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 + q2 + 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 = 900 - 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.

1. What is the equilibrium quantity and price in this market given this information?
2. What is the firm’s MC equation?
3. What is the firm’s profit maximizing level of production?
4. What is the total revenue?
5. What is the total cost?
6. What is the profit at this market equilibrium?

Answer 1

Answer : Equilibrium price and quantity are :

Market demand:

P=900-2Q

Market supply:

P=100+Q

900-2Q= 100+Q

900-100=3Q

800/3=Q

Q= 267 units

P= 100+267=$367

2. ) TC= 100+q²+q

MC = 2q+1

3) firm profit maximization level is MR= MC

TR= 900Q-2Q ²

MR = 900-4Q

900-4q= 2q+1

900-1= 6q

899/6=q

Q= 150 units

4) TR=P*Q=( 900-2Q)*Q= 900Q-2Q²= 900*(150)-2(150)² = $90,000

5)TC= 100+q² +q = 100+(150)²+150= $22750

6) Profit= TR - TC = $90,000-$22,750= $67,250