Suppose that you are given the following information about a particular perfectly
competitive industry’s market demand: QD = 6500 – 100P and Market Supply: Qs =
1200P. Firm total cost function is given by: 𝐶(𝑞) = 722 +
𝑞
2
200
and assume that all firms
are identical and that the market is characterized by perfect competition.
A. Find the market equilibrium price and quantity supplied by each firm (1 pts.).
B. Determine the profit of a firm (1 pts.)
C. Would you expect entry into or exit from the industry in the long run? Explain (1 pts.)
D. What is the lowest price at which each firm would sell in the long run? (�
A. To find the market equilibrium price, we need to equate the market demand and market supply:
QD = Qs
6500 - 100P = 1200P
6500 = 1300P
P = 5
To find the quantity supplied by each firm, we substitute the equilibrium price back into the market supply equation:
Qs = 1200P
Qs = 1200(5)
Qs = 6000
Therefore, the market equilibrium price is $5 and each firm supplies 6,000 units.
B. To determine the profit of a firm, we need to calculate total revenue and total cost.
Total revenue = Price x Quantity
Total revenue = 5 x 6000
Total revenue = $30,000
Total cost = Fixed cost + Variable cost
Total cost = 722 + (6000^2/200)
Total cost = 722 + 180,000
Total cost = $180,722
Profit = Total revenue - Total cost
Profit = $30,000 - $180,722
Profit = -$150,722
The firm is making a loss of $150,722.
C. In the long run, we would expect exit from the industry. This is because firms are making a loss, and in perfect competition, there is free entry and exit. Firms will exit the industry if they are unable to cover their costs and make a profit. As long as firms are making a loss, some firms will choose to exit the industry until the remaining firms are able to make a profit.
D. The lowest price at which each firm would sell in the long run is equal to the minimum average variable cost (AVC), as firms will not produce if they cannot cover at least their variable costs.
The minimum AVC can be calculated by finding the quantity at which the marginal cost (MC) equals the average variable cost (AVC). In this case, the total cost function is quadratic, so we need to differentiate it to find MC:
MC(q) = dC(q)/dq = 2q/200
Equating MC and AVC:
2q/200 = 722 + q^2/200
q^2 + 722q - 144,000 = 0
Solving for q using the quadratic formula, we find:
q ≈ 113.94
Therefore, the lowest price at which each firm would sell in the long run is approximately $113.94.