The chief economist for Argus Corp., a large appliance manufactiuer, 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: 19 0.7360 39.428 0.0001

VARIABLE PARAMETER EST. STD ERR T-RATIO P-VALUE

INTERCEPT 191.93 54.65 3.512 0.0029
Q -0.0305 0.00789 23.866 0.0014
Q2 0.0000024 0.00000098 2.449 0.0262

a) Are the estimates a,b, and c statistically significant at the 2% level of significance?
b) Do the results indicate that the average variable cost curve is U-shaped? How do we know?
c) If Argus Corp. produces 8,000 vacuums 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 the average variable cost be at a minimum> What is the minimum average variable cost?