You are the new economic policy advisor for the mayor of Collegeville (Congratulations!). Your first project is understanding the market for widgets, a huge market in Collegeville. You look at this market and you see that there are N = 3 identical sellers, indexed as i = 1, 2, 3.
All widgets are the same, no matter who produced them. So, you observe the following:
q1 = q2 = q3 = 4, and P = 12.
(Note that firms are assumed to be in equilibrium.) From your predecessor, you also know that demand for widgets is linear, or takes the general linear form
Q = A − BP,
and that each seller’s marginal cost is linear (not constant) in q, or that
mc1 = mc2 = mc3 = cq.
Finally, you know the town charges a fixed licensing fee of FC = $10 to sell widgets, and there are no other costs associated with selling (or buying) widgets.
Part 1: Suppose that you believe this market is perfectly competitive. What is the total cost function, TC(q), for an individual firm?
TC(q) = 10 + (q^2)
TC(q) = 1.5*(q^2)
TC(q) = 10 + 2.5*q
TC(q) = 10 + 1.5*(q^2)
TC(q) = 10 + 2.5*(q^2)
TC(q) = 10 + 4.5*q