a firm in a purely competitive industry is currently producing a 1000 unir per day at a total cost of $450. if the firm produced 800 units per day, it total cost will be $300, and it it produced 500 units per day, it total cost will be $275. Requirements: (1) what are the firm's ATC per unit at these three levels of production? (2) if every firm in this industry has the same cost structure, is the industry in long-run competitive equilibrium? (3) from what you know about these firms's cost structure, what is the highest possible price per unit that could be exist as the market price in the long run equilibrium? (4) if that price ends up being the market price and if the normal rate of profit is 10 percent , the how big will each firm's accounting profit per unit be?

For the first one, average cost per unit would be 450/1000, 300/800, and 275/500, just dividing the price by the units produced.

Apologies that I can't help any further; I haven't taken Economics or Statistics yet and don't know what a lot of those terms mean (purely competitive??)

Also:
Economics isn't Home Economics. This belongs under Math. (If it's automatically categorized, this message is to the Jiskha team, then.)

(1) To calculate the firm's average total cost (ATC) per unit, we divide the total cost by the number of units produced.

At 1000 units:
ATC = Total Cost / Number of Units
= $450 / 1000
= $0.45 per unit

At 800 units:
ATC = Total Cost / Number of Units
= $300 / 800
= $0.375 per unit

At 500 units:
ATC = Total Cost / Number of Units
= $275 / 500
= $0.55 per unit

Therefore, the firm's ATC per unit at these three levels of production are:
- 1000 units: $0.45 per unit
- 800 units: $0.375 per unit
- 500 units: $0.55 per unit

(2) To determine if the industry is in long-run competitive equilibrium, we compare the market price with the minimum average total cost (ATC) of firms in the industry. If the market price is equal to or greater than the minimum ATC, the industry is in long-run competitive equilibrium.

Since we don't have information about the market price, we cannot determine if the industry is in long-run competitive equilibrium based solely on the cost structure provided.

(3) The highest possible price per unit that could exist in the long-run equilibrium is equal to the minimum ATC. From the information provided, the minimum ATC is $0.375 per unit when the firm produces 800 units per day.

(4) If the market price ends up being $0.375 per unit and the normal rate of profit is 10%, then each firm's accounting profit per unit would be the difference between the price per unit and the average total cost:

Accounting Profit per Unit = Market Price - ATC
= $0.375 - $0.375
= $0 per unit

In this case, each firm would not have any accounting profit per unit, as the market price just covers the average total cost.

To find the firm's average total cost (ATC) per unit at each level of production, we can use the formula ATC = Total Cost / Quantity.

(1) ATC per unit at 1000 units per day:
Total Cost = $450
Quantity = 1000 units
ATC = $450 / 1000 = $0.45 per unit

ATC per unit at 800 units per day:
Total Cost = $300
Quantity = 800 units
ATC = $300 / 800 = $0.375 per unit

ATC per unit at 500 units per day:
Total Cost = $275
Quantity = 500 units
ATC = $275 / 500 = $0.55 per unit

(2) For the industry to be in long-run competitive equilibrium, firms within the industry must be making zero economic profit. Economic profit is calculated by subtracting total costs (including opportunity costs) from total revenue. If all firms have the same cost structure, we can determine if the industry is in long-run competitive equilibrium by comparing the market price to the ATC per unit.

If the market price is higher than the ATC per unit, firms in the industry are making economic profit and new firms will enter the industry, increasing competition and eventually driving the market price down. Conversely, if the market price is lower than the ATC per unit, firms are experiencing losses, which will lead to some firms exiting the industry, reducing competition and eventually pushing the market price up.

(3) The highest possible price per unit that could exist in long-run competitive equilibrium would be equal to the ATC per unit at the quantity produced where the ATC is the lowest. In this case, that would be when the firm produces 800 units per day, resulting in an ATC of $0.375 per unit.

(4) If the market price ends up being $0.375 per unit and the normal rate of profit is 10 percent, each firm's accounting profit per unit would be equal to the difference between the market price and the average variable cost (AVC) per unit. We do not have information about the firm's AVC, so we cannot calculate the exact accounting profit per unit in this scenario.