Q1. Given a firm's long-run total cost function operating in a competitive industry with market demand , what is the long-run equilibrium number of firms?

Background

Topic: Long-Run Competitive Equilibrium

This question tests your understanding of how to determine the number of firms in a perfectly competitive industry in the long run, using cost functions and market demand.

Key Terms and Formulas

• Long-Run Equilibrium: In perfect competition, firms earn zero economic profit in the long run, so (price equals minimum average cost).

• Total Cost (TC):

• Average Cost (AC):

• Market Demand:

Step-by-Step Guidance

1. Find the firm's average cost function: .

2. Set marginal cost (MC) equal to price () for competitive equilibrium. First, calculate from :

3. In long-run equilibrium, . Set and solve for to find the output per firm at minimum average cost.

4. Once you have , plug it into to find the equilibrium price .

5. Substitute into the market demand equation to find total industry output .

6. To find the number of firms, divide total industry output by the output per firm : .

Try solving on your own before revealing the answer!

Q2. Given the same cost function and market demand , what is the long-run equilibrium industry output?

Background

Topic: Industry Output in Long-Run Competitive Equilibrium

This question asks you to determine the total quantity produced by the industry in long-run equilibrium, using the cost structure and market demand.

Key Terms and Formulas

• Industry Output (): The total quantity supplied by all firms at the equilibrium price.

• Equilibrium Price (): Found where for the representative firm.

• Market Demand:

Step-by-Step Guidance

1. Recall from the previous question that the equilibrium price is found where for the firm.

2. Plug into the market demand equation to solve for :

3. Use the value of you found previously to calculate , the total equilibrium output for the industry.

Try solving on your own before revealing the answer!