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)?  

Answer 1

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