Question

1) Suppose there are 1000 identical strawberry producers. For each, TC = 10 + q². Market demand is Q = 600,000 - 100p.

a) Derive the short-run equilibrium Q, q, and p.

b) Does the typical firm earn a short-run profit?

Answer 1

a) Individual supply is P = MC
MC = d(TC)/dq = 2q
So, p = 2q
So, q = p/2

Market supply, Q = 1000q = 1000(p/2)
So, Q = 500p

At equilibrium, market demand = market supply.
So, 600,000 - 100p = 500p
So, 500p + 100p = 600p = 600,000
So, p = 600,000/600
So, p = 1,000

Q = 500p = 500(1000)
So, Q = 500,000

q = p/2 = 1000/2 = 500
So, q = 500

b) Profit of a firm = Total reveue - TC = p*q - (10 + q2) = (1000*500) - 10 - (500)2 = 500,000 - 10 - 250,000 = $249,990
Thus, the typical firm earn a short run profit.