1)The chief economist for Argus Corporation, a large appliance mfg., estimated the firm’s short-run cost function for vacuum cleaners using an average variable cost function of the form:

Question

3
AVC = a + bQ + cQ

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 RSquare:0.7360 F-Ratio: 39.428 P-Value on F: 0.0001
Observations: 19
Variable Parameter Standard T
Estimate Error
InterCEPT 191.93 54.65
Q -o.o305 o.o0789
Q2 0.0000024 0.00000089
T-Ratio PValue
Intercept 3.512 0.0029
Q 23.866 0.0014
Q2 2.499 0.0262

Degrees of Freedom: 17 (19-3 obs = 17)
Significance level at 2%: 2.567
^ ^ ^
a)Are the estimates a, b, c statistically significant at
the 2% level of significance?
ANSWER: No, c falls under the 2.567 level (Is this right?) (I haven’t observed one like this, what does this mean if c is not at a significant level?)

b)Do the results indicate that the average variable cost is U-shaped? How do you know?
ANSWER: yes, because a and c are positive, b is negative, this is indicative of a U-shaped curve.

c) If Argus Corporation produces 8,000 vacuum cleaners, what is the estimated average cost variable cost?
ANSWER: 2
AVC = AVC= a + bQ + cQ
AVC = 191.93 + - 0.0305(8000) + 0.0000024(8000)
AVC = 191.93 + (-244) + 0.0000024(640000000)
AVC = - 52.47 + 153.60
AVC = 101.13

What is the marginal cost?ANSWER: 2
MC = a + 2bQ + 3cQ 2
MC = 191.93 + 2(-0.0305)(8000) + 3(0.0000024)(8000)
MC = 191.93 + 2(- 244) + 3(0.0000024)(64000000)
MC = 191.93 + (- 488) + 460.8
MC = 652.73 + (- 488)
MC = 164.73

What is the total variable cost?ANSWER:
2 3
TVC = aQ + bQ + cQ
TVC = 191.93(8000) + - 0.0305(64000000) + 0.0000024(512000000000)
TVC = 1535440 + (- 1952000) [phone]
TVC = 5121535440 + (-1952000)
TVC = 5119583440

There is another formula here I am unsure of:
TVC = AVC x Q
TVC = 101.13 x 8000
TVC = 809040

What is the total cost?
ANSWER: Qm = -b/2c
Qm = - 0.0305/2(0.000024)
Qm = - 6354.166667

d) Answer part c, assuming Argus produces 10,000 vacuum cleaners monthly?
ANSWER:
Same as above as long as my formulas are Correct.

e)At what level of output will the averagevariable cost be at a minimum?
Whatever the lowest of the two is (8 and 10K Produced per month).
What is the minimum average variable cost?
Whatever the lowest AVC is?

Do these seem correct?!?!?!
Thanks,
EY


a) You are testing to see if the parameter estimate is significantly different from zero; the null hypothesis is that the estimate is zero. So, divided the parameter estimate by the Standard T and compare that to your significance level cutoff (2.567 in your example); if less than the cutoff, then the parameter is not significantly different from zero. So for the b parameter 0.0305/.00789 = 3.86. Ergo, the parameter is significant. Repeat for the other parameters.

b) I agree.

c-AVC) I agree with your methodology, except I get 101.53

c-MC) I agree

c-TVC) I agree with your methodology, you made a silly math error. Rework and you should get 812240.

d) I agree.

e) no no no. Use calculus. Take the first derivitive of the AVC function, set that equal to zero and solve for Q. (Hint: I get Q=6354)