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A firm has developed a new product for which it has a registered trademark. The firm's market research department has estimated that the demand for

A firm has developed a new product for which it has a registered trademark. The firm's market research department has estimated that the demand for this product is Q(P,A)=11,600-1,000P+20A^(1/2)where Q is annual output, P is the price, and A the annual expenditure for advertising. The total cost of producing the new good is C(Q)=.001Q2+4Q. The unit cost of advertising is constant at m=1.

What is the optimal price P*?

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