Suppose a YouTube content creator $($i$.$e$.,$ a YouTuber$)$ in a perfectly competitive market

with the following total cost function: TC $=50+3$q$3$

$.$

a$.$ Find the supply curve for this YouTuber $($as a function of P$).[$Hint: Find the MC

and equate it to the market price P$.$ Then, solve for q as a function of P to obtain the

supply curve q $=$ f$($P$)].$

b$.$ Suppose that the market price is P $=81.$ What is the profit maximizing output level

$($q$*)?$

c$.$ Calculate the YouTuber$$s producer surplus for the market price given in $($b$).$

d$.$ Find the market supply curve $($as a function of P$)$ if there are $300$ identical YouTubers

in this market. What is the market output level, Q$,$ if P $=81?$ What is the market

output level, Q$,$ if P $=25?$