A firm's short-run cost curve for any given level of capital K isC(K,Q) K+K-1/2Q2:Find the equation of the long-run average cost curve and sketch its graph.Explain why this curve is different from the curve traced out by the minimum points of the short-run average cost curves.

Approach to solving the question:Understand the given short-run cost function, which is (C(K,Q) = K…

Answered: A firm's short-run cost curve for any…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The demand function for a good is given by the equation P = a − bQ while the totalcost function is TC = dQ2 + eQ + f, where a, b, d, e and f are positive constants.(a) Derive the equation for profit.(b) Derive an expression for the value of Q for which profit is maximized.
The chief economist for Argus Corporation, a large appliance manufacturer, estimated the firm’s short-run cost function for vacuum cleaners using an average variable cost function of the form AVC = a + bQ + cQ2 where AVC = dollars per vacuum cleaner and Q = number of vacuum cleaners produced each month. Total fixed cost each month is $180,000. The following results were obtained: DEPENDENT VARIABLE: AVC R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 19 0.7360 39.428 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 191.93 54.65 3.512 0.0029 Q -0.0305 0.00789 23.866 0.0014 Q2 0.0000024 0.00000098 2.449 0.0262 c) If Argus Corporation produces 8,000 vacuum cleaners per month, what is the estimated average variable cost?
The total revenue curve of a firm is R(q) 40q – 12q? and its average cost A(q) = 9? – 12.85q + 20 + 400 where q is the firm's output. 30 Derive an expression C(q) for the firm's total cost function. ii. Derive an expression II(q) for the firm's profit function. iii. Is the rate of change of profit increasing or decreasing when the i. ouput level of the firm is 10 units? iv. Determine the level of output for which the firm's profit is maximized. v. What is the firms's maximum profit?
Your college newspaper, The Collegiate Investigator, has fixed production costs of $72 per edition and marginal printing and distribution costs of 39¢ per copy. The Collegiate Investigator sells for 49¢ per copy. (a) Write down the associated cost function C(x) in dollars. C(x) = Write down the revenue function R(x) in dollars. R(x) = Write down the profit function P(x) in dollars. P(x) = (b) What profit (or loss) results from the sale of 500 copies of The Collegiate Investigator? $ (c) How many copies should be sold in order to break even? copies

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A firm's short-run cost curve for any given level of capital K is C(K,Q) K+K-1/2Q2: Find the equation of the long-run average cost curve and sketch its graph. Explain why this curve is different from the curve traced out by the minimum points of the short- run average cost curves.