managerial economics

A firm uses a single plant with costs C= 160 +16Q +.1Q2 and faces the price equation P= 96 – .4Q.
a) Find the firm’s profit-maximizing price and quantity. What is the profit?

b) The firm’s production manager claims that the firm’s average cost of production is minimized at an output of 40 units. Furthermore, she claims that 40 units is the firm’s profit-maximizing level of output. Explain whether these claims are correct.

c) Could the firm increase its profit by using a second plant (with costs identical to the first) to produce the output in part (a)? Explain.

  1. 👍 0
  2. 👎 0
  3. 👁 961
  1. a) Given total cost function as C=160+16Q+0.1Q(2){squared} and price equation P=96-0.4Q.

    Total Revenue function is R=PQ=96Q-0.4Q(2).

    The profit function is F=R-C=(96Q-0.4Q(2))-(160+16Q+0.1Q(2))=80Q-0.5Q(2)-160.

    Profit attains maximum when and is negative dF/dQ=0 and d(2)F/dQ(2) is negative.

    dF/dQ(fraction)=0 -> 80-Q= 0 -> Q=80

    d(2)F/dQ(2) (fraction)= -1

    Now it is clear that profit attains maximum when Q = 80
    Price when Q = 80 is P=96-0.4*80=64

    The profit-maximizing price = 64 and quantity = 80

    Maximum Profit = [80Q-0.5Q(2)-160]Q=80(subscript) = 3040

    b) The average cost function is AC = C/Q= 160/Q{fraction}+16+0.1Q

    The AC function attains minimum when dAC/dQ {fraction}=0 and d(2)AC/dQ(2){fraction} is positive

    dAC/dq{fraction}=0 -> -160/q(2){fraction} +0.1=0 -> -160+0.1Q(2)=0

    i.e., Q(2) -1600=0 -> (q+40)(Q-40)=0 -> 40 or -40

    Since Q cannot be negative Q = 40

    d(2)AC/dQ(2){fraction}=320/Q(3){fraction}

    Clearly d(2)AC/dQ(2){fraction} is positive when Q = 40

    It is clear that the firms average cost of production is minimized at an output of 40 units.

    The firm’s production manager’s first claim is the firm’s average cost of production is minimized at an output of 40 units, is correct.

    But, her second claim, the firms’ profit maximizing level of output is 40 units, is not correct.
    Note that from (a) we got the firms’ profit maximizing level of output is 80 units.
    When Q = 40 the firms profit is (F=80*40-0.5*40(2)-160) = 2240,
    But, when Q = 80 we got profit = 3040

    c) If the firm uses a second plant with costs identical to the first. Then the cost function becomes C=320+32Q+0.2Q(2).

    But, the demand function remains the same; unfortunately the revenue function remains unchanged. i.e.,R=PQ=96Q-0.4Q(2).

    Now the new profit function becomes

    F=R-C=96Q-0.4Q(2))-(320+32Q+0.2Q(2))=64Q-0.6Q(2)-320

    dF/dQ{fraction}=0 -> 64-1.2Q= 0->Q=53.33

    d(2)F/dQ(2){fraction}=-1.2

    That is profit attains maximum when Q = 53.33

    The maximum profit is[64Q-0.6Q(2)-320]Q=53.33{subscript} = 1386.67
    So the firm cannot increase its profit by adding a second plant.

    1. 👍 0
    2. 👎 0
  2. 1. Given a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36 + 3/Q,
    calculate the level of output Q which
    a) maximizes total revenue b) maximizes profits

    1. 👍 0
    2. 👎 0
  3. what is the relationship of investment and interest rates

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Economics

    An industry currently has 100 firms, all of which have fixed costs of $16 and avg. variable cost as follows: Q Avg. Variable Cost ($) 1 1 2 2 3 3 4 4 5 5 6 6 a. Compute marginal cost and avg. total cost. b. the price is $10. what

  2. Economics

    A monopoly firm faces a demand curve given by the following equation: P = $500 − 10Q, where Q equals quantity sold per day. Its marginal cost curve is MC = $100 per day. Assume that the firm faces no fixed cost. You may wish to

  3. Economics

    Suppose that a typical firm in a monopolistically competitive industry faces a demand curve given by: q = 60 - (1/2)p, where q is quantity sold per week. The firm's marginal cost curve is given by: MC = 60. 1. How much will the

  4. Microeconomics

    Correcting for negative externalities - Regulation versus tradablepermits Suppose the government wants to reduce the total pollution emitted by three local firms. Currently, each firm is creating 4 units of pollution in the area,

  1. Econ MC

    Two firms, A and B, each currently dump 50 tons of chemicals into the local river. The government has decided to reduce the pollution and from now on will require a pollution permit for each ton of pollution dumped into the river.

  2. finance (net income)

    If a firm has a break-even point of 20,000 units and the contribution margin on the firm's single product is $3.00 per unit and fixed costs are $60,000, what will the firm's net income be at sales of 30,000 units? A. $90,000 B.

  3. Economics

    you are hired as the consultant to a monopolistically competitive firm. The firm reports the following information about its price, marginal cost, and average total cost. Can the firm possibly be maximizing profit? If the firm is

  4. math

    A manufacturer of hospital supplies has a uniform annual demand for 320,000 boxes of bandages. It costs ​$10 to store one box of bandages for one year and $ 160 to set up the plant for production. How many times a year should

  1. Economics

    A monopoly produces widgets at a marginal cost of $8 per unit and zero fixed costs. It faces an inverse demand function given by P = 38 - Q. Suppose fixed costs rise to $200. What will happen in the market? A.The firm will

  2. Economics

    For the following characteristic say whether it describes a perfectly competitive firm, a monopolistically competitive firm, monopoly firm, or neither. a. Has marginal revenue less than price. I would think this would be neither.

  3. Finance 200

    If a firm has fixed costs of $20,000, variable cost per unit of $.50, and a breakeven point of 5000 units, the price is?

  4. ECONOMICS

    A firm uses a single plant with costs C= 160 +16Q +.1Q2 and faces the price equation P= 96 – .4Q. a) Find the firm’s profit-maximizing price and quantity. What is the profit? b) The firm’s production manager claims that the

You can view more similar questions or ask a new question.