The chief economist for Argus Corporation, a large appliance manufacturer, estim
ID: 2947547 • 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.) If Argus Corporation produces 8,000 vacuum cleaners per month, what is the estimated marginal costs?
b.) 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
here we see that R-Squared value is 0.736, That's mean, 73.6% values fit to the model.
And sample size N=19.
Also we see that p-value of independent variables are less than significant level 0.05. So we, reject null hypothesis. That is , there is a non-zero correlation between 2 independent variables and dependent variable. This variables are statistically significant.
So we use these 2 independent variables for future prediction of y.
a) Let, Regression equation is as
AVC = a + bQ + cQ2
Here, a = 191.93 , b = 0.0305 , c = 0.0000024
Q = Number of vacuum cleaners produced in each month.
Q2 = $180000 Fixed price for each month
Let we calculate AVC for Q=8000
AVC = 191.93 + 0.0305*8000 + 0.0000024*180000
AVC = $436.362
That is Estimated marginal cost is $436.362 for per vacuum cleaner.
b) Profit = Total Revenue - Total Costs
Profit = 8000(436.362 - 200) = 8000 * 236.362
Profit = $1890896
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.