Question

9. The Dijon Company's total variable cost function is TVC=50Q-10Q2 +Q3 where Q is the number of units of output produced. The total Fixed cost is $2000. a. What is the output level where marginal cost is a minimum? b. What is the output level where the average variable cost is a minimum? c. What is the value of average variable cost and marginal cost at the output specified in the answer to part (b)? d. What is the ATC at the b. output level?

Answer 1

TVC=SoQ – 10 Q² + 8 MC=dTVC me=so (1)-200 + 30² rinimization of Me duc da = o-2001 +6Q da -20 +6 P = 0 6Q = 20 7 Q = 3.33 AVC = TVC units. AVC = SoQ-100? +03 AVC - so minimization loQ+Q? of AVC

d AVC - o – 10 (1) +22 da d AVC = 0 da -10+20=0 = 10 a = 10 Q =5 units. (① when ass MC = so -200 +30 ° =So-2015) +3(5)? =so - 100 + 75 = 25. AVC= so loQ+Q² = 50-10 (6) + (s) 2 =so-so +25 = 25 (d) when a=5 TC = FC + TVC

TC = pooo tsO Q -100? +Q3 АТС - TC = 2000 450 Q-10Q²+Q3 = 2000 tso -1oQ+Q = 2000 tsorloos) +(s) tsa 5 - yoo tso-so +25 - uas

Answer 2

300 +200= 500

Answer 3

SOLUTION :

a.

TVC = 50Q - 10Q^2 + Q^3

=> MC = dTVC/dQ = 50 - 20Q + 3Q^2 

For minimum MC, dMC/dQ = 0  and d2MC/dQ2 = positive

=> - 20 + 6Q = 0    and d2MC/dQ2 = + 6 (positive)

=> Q = 20/6 = 10/3 = 3.33 is the output level at which MC is minimum (ANSWER)

b.

AVC = TVC/Q = 50 - 10Q + Q^2 

For minimum AVC, dAVC/dQ = 0  and d2AVC/dQ2 = positive

=> - 10 + 2Q = 0    and d2ACC/dQ2 = + 2 (positive)

=> Q = 10/2 = 5 is the output level at which AVC is minimum (ANSWER)

c.

At Q = 5,   AVC = 50 - 10(5) + (5)^2 = 25 (ANSWER).

AT Q = 5, MC = 50 - 20(5) + 3(5)^2 = 25 (ANSWER).

d.

TC = TVC + FC = (50Q - 10Q^2 + Q^3) + 2000 

=> ATC = TC/Q = 50 - 10Q + Q^2 + 2000/Q

=> ATC( at Q = 5) = 50 - 10(5) + 5^2 + 2000/5 = 425 (ANSWER)