Suppose the Total Cost function of a firm in Perfect Competition is given by: $$C(q) = 450 + 15q + 2q^2$$
The market price is $P = 15$ per unit
Determine the optimal quantity produced by the firm
The trouble I'm having with this is a friend suggests the optimal quantity is q = 25 but that doesn't make sense to me.
Because when we calculate Marginal Cost = Marginal Revenue we get:
$$4q + 15 = 15$$
Which will yield an optimal quantity of 0 and not 25 when we solve for q.
The only way I can see it being equal to 25 is if the price is 115 and not 15 because of some typo. Any thoughts?