A profit-maximizing firm in a competitive market is currently producing 100 units of output. It has average revenue of $10, average total cost of $8, and fixed cost of $200. Would the prevailing price be the same, higher, lower or two times the price at which the firm produes the efficient scale?
To determine whether the prevailing price would be the same, higher, lower, or two times the price at which the firm produces the efficient scale, we need to understand a few concepts.
1. Average Revenue (AR): It is the revenue earned per unit of output, calculated by dividing total revenue by the quantity sold. In this case, the average revenue is given as $10.
2. Average Total Cost (ATC): It is the cost per unit of output, calculated by dividing the total cost by the quantity produced. In this case, the average total cost is given as $8.
Now, let's break down the situation:
The profit-maximizing condition for a firm in a competitive market is to produce at a quantity where marginal cost (MC) equals marginal revenue (MR). This condition ensures that no further changes in production will increase profits.
In a perfectly competitive market, the price (P) is equal to the average revenue (AR). So, in this case, the prevailing price (P) is also $10.
Also, we have the formula for average total cost (ATC) as:
ATC = Total Cost / Quantity
If we rearrange this formula, we can find the total cost:
Total Cost = ATC * Quantity
Given that the average total cost (ATC) is $8 and the quantity produced is 100 units, we can calculate the total cost as:
Total Cost = $8 * 100 = $800
Now, we can calculate the variable cost (VC) by subtracting the fixed cost (FC) from the total cost:
Variable Cost = Total Cost - Fixed Cost
Variable Cost = $800 - $200 = $600
Since the firm is a profit-maximizer in a competitive market, the firm's profit will be the difference between revenue and cost:
Profit = Total Revenue - Total Cost
Total Revenue = Price * Quantity
Total Revenue = $10 * 100 = $1000
Profit = $1000 - $800 = $200
Given that profit is positive, it means the firm is earning economic profits.
Now, coming back to the efficient scale of production. The efficient scale occurs at the quantity where average total cost (ATC) is at its minimum. In this case, we don't have information about the minimum point of ATC or the quantity at which it occurs.
Therefore, we cannot determine if the prevailing price will be the same, higher, lower, or two times the price at which the firm produces the efficient scale, as we don't have sufficient information about the cost structure at different production levels.