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 1500-50P
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.
Really need help here.
To determine the industry's long-run supply schedule, we need to find out the quantity supplied by each firm at different price levels. In a perfectly competitive market, each firm will produce at the point where its marginal cost (MC) equals the market price (P).
1. The industry's long-run supply schedule can be determined by adding up the quantities supplied by each firm at different price levels. To do this, we need to find the minimum of the industry's total cost and divide it by the minimum long-run average cost.
Let's start by finding the minimum long-run average cost (LRAC) for each firm. Given that the long-run average cost is minimized at an output of 20 units and the minimum average cost is $10 per unit, we can calculate the total cost (TC) for producing 20 units:
TC = LRAC x Quantity
TC = $10 x 20
TC = $200
Next, we need to determine the quantity supplied by each firm. We can find the quantity that maximizes profit or minimizes losses by comparing the market price (P) to the marginal cost (MC). Since the cost structure is identical for all firms, the MC for each firm will be the same. So, we can set MC equal to the market price and solve for the quantity.
MC = P = $10 (since MC is minimized at an output of 20 units as given)
To find the quantity supplied, we need to solve the market demand equation for P:
1500 - 50P = P
Simplifying the equation:
1500 = 51P
P = 1500/51
P ≈ 29.41
Now that we have the market price, we can substitute it back into the MC equation to find the quantity supplied by each firm:
MC = P = $10
MC = 29.41
Therefore, each firm will supply 29.41 units of painted neckties in the long run. The number of firms in the industry can be determined by dividing the total industry output by the output of each firm:
Total industry output = Quantity supplied by each firm x Number of firms
Total industry output = 29.41 x Number of firms
We don't have enough information to calculate the specific number of firms or the profits of each firm without additional data on cost and revenue. However, in the long-run equilibrium of a perfectly competitive market, firms will earn zero economic profit.