To determine the profit-maximizing level of output for a monopolist, you need to understand the relationship between total revenue (TR) and total cost (TC).
The profit (\(\pi\)) is calculated as the difference between total revenue and total cost:
[tex]\[ \pi = TR - TC \][/tex]
To maximize profit, a monopolist should find the level of output where this difference is greatest.
Here are the steps involved to identify this level of output:
1. Understand the Total Revenue (TR) Curve: Total revenue is calculated as the price (P) times the quantity (Q) sold. The TR curve shows how total revenue changes with different levels of output.
2. Understand the Total Cost (TC) Curve: Total cost includes all costs incurred to produce a given level of output. The TC curve shows how total costs change with different levels of output.
3. Calculate Profit for Different Levels of Output: For various quantities of output (Q), calculate the profit by subtracting total cost (TC) from total revenue (TR):
[tex]\[ \pi = TR(Q) - TC(Q) \][/tex]
4. Identify the Level of Output with the Greatest Profit: After calculating the profit for different levels of output, the profit-maximizing level of output is where the profit (\(\pi\)) is the highest, which means the greatest positive difference between total revenue and total cost.
5. Optimal Choice: The profit-maximizing level of output is where the difference \( TR - TC \) is maximized.
Based on these steps, the correct answer to the question is:
D. The profit-maximizing level of output will be where there is the greatest difference between total revenue and total cost.
