Index-Fund Fees Suppose that the cost function in Exercise is C(x) = −2.5x+1, where x is the index-fund fee. (The company has a fixed cost of $1 billion, and the cost decreases as a function of the index-fund fee.) Find the value of x that maximizes profit. How well did Fidelity Mutual do before and after lowering the index-fund fees?
Excercise
Index-Fund Fees When a mutual fund company charges a fee of 0.47% on its index funds, its assets in the fund are $41 billion. And when it charges a fee of 0.18%, its assets in the fund are $300 billion.
(a) Let x denote the fee that the company charges as a percentage of the index fund and A(x) its assets in the fund. Express A(x) as a linear function of x.
(b) In September 2004, Fidelity Mutual lowered its fees on various index funds from an average of 0.3% to 0.10%. Let R(x) denote the revenue of the company from fees when its index-fund fee is x%. Compare the revenue of the company before and after lowering the fees. [Hint: Revenue is x% of assets.]
(c) Find the fee that maximizes the revenue of the company and determine the maximum revenue.
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