A perfectly competitive painted necktie industry has a large number of potential entrants. Each firm has an identical cost structure such that long-run average cost is minimized at an output of 20 units . The minimum average cost is $10 per unit. Total market demand is given by 1500-5P
1.What is the industry’s long-run supply schedule?
2.What is the long-run equilibrium price The total industry output The output of each firm ? The number of firms? The profits of each firm?
I think I got most of #2 right, but #1 is the one giving me problems.
*Sorry, Total market demand is 1500-50P
To determine the industry's long-run supply schedule, we need to understand the concept of long-run equilibrium in a perfectly competitive market.
In the long run, firms in a perfectly competitive market can enter or exit the industry in response to profit opportunities. The industry is in long-run equilibrium when all firms are earning zero economic profits, producing at their efficient scale, and no firms have an incentive to enter or exit the market.
Let's solve each part of the question step by step:
1. Determining the industry's long-run supply schedule:
To find the industry's long-run supply schedule, we need to consider the firms' long-run average cost (LRAC) curve and the market demand equation.
The LRAC curve tells us the minimum average cost at which firms can produce, and it is given as $10 per unit for an output of 20 units.
The market demand equation is given by 1500 - 5P, where P represents the price in the market.
From the LRAC curve, we know that the minimum average cost of production is $10 per unit. Therefore, the minimum average cost of the industry is $10 * 20 units = $200.
To determine the industry's long-run supply schedule, we need to find the quantity at which the market price equals the minimum average cost. So, we set the market demand equation equal to the minimum average cost:
1500 - 5P = $200
Rearranging the equation:
5P = 1500 - $200
5P = $1300
P = $1300 / 5
P = $260
This means that in the long-run, the industry will supply the quantity at which the market price equals $260. Let's call this quantity Q*.
To find Q*, we substitute the price into the market demand equation:
1500 - 5P = 1500 - (5 * $260)
1500 - 5P = 1500 - 1300
1500 - 5P = 200
5P = 1500 - 200
5P = 1300
P = 1300 / 5
P = $260
So, the long-run equilibrium price for the industry is $260.
2. Long-run equilibrium parameters:
a) Total industry output: To find the total industry output, we substitute the long-run equilibrium price ($260) into the market demand equation:
Q* = 1500 - 5P
Q* = 1500 - 5(260)
Q* = 1500 - 1300
Q* = 200
Therefore, the total industry output in the long run is 200 units.
b) Output per firm: Since there is a large number of identical firms and each firm produces at its efficient scale, the output per firm would be the same as the total industry output:
Output per firm = Total industry output / Number of firms
Output per firm = 200 units / Number of firms
In this case, we don't have enough information to determine the exact number of firms, so we cannot calculate the output per firm or the number of firms.
c) Profits of each firm: In long-run equilibrium, firms in a perfectly competitive market earn zero economic profits. Since the industry is perfectly competitive and each firm has an identical cost structure, all firms will have the same costs and revenues. Therefore, the profits of each firm will be zero.
In summary, the long-run supply schedule for the industry is determined by the market price at which it equals the minimum average cost. The long-run equilibrium price is $260, with a total industry output of 200 units. The output per firm and the number of firms cannot be determined without additional information. Lastly, each firm will earn zero economic profits in long-run equilibrium.