Question

Assume that a competitive firm has the total cost function: TC=1q3−40q2+740q+1500 Suppose the price of the...

Assume that a competitive firm has the total cost function:

TC=1q3−40q2+740q+1500

Suppose the price of the firm's output (sold in integer units) is $750 per unit.

Using calculus and formulas (but no tables and restricting your use of spreadsheets to implementing the quadratic formula) to find a solution, what is the total profit at the optimal integer output level?

Please specify your answer as an integer.

Hint 1: The first derivative of the total cost function, which is cumulative, is the marginal cost function, which is incremental. The narrated lecture and formula summary explain how to compute the derivative.

Set the marginal cost equal to the marginal revenue (price in this case) to define an equation for the optimal quantity q.

Rearrange the equation to the quadratic form aq2 + bq + c = 0, where a, b, and c are constants.

Use the quadratic formula to solve for q:

q=−b±b2−4ac−−−−−−−√2aq=-b±b2-4ac2a

For non-integer quantity, round up and down to find the integer quantity with the optimal profit.

Hint 2: When computing the total cost component of total profit for each candidate quantity, use the total cost function provided in the exercise statement (rather than summing the marginal costs using the marginal cost function).

0 0
Add a comment Improve this question Transcribed image text
Answer #1

r Hae TC 2. 2- 2-3= 202.50-12U03

Thanks!

Add a comment
Know the answer?
Add Answer to:
Assume that a competitive firm has the total cost function: TC=1q3−40q2+740q+1500 Suppose the price of the...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • Assume that a competitive firm has the total cost function: TC=1q3−40q2+740q+1900 Suppose the price of the...

    Assume that a competitive firm has the total cost function: TC=1q3−40q2+740q+1900 Suppose the price of the firm's output (sold in integer units) is $550 per unit. Using tables (but not calculus) to find a solution, what is the total profit at the optimal output level? Please specify your answer as an integer.

  • A firm produces a product in a competitive industry and has a total cost function (TC)...

    A firm produces a product in a competitive industry and has a total cost function (TC) of TC(a) 60+4q+2q2 and a marginal cost function (MC) of MC(q) = 4 + 4q. At the given market price (P) of $20, the firm is producing 4.00 units of output. Is the firm maximizing profit?V What quantity of output should the firm produce in the long run? The firm should produce unit(s) of output. (Enter your response as an integer.)

  • Suppose a competitive firm has cost function: C(q) = a + bq + cq2 + dq3,...

    Suppose a competitive firm has cost function: C(q) = a + bq + cq2 + dq3, where a,b,c,d are constants. What is the marginal cost function? What is the firm’s variable and average cost of output, in terms of q? What is the firm’s fixed cost? What is the firm’s profit maximization condition?

  • A firm operates in a perfectly competitive market with a price of P = 50 for...

    A firm operates in a perfectly competitive market with a price of P = 50 for the product. TVC = 0.5Q3 − 18Q2 + 170Q Q (output) TFC = 300. Write an equation expressing the firm’s total revenue (TR) as function of Q. Write an equation expressing the firm’s total cost (TC), as a function of Q. Write an equation expressing the firm’s profit (π), as a function of Q.Find the first-order condition for the firm’s profit-maximization decision. Find the...

  • Suppose that each firm in a competitive industry has the following costs: Total Cost: TC =...

    Suppose that each firm in a competitive industry has the following costs:Total Cost: TC=50+1/2 q2Marginal Cost: MC=qwhere q is an individual firm's quantity produced.The market demand curve for this product is:Demand QD=160-4 Pwhere P is the price and Q is the total quantity of the good.Each firm's fixed cost is $_______ What is each firm's variable cost?1/2 q50+1/2 q1/2 q^{2}qWhich of the following represents the equation for each firm's average total cost?50/q+1/2 q50+1/2 q50/q1/2 qComplete the following table by computing the...

  • Suppose a perfectly competitive firm has the short-run cost function C = 125 + q2. Use...

    Suppose a perfectly competitive firm has the short-run cost function C = 125 + q2. Use the derivative formula or marginal cost to determine the firm’s output level and profit at prices of $30 and $20. At what price does the firm reach the shut-down point?

  • 1. Suppose a perfectly competitive firm has a cost function described by TC = 200Q +...

    1. Suppose a perfectly competitive firm has a cost function described by TC = 200Q + Q 2 + 225 Each firm’s marginal revenue is $240. a. Find the profit maximizing level of output. b. Is this a short-run or long-run situation? How do you know? c. Assuming that this firm’s total cost curve is the same as all other producers, find the long-run price for this good.

  • orstops, INC. (DD) is a monopolist in the doorstop industry. ts total cost function the quadratic...

    orstops, INC. (DD) is a monopolist in the doorstop industry. ts total cost function the quadratic function of output C(Q) -100-5Q+ Q?. The inverse demand for doorstops Pl) is given by the linear function P/Q) 55-2Q. Note that the marginal C) is not constant. (Also, it happens to be negative for 0s Q <2.5.) ft-maximizing problem for DD, and determine its optimal rate of output (a) Write down the for С" (b) Find the profit-maximizing price set by DD, PM...

  • Suppose that each firm in a competitive industry has the following costs: Total Cost: TC= 50+1/2...

    Suppose that each firm in a competitive industry has the following costs: Total Cost: TC= 50+1/2 q^2 Marginal Cost: MC= q where qq is an individual firm's quantity produced. The market demand curve for this product is Demand QD=160−4PQD=160−4P where PP is the price and QQ is the total quantity of the good. Each firm's fixed cost is $_____ What is each firm's variable cost? q 50+1/2 q 1/2q 1/2q^2 Which of the following represents the equation for each firm's...

  • Given the total cost function for a firm is Q = output and TC = total...

    Given the total cost function for a firm is Q = output and TC = total cost Q   TC 0    20 1    40 2    60 3    80 4 100 5 120 6 140 the production function that generated these costs must have increasing marginal product of the variable input (labor) TURE OR FLASE

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT