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# Analyzing Cost Functions

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1.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+ cQ^2 (the 2 is suppose to be exponent)
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
Variable Parameter Estimate Standard 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 a,b,c statistically significant at the 2 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 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? What is minimum average variable cost?

2. Ever Kleen Pool Services provides weekly swimming pool maintenance in Atlanta. Dozens of firms provide this service. The service is standardized;each company cleans the pool and maintains the proper levels of chemicals in the water. The service is typically sold as a four month summer contract. The market price for the four month service contract is \$115.
Ever Kleen Pool Services has fixed costs of \$3500. The manager if Ever Kleen has estimated the following marginal cost function for Ever Kleen, using data for the last two years:

SMC=125 - 0.42Q +0.0021Q^2 (suppose to be exponent 2)

Where SMC is measured in dollars and Q is the number of pools serviced each summer. Each of estimated coefficients is statistically significant at the 5 percent level.

a.Given the estimated marginal cost function, what is the average variable cost function for EverKleen?
b.At what output level does AVC reach its minimum value? What is the value of AVC at its minimum point?
c.Should the manager of EverKleen continue to operate, or should the firm shut down? Explain.
d.The manager of EverKleen finds two output levels that appear to be optimal. What are these levels of output and which one is actually optimal?
e.How much profit (or loss) can the manager of EverKleen Pool Services expect to earn?
f.Suppose EverKleen's fixed costs rise to \$4000. How does this affect the optimal level of output ? Explain.

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#### Solution Preview

Please refer attached file for better clarity of expressions.

Solution:

a.Are the estimates a,b,c statistically significant at the 2 percent level of significance?
Look for p vales for a, b, c
P value for a=0.0029, It is less than 0.02, It is statistically significant at 2% level.
P value for b=0.0014, It is less than 0.02, It is statistically significant at 2% level.
P value for c=0.0262, It is greater than 0.02, It is not statistically significant at 2% level.

But we see that all coefficients are significant at 3% level.

b.Do the results indicate that the average variable cost curve is U-Shaped? How do you know?
Regression model gives
AVC=191.93-0.0305Q+0.0000024Q^2

Conditions for curve to be U-shaped
Format: ax^2+bx+c
Where a & c>0
And b<0

which hold true for given expression. We can say that AVC is U shaped.

c.If Argus Corporation produces 8,000 vacuum cleaners per month, what is the estimated average variable cost? Marginal cost? Total variable cost? Total ...

#### Solution Summary

There are two problems. Solution to first problems steps for checking significance of regression coefficients. It explains steps to calculate marginal cost, average variable cost, total variable cost, total cost and minimum AVC. Solution to second problem explains the steps to calculate minimum AVC, optimal level of output and profits.

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