Appendix 123

Appendix
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124 Part 3 Markets and Prices
Solution
:
– Q
Q :
Q
*:
2
)
2
3. Suppose that American Borax is a monopolist and that the worldwide demand for borax is Q = 100 –
where Q is tons of borax and P is the price per ton. The total cost function for American Borax is
TC = 10 Q + 0.5 Q
2
.
a. Write out the firm’s total revenue as a function of Q
b. What is the profit function for American Borax?
c. Find the firm’s profit-maximizing quantity by applying calculus to the profit function.
d. Find American Borax’s profit-maximizing price and profit.
P
.
P
Q
2
)
2
30
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Appendix: The Calculus of Profit Maximization Chapter 9 125
Solution
Solution