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d. At what level of output (Q) is AC minimized?

d. At what level of output (Q) is AC minimized?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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= 5Q=187.5 => Q = 187.5/5 = 37.5 And at this quantity, Price 187.5 (2.5 × 37.5) = 93.75 The quantity at which the TR is maximum = 37.5 The price at which the TR is maximum is 93.75 Problem 2: Your company's cost function (monthly) can be defined as; TC = cost per unit (AC) × quantity supplied (Q). If the cost per unit (average cost) for your firm is AC = (800/Q) - 10 +2Q: a. What is the total cost function for your firm in terms of Q? AC(Q)=800/Q-10+2Q When average cost function is given, total cost can be calculated as average cost multiplied by quantity. TC(Q)=AC(Q)XQ TC(Q)=(800/Q−10+2Q)×Q TC(Q)=2Q2-10Q+800 Total cost function in terms of Q. Total cost function in terms of Q. b. How would you interpret the intercept term in this function? TC(Q)=2Q2-10Q+800 The intercept which is 800 is the Total fixed cost the firm faces and the rest of the costs are the firms total variable costs Then the firms total fixed cost are and firms total variable cost are TVC(Q)=2Q2-10Q Total cost can be written as the sum of total fixed cost and total variable cost TC(Q)=TFC+TVC(Q) The intercept term can be interpreted as Total fixed cost of the firm. C. What is the marginal cost function for your firm?
Transcribed Image Text:= 5Q=187.5 => Q = 187.5/5 = 37.5 And at this quantity, Price 187.5 (2.5 × 37.5) = 93.75 The quantity at which the TR is maximum = 37.5 The price at which the TR is maximum is 93.75 Problem 2: Your company's cost function (monthly) can be defined as; TC = cost per unit (AC) × quantity supplied (Q). If the cost per unit (average cost) for your firm is AC = (800/Q) - 10 +2Q: a. What is the total cost function for your firm in terms of Q? AC(Q)=800/Q-10+2Q When average cost function is given, total cost can be calculated as average cost multiplied by quantity. TC(Q)=AC(Q)XQ TC(Q)=(800/Q−10+2Q)×Q TC(Q)=2Q2-10Q+800 Total cost function in terms of Q. Total cost function in terms of Q. b. How would you interpret the intercept term in this function? TC(Q)=2Q2-10Q+800 The intercept which is 800 is the Total fixed cost the firm faces and the rest of the costs are the firms total variable costs Then the firms total fixed cost are and firms total variable cost are TVC(Q)=2Q2-10Q Total cost can be written as the sum of total fixed cost and total variable cost TC(Q)=TFC+TVC(Q) The intercept term can be interpreted as Total fixed cost of the firm. C. What is the marginal cost function for your firm?
TC(Q)=2Q2-10Q+800 Marginal cost of the firm can be derived by differentiation of the total cost function with respect to Q MC(Q)=d TC(Q)/dQ=d(2Q2-10Q+800)/dQ=4Q-10 Thus marginal cost function for the firm is given as MC(Q)=4Q-10 d. At what level of output (Q) is AC minimized? e. Is MC always less than AC? Given AC = and TC So, OT, or, or, OT, MC or, 800 Q AC x Q = {(800) - 10+2Q} Q 800 - 10Q +2Q² 8TC 8Q Now, the minimum of AC occurs at that level of Q where AC ƏQ Accordingly, {(800) 10 + 2Q - 2Q } 800 +2 - = 8TC ƏQ = -10 + 4Q - 800 800 800 Q² (800 – 10Q + 2Q² ) 8AC 8Q +2=0 2 0 2Q² Q² = 2 10+2Q 800 = 400 = 20 JAC 8Q 0 MC is NOT ALWAYS lesser than the AC. When AC is falling then MC happens to be greater than AC, while, on the other hand, when AC is rising, MC is less than that of AC. At the minimum point of AC, both MC and AC are equal. In this case, MC will be lesser than AC only for output less than 20. Thereafter, the MC will be greater than AC. Thus, MC is less than AC only till the minimum of AC is reached. Beyond that MC is more than AC. 3
Transcribed Image Text:TC(Q)=2Q2-10Q+800 Marginal cost of the firm can be derived by differentiation of the total cost function with respect to Q MC(Q)=d TC(Q)/dQ=d(2Q2-10Q+800)/dQ=4Q-10 Thus marginal cost function for the firm is given as MC(Q)=4Q-10 d. At what level of output (Q) is AC minimized? e. Is MC always less than AC? Given AC = and TC So, OT, or, or, OT, MC or, 800 Q AC x Q = {(800) - 10+2Q} Q 800 - 10Q +2Q² 8TC 8Q Now, the minimum of AC occurs at that level of Q where AC ƏQ Accordingly, {(800) 10 + 2Q - 2Q } 800 +2 - = 8TC ƏQ = -10 + 4Q - 800 800 800 Q² (800 – 10Q + 2Q² ) 8AC 8Q +2=0 2 0 2Q² Q² = 2 10+2Q 800 = 400 = 20 JAC 8Q 0 MC is NOT ALWAYS lesser than the AC. When AC is falling then MC happens to be greater than AC, while, on the other hand, when AC is rising, MC is less than that of AC. At the minimum point of AC, both MC and AC are equal. In this case, MC will be lesser than AC only for output less than 20. Thereafter, the MC will be greater than AC. Thus, MC is less than AC only till the minimum of AC is reached. Beyond that MC is more than AC. 3
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