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 F-RATIO P-VALUE ON F
OBSERVATIONS: 190 0.7360 39.428 0.001
VARIABLE PARAMETER STANDARD T-RATIO P-VALUE
Estimate Error
INTERCEPT 194.93 54.65 .512 0.0029
Q -0.0305 0.00789 23.866 0.0014
Q2 0.0000024 0.00000098 2.449 0.0262
a. Are the parameter estimates a, b, and c 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?