Suppose the total cost function of a firm that produces hotdogs is C= 150q - 4q +2q where q is the output level of the firm. i. Find the average cost function of the firm. Show your workings. ii. If the firm's marginal cost function is 150-8q+ 6q², at what output level, the average cost is minimized? Show your workings. iii. Show your answer of part ii) in a well-labeled diagram. ... 2.

Suppose the total cost function of a firm that produces hotdogs is C= 150q - 4q +2q where q is the output level of the firm. i. Find the average cost function of the firm. Show your workings. ii. If the firm's marginal cost function is 150-8q+ 6q², at what output level, the average cost is minimized? Show your workings. iii. Show your answer of part ii) in a well-labeled diagram. ... 2.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.3P

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Question four Suppose that a firm's total cost equation is TC= 10,000+ 1000 + 0.25Q2 Where TC is total cost and Q is the level of output. (a) What output level will minimize the firm's average total cost? (b) Calculate the average and marginal cost at the average cost minimizing output level
1. Suppose a firm’s cost function is given by C(q) = 20 + 10q − 4q^2 + q^3(a) What is fixed cost?(b) What is variable cost?(c) Compute average cost, average fixed cost, and average variable cost, assuming q > 0.(d) Derive marginal cost.(e) Solve for the shut-down level of production, qSD. (Hint: The minimum of a well-behavedcurve can be found by setting the first derivative equal to zero.)
Suppose a firm faces a short-run total cost function of SRTC = 20 + 3Q + 2Q2 . a) Write the firm’s function for short-run marginal cost? b) What is the firm’s function for short-run average fixed cost? c) What is the firm’s function for short-run average variable cost?
Month (m): 4 Day (d): 1 Use the two numbers above, m and d, to complete the cost function for a perfectly competitive firm: Cost (q) = m q2 + d = (30) For a cost function like yours, Marginal Cost (MC) = 2 m q . Specifically, what are the following for the cost function you wrote out above? Fixed Cost = Average Total Cost = Cost (q)/q = Variable Cost = Average Fixed Cost = FC/q = Marginal Cost = 2 m q = Average Variable Cost = VC/q = (15) Fill in the table with your values from your cost function. q Total Cost AVC AFC ATC MC 0 0 0 -- -- -- 1 2 3 4 5 6
A competitive firm has the following average cost function: AC=y2 - 8y + 30 + 5/y. The corresponding marginal cost function is MC = 3y2 - 16y + 30 a) Derive the total cost function, then find the firm’s average variable cost, average fixed cost, and fixed cost. Is this firm in the short run or the long run? How do you know? b) At what quantity is marginal cost equal to average variable cost? At what quantity is average variable cost minimized? The firm will supply zero output if the price is less than what? c) What is the smallest positive amount that the firm will ever supply at any price? At what price would the firm supply exactly 6 units of output?
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7. An economist estimated that the cost function of a single product firm is given by C (Q) = 100 +25Q+40Q2+2Q3 Based on this information, determine the followings. a. The fixed cost of producing 8 units of output b. The variable cost of producing 8 units of output c. The total cost of producing 8 units of output d. The average fixed cost of producing 8 units of output e. The average variable cost of producing 8 units of output f. The average total cost of producing 8 units of output g. The marginal cost when Q=8
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