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 Q=1500-50P.

a. What is the industry's long-run supply schedule?

From the information, you have given, Price will be $10. If demand increase an prices rises above $10 in the short run, more firms will enter and drive the price back down to $10. If demand falls and and price falls below $10, all firms will begin to lose money in the short run, some firms will drop out lowering Q and therefore raising the price back up to $10.

Long-run supply is therefore perfectly elastic at $10.

$10

To determine the industry's long-run supply schedule, we need to understand the conditions of perfect competition and how firms in the industry make their production decisions.

In perfect competition, there are a large number of potential entrants, and each firm in the industry has identical costs and operates on the basis of profit maximization. In the long run, firms can freely enter or exit the market, which means that they can adjust their production levels and investment in the long run.

In this case, each firm in the painted necktie industry has a minimum average cost of $10 per unit at an output of 20 units. This means that if a firm produces more or less than 20 units, its average cost will be higher than $10 per unit.

To determine the industry's long-run supply schedule, we need to find the price at which firms will be willing to enter or exit the market. In other words, we need to find the price at which the firms in the industry will cover their costs and make a normal profit.

The market demand function is given by Q = 1500 - 50P, where Q is the quantity demanded and P is the price.

To find the market price at which firms will enter or exit the market, we need to find the price at which the quantity supplied by firms in the industry equals the quantity demanded by consumers. This is the long-run equilibrium price.

To start, let's set the quantity supplied equal to the quantity demanded and solve for the price:

Quantity supplied = Quantity demanded
Q = 1500 - 50P (market demand function)

Since we want to find the long-run equilibrium price, we set the quantity supplied equal to the quantity demanded:

20 * number of firms = 1500 - 50P

To find the number of firms, we divide the total quantity supplied by the quantity produced per firm:

Number of firms = total quantity supplied / quantity produced per firm
Number of firms = (1500 - 50P) / 20

Now, we have an expression for the number of firms in terms of the price. However, we need to determine the range of prices at which firms will enter or exit the market.

Since the industry operates under perfect competition, firms will only produce if the price is equal to or above their minimum average cost of $10 per unit. This means that firms will only enter or stay in the market if the price is greater than or equal to $10.

So, we set the price equal to $10 and solve for the number of firms:

Number of firms = (1500 - 50 * 10) / 20
Number of firms = 100

Now, we have the number of firms at a price of $10. To determine the long-run supply schedule, we need to find the number of firms at each price above $10.

We can use the expression we derived for the number of firms in terms of the price:

Number of firms = (1500 - 50P) / 20

Substitute different prices above $10 into this equation and calculate the corresponding number of firms. The resulting values will give us the long-run supply schedule for the painted necktie industry.

For example, if we substitute a price of $15:

Number of firms = (1500 - 50 * 15) / 20
Number of firms = 75

Repeat this process for different prices above $10 to obtain the complete long-run supply schedule.