Question

Suppose there is a perfectly competitive industry where all the firms are identical with identical cost curves. Furthermore, suppose that a representative firm’s total cost is given by the equation. TC = 100 + q^2 + q where q is the quantity of output produced by the firm. You also know that the market demand for this product is given by the equation P = 1000 - 2Q where Q is the market quantity. In addition, you are told that the market supply curve is given by the equation P = 100 + Q

a. What is the equilibrium quantity and price in this market given this information?

b. What is the firm’s MC equation?

c. What is the firm’s profit maximizing level of production?

d. What is the total revenue?

e. What is the total cost?

f. What is the profit at this market equilibrium?

Answer 1

Answer : a) Given,

Demand : P = 1000 - 2Q

Supply : P = 100 + Q

At market equilibrium for perfect competition, Demand = Supply.

=> 1000 - 2Q = 100 + Q

=> 1000 - 100 = Q + 2Q

=> 900 = 3Q

=> Q = 900 / 3

=> Q = 300

Now from demand function we get,

P = 1000 - (2*300)

=> P = $400

Therefore, the market equilibrium price is $400 and quantity is 300 units.

b) Given,

Firm's total cost : TC = 100 + q^2 + q  

MC = MC / q

=> MC = 2q + 1

Therefore, firm's MC function is : MC = 2q + 1.

c) From above calculation, we get that P = $400.

For competitive market firm's profit maximizing output level is that output level where market price (P) = MC.

400 = 2q + 1

=> 400 - 1 = 2q

=> 399 = 2q

=> q = 399 / 2

=> q = 199.5

Therefore, firm's profit maximizing output level is 199.5 units.

d) Total Revenue (TR) = P * q

=> TR = 400 * 199.5

=> TR = 79,800

Therefore, firm's total revenue is $79,800.

e) Total Cost (TC) = 100 + q^2 + q = 100 + (199.5)^2 + 199.5

=> TC = 40,099.75

Therefore, firm's total cost is $40,099.75.

f) Profit = TR - TC = 79,800 - 40,099.75

=> Profit = 39,700.25

Therefore, in this market firm's profit is $39,700.25.