50 - 0.1 Q
    Then firm's total revenue is
    TR = P*Q= (50 - 0.1Q)*Q = 50Q - 0.1Q^2
    it's marginal revenue is
    MR = dTR / dQ = 50 - 0.2 Q
    Also we know Q= Q1 + Q2, then
    MR = dTR / dQ = 50 - 0.2 (Q1+Q2)

    The ...

    Solution Summary

    Determine transfer price and other factors.

    $2.19