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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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