Question

Suppose the market for wheat consists of 500 identical firms, each with the following total and marginal cost functions:

TC(q) = 90,000 + 0.00001q2

MC(q) = 0.00002q

where q is measured in bushels per year. The market demand for wheat is Q = 90,000,000 – 20,000,000P

a. Find the market equilibrium price and quantity.

b. Find the profit-maximizing quantity of production for each firm and the profit at that quantity.

Answer 1

Market consists of 500 identical firms. TC(q) = 90,000 + 0.00001q2. MC(q) = 0.00002q

Supply function of 1 firm is P = MC = 0.00002q or q = 50000P. For 500 firms market supply is Qs = 500*50000P = 25,000,000P

The market demand for wheat is Q = 90,000,000 – 20,000,000P

a. The market equilibrium price and quantity is determined when Qs = Qd

25,000,000P = 90,000,000 – 20,000,000P

P* = 90,000,000/45,000,000 = $2

Qs = Qd = 90,000,000 – 20,000,000*2 = 50,000,000

b. The profit-maximizing quantity of production for each firm is found at P = MC

2 = 0.00002q

q = 100,000

and the profit at that quantity is (TR - TC) = (2*100,000 - 90,000 - 0.00001*(100000^2)) = $10000