economics

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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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