Question

Problem 1: What Do We Learn from Economic Models?

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

Answer 1

In this case, the total number of firms in the market for widgets is 3 and the quantities of each individual firm is denoted as q which is 4. The price of each widget is given as P=12 and the marginal cost of each firm is given as cq. Therefore, the total variable cost or TVC of each firm=(cq)*q=cq^2. The fixed licensing fee which has to be paid by each firm to sell widgets is given as FC=10. The market demand function for widgets is given as Q=A-BP and since all the individual firms produce the same quantity of output the total market supply of widgets at the equilibrium is 12 widgets. Therefore, the total cost function of each firm or TC(q), in this case would be=(FC+TVC)=10+cq^2. In the marginal cost function of each firm the c can be considered as a constant and q is variable implying that the total cost function of each firm could be TC(q)=10+q^2