Answer to Question #64949 in Microeconomics for David

Question

The market demand for woozles is given by:
Qd 2, 400 – 20p
There is only one available technology, and it is employed by all producers—
actual and potential. It implies the following average cost function: AC 625q–1 0.25q
Currently, 20 firms serve the market.
a. Find the individual firm’s supply curve. (3 marks)
b. Find the industry supply curve. (3 marks)
c. Determine the short‐run competitive price and output. (3 marks)
d. How much profit is the typical firm making? (3 marks)
e. Determine the long‐run competitive market price and quantity and how many firms will operate. (8 marks)

Answer 1

Qd = 2,400 – 20p, p = 120 - q/20, AC = 625/q + 0.25q
Currently, 20 firms serve the market.
a. The individual firm’s supply curve is the part of MC curve after the intersection with AVC curve. So, S(firm) = MC = TC' = (AC*q)' = (625 + 0.25q^2)' = 0.5q.
b. The industry supply curve is S(industry) = 20*S(firm) = 20*0.5q = 10q.
c. The short‐run competitive price and output are in the equilibrium point, at which Qd = Qs, so:
As S = p = 10q, then Qs = 0.1p, Qd = 2,400 – 20p,
2,400 - 20p = 0.1p,
20.1p = 2,400,
p = $119.4,
q = 11.94 units.
d. The total profit that typical firm is making is:
TP = (p - AC)*q = (119.4 - 625/11.94 - 0.25*11.94)*11.94 = $765.
e. In the long‐run all firms receive zero profits and p = AC, so the market price and quantity are:
p = 625/q + 0.25q,
120 - 0.05q = 625/q + 0.25q,
625/q + 0.3q - 120 = 0,
0.3q^2 - 120q + 625 = 0,
q = (120 - 116.83)/0.6 = 5.28 units, so less firms will operate.
p = 120 - 5.28/20 = $119.74.