perfectly competitive industry. Each firm having identical cost structures. long-run average cost is minimized at an output of 20 units. Minimum average cost is $10 per unit. total market demand is Q=1500-50P.
What is the long-run equilibrium price? Total industry output? output of each firm? number of firms? profits of each firm?
With identical cost structures, the firms, in the long run, will all end up producing where the AC is minimized. So, P=10, plug this into the demand equation to get total Q.
Take it from here
am i doing this correctly? total output = 1000. output of each firm 20. number of firms 50. ?finding equilibrium price and profits from firms?
Yes, you are on the right track. You have the equilibrium price, P=10. At P=10, average revenue must also be 10. Average cost is 10, so profits are zero.
To find the long-run equilibrium price, total industry output, output of each firm, number of firms, and profits of each firm in a perfectly competitive industry with identical cost structures, we need to follow these steps:
Step 1: Determine the equilibrium price.
In a perfectly competitive market, the price is determined by the intersection of market demand and market supply. The market demand equation given is Q = 1500 - 50P, where Q represents total market output and P represents the price. The total market output is the sum of the outputs of each firm in the industry. We need to find the equilibrium price where market demand equals total market output.
To find the equilibrium price, we equate market demand and total market output:
Q = 1500 - 50P
Sum of firm outputs = Total market output
Step 2: Determine the total industry output.
Once we find the equilibrium price, we can substitute it back into either the market demand equation or the sum of the firm outputs equation to calculate the total industry output. This will give us the level of industry-wide production at the equilibrium price.
Step 3: Determine the output of each firm.
Since each firm's cost structure is identical, they will all aim to produce at the output level that minimizes their long-run average cost. It is given that the long-run average cost is minimized at an output of 20 units. Therefore, each firm in the industry would produce 20 units of output.
Step 4: Determine the number of firms.
To find the number of firms in the industry, we divide the total industry output by the output of each firm. The result will give us the number of firms required to produce the equilibrium level of output.
Step 5: Determine the profits of each firm.
In a perfectly competitive industry, firms earn zero economic profits in the long run. This means that their total revenue equals their total cost. To calculate the profits of each firm, we need to calculate their total revenue and total cost.
Now let's go through these steps to find the answers:
Step 1: Equilibrium Price
Equate market demand and total market output:
1500 - 50P = Sum of firm outputs
Step 2: Total Industry Output
Substitute the equilibrium price into the market demand equation or the sum of the firm outputs equation to calculate the total industry output.
Step 3: Output of Each Firm
Each firm produces at the output level that minimizes the long-run average cost. In this case, it is given that the output level that minimizes the cost is 20 units.
Step 4: Number of Firms
Divide the total industry output by the output of each firm to determine the number of firms.
Step 5: Profits of Each Firm
Calculate the total revenue and total cost of each firm. Since firms in a perfectly competitive industry earn zero economic profits in the long run, the total revenue should equal total cost for each firm.