EverKleen Pool Services provides weekly swimming pool maintenance in Atlanta. Do

Question

EverKleen 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. EverKleen Pool Services has fixed costs of $3,500.

The manager of EverKleen has estimated the following marginal cost function for EverKleen, using data for the last two years:

SMC = 125 ? 0.42Q + 0.0021Q2 where SMC is measured in dollars and Q is the number of pools serviced each summer.

a - Given the estimated marginal cost function, what is the average variable cost function for EverKleen?

b - Should the manager of EverKleen continue to operate, or should the firm shut down? Explain.

c - How much profit (or loss) can the manager of EverKleen Pool Services expect to earn?

TYPE ANSWER - NO PICTURES PLEASE.

Explanation / Answer

a) AVC = 125 - 0.21Q + 0.0007Q^2

b) differentiate average variable cost with respect to Q and then equate to zero

dAVC/dQ = -0.21+ 0.0014Q = 0 implies Q = 150. Put the value of Q in AVC

AVC = 125 - 0.21(125) + 0.0007(125)^2 = 109.25. Since the price is more than AVC, the firm should continue to operate

c) at profit maximisation

125 - 0.42Q + 0.0021Q^2 = 115 implies Q= 172

So profit = total revenue - total cost

115q-(125Q-.21Q^2+0.0007Q^3+3500)

Q=172115(172)-(125(172)-.21(172)^2+.0007(172)^3+3500)

P=-2569.27 The firm will expect a loss of 2569.2

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.