homework, microeconomic-theoryFor a monopolist, if
$C = F+4q+q^2$
where $C$ is total cost, $F$ is fixed cost, $p$ is price and $q$ is quantity,
This was added into the question by the OP but should have been an answer:
Monopolists choose output such that $MR$ = $MC$, where $MR$ is marginal revenue and $MC$ is marginal cost.
Fixed costs are never involved. So price and quantity can’t change, since the demand curve is not affected. Although, if $F$ is very large, the monopolist may shut down operations.
So a profit maximizing firm will worry about making marginal cost equal marginal revenue. We measure the firm’s profit function as The derivative of this gives us Which we set equal to zero and solve for $q$ in order to maximize profit. Since the firm is a monopoly, we can set $p(q)=p$ since it controls the quantity supplied in the market and $p’(q)=0$. We take the derivative of your cost function then and solve. Notice that the derivative of $c(q)$ does not include $F$ the fixed cost, since we treated it as a constant. In the end, you get $q*=(p-4)/2$, and we see that the quantity supplied is not dependent on $F$.
If $F$ sharply increases, then the firm may shut down depending on whether the fixed costs are sunk. A sunk cost is a fixed cost that cannot be recuperated by shutting down, so if $F$ is sunk, then the firm’s behavior will not change.
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