Assume the ABC Inc. estimated a short-run average variable cost function for its

Question

Assume the ABC Inc. estimated a short-run average variable cost function for its product as: AVC = a + bQ + cQ 2 , using time-series data for 15 years where Q = number of units of output. The output obtained from the computer is below:

d. What is the estimated Marginal Cost when output is 700 units?

e. What is the estimated AVC curve?

f. What is the estimated AVC when output is 700 units?

DEPENDENT VARIABLE: AVC R-SQUARE OBSERVATIONS: 15 F-RATIO 4.230 P-VALUE ON F 0.4135 0.0407 STANDARD ERROR PARAMETER T-RATIO P-VALUE VARIABLE ESTIMATE 30.4202 0.000088 6.4659 0.0308 0.000032 4.70 2.60 2.75 INTERCEPT 0.0005 0.0232 0.0176 0.0799

Explanation / Answer

d.)TVC=AVC(Q)

    TVC=(a + bQ + cQ 2)Q

      TVC=aQ+bQ2+cQ3

MC=dTVC/dQ

MC=a+2bQ+3cQ2

MC=30.4202+2(-0.0799)Q+3(0.000088)Q2

MC=30.4202-0.1598Q+0.000264Q2

Q=700

MC=30.4202-0.1598(700)+0.000264(700)2

MC=30.4202-111.86+129.36

MC=47.92

e)AVC=a + bQ + cQ 2

AVC=30.4202+(-0.0799)Q+(0.000088)Q2

f) Q=700

AVC=30.4202+(-0.0799)Q+(0.000088)Q2

AVC=30.4202+(-0.0799)(700)+(0.000088)(700)2

AVC=30.4202-55.93+43.12

AVC=17.61

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