Suppose you are an active fund manager with a limited capacity to generate

alpha of $2\mathrm{.}5$ million$/$year$.$ You charge a fee of $0\mathrm{.}5\%$ per year. Currently, your

portfolio has AUM of $150$ million.

a$.$ How much alpha is earned by you as fees? How much is left over for

your investors?

b$.$ Investors saw you had good performance and you got inflows of $200$

million, how much alpha is earned by you as fees? How much is left over

for your investors?

c$.$ What should be your AUM when there is no alpha left for your

investors?