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# Finding Profit maximisation activity level

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21st Century Insurance offers mail-order auto insurance to preferred risk drivers in the New York area. The company is the low-cost provider of insurance in this market, but does not believe its annual premium of \$1,500. can be raised for competitive reasons. Rates are expected to remain stable during coming periods; hence, P = MR = \$1,500. Total and marginal cost relations for the company are as follows
TC = \$41,000,000 + \$500 Q + \$0.005 Q^2

1) Calculate the profit-maximizing activity level

2) Calculate the company's optimal profit and optimal profit as a percentage of sales revenue (profit margin).

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#### Solution Preview

1) Calculate the profit-maximizing activity level
TC = \$41,000,000+500Q+0.005Q^2
TR = 1500*Q
Profit = TR-TC
= 1500Q-41000000-500Q-0.005Q^2
= 1000Q-0.005Q^2-41000000
For profit ...

#### Solution Summary

Solution describes the steps in finding out profit maximising activity level for 21st Century Insurance.

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