Step 1: Understanding the Concept:
In microeconomics, a firm aims to maximize its total profit, defined as the difference between total revenue (TR) and total cost (TC).
Key Formula or Approach:
The profit function is represented as:
\[ \Pi = TR - TC \]
To find the profit-maximizing level of output (\(Q\)), we take the derivative of profit with respect to quantity and set it equal to zero:
\[ \frac{d\Pi}{dQ} = \frac{d(TR)}{dQ} - \frac{d(TC)}{dQ} = 0 \]
Since \(\frac{d(TR)}{dQ}\) is Marginal Revenue (\(MR\)) and \(\frac{d(TC)}{dQ}\) is Marginal Cost (\(MC\)), we get:
\[ MR - MC = 0 \implies MR = MC \]
Step 2: Detailed Explanation:
The firm will continue to expand production as long as the revenue from selling an additional unit (MR) is greater than the cost of producing that unit (MC).
If production increases beyond the point where \(MR = MC\), the cost of producing more units will exceed the revenue they generate, lowering overall profit.
Thus, the optimal output for profit maximization is precisely where \(MR = MC\).
Step 3: Final Answer:
Therefore, profit maximization of a firm is achieved when Marginal Revenue equals Marginal Cost.