The chief economist for Argus Corporation, a large appliance manufacturer, estim
ID: 1166983 • Letter: T
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 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 parameter estimates (a, b and c) statistically significant at the 1 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 marginal costs?
d.) f Argus Corporation produces 8,000 vacuum cleaners per month, and sell all of them in the market at price of $200 each. How much will be the total profit (i.e. total revenue – total costs)?
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
Explanation / Answer
Answer : Degrees of Freedom: 17 (19-3 obs = 17)
Significance level at 1%: 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
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