The chief economist for Argus Corporation, a large appliance manufacturer, estim

Question

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 0.7360 F-RATIO 39.428 P-VALUE ON F 0.0001
OBSERVATIONS:19 0

pARAMETER STANDARD
VARIABLE ESTimate error
INTERCEPT 191.93 54.65
-0.0305 0.00789
0.0000024 0.00000098

T-RATIO P-VALUE
3.512 0.0029
23.866 0.0014
2.449 0.0262

a. Are the parameter estimates statistically significant at the 2 percent level of significance?
b. Do the results indicate that the average variable cost curve is U-shaped? How do you know?
c. If Argus Corporation produces 8,000 vacuum cleaners per month, what is the estimated average variable cost? Marginal cost? Total variable cost? Total cost?
d. Answer part c, assuming that Argus produces 10,000 vacuum cleaners monthly.
e. At what level of output will average variable cost be at a minimum? What is minimum average variable cost?

Explanation / Answer

Degrees of Freedom: 17 (19-3 obs = 17) Significance level at 2%: 2.567 (a) No, c falls under the 2.567 (b) yes, because a and c are positive, b is negative, this is indicative of a U-shaped curve. (c) 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 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 TVC = aQ + bQ + cQ TVC = 191.93(8000) + - 0.0305(64000000) + 0.0000024(512000000000) TVC = 1535440 + (- 1952000) +512000000000 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 Qm = -b/2c Qm = - 0.0305/2(0.000024) Qm = - 6354.166667 (d)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.

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