. 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: 19 0.7360 39.428 0.0001 PARAMETER STANDARD VARIABLE ESTIMATE ERROR 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 ˆa , ˆb , and cˆ statistically significant at the 2 percent level of significance? Which is/are significant and which is/are not? b) Do the results indicate that the average variable cost curve is ∪-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? f) What is the minimum average variable cost?
2. The chief economist for Argus Corporation, a large appliance manufacturer, estimated the firm’s short-run cost function for vacuum cleaners using an
DEPENDENT VARIABLE: AVC R-SQUARE F-RATIO P-VALUE ON F
OBSERVATIONS: 19 0.7360 39.428 0.0001
PARAMETER STANDARD
VARIABLE ESTIMATE ERROR 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 ˆa , ˆb , and cˆ statistically significant at the 2 percent level of significance? Which is/are significant and which is/are not?
b) Do the results indicate that the average variable cost curve is ∪-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?
f) What is the minimum average variable cost?
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