Question:
For a firm operating in a perfectly competitive market which of the following statements is CORRECT?
For a firm operating in a perfectly competitive market which of the following statements is CORRECT?
Updated On: Nov 18, 2025
- Profit function is convex and homogeneous of degree 1 in prices
- Profit function is concave and homogeneous of degree 1 in prices
- Profit function is convex but not homogeneous in prices
- Profit function is neither concave nor convex in prices
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The Correct Option is A
Solution and Explanation
To understand the correct statement regarding a firm operating in a perfectly competitive market, we need to explore the properties of profit functions in economics, particularly focusing on convexity, concavity, and homogeneity.
- Definition and Properties of the Profit Function:
- The profit function in economics represents the maximum profit a firm can achieve given the prices of inputs and outputs, considering its production technology.
- The profit function depends on the prices of inputs and outputs and is derived through the firm's cost and production functions.
- A crucial characteristic of the profit function is that it can exhibit both convexity and homogeneity properties.
- Convexity of the Profit Function:
- The profit function is convex in prices because the firm always strives to maximize profit, and the marginal profit increases when prices change.
- Convexity implies that as the firm's output prices increase, potential profit levels increase, encouraging production.
- Homogeneity of the Profit Function:
- In a perfectly competitive market, the profit function is homogeneous of degree 1, meaning if all prices are scaled by a constant factor, the maximum profit scales by the same factor.
- This property reflects the linearity in price adjustments, allowing for proportional changes in profit with changes in price levels.
- Conclusion and Correct Statement:
- Based on the characteristics discussed, the correct statement regarding the firm's profit function is: "Profit function is convex and homogeneous of degree 1 in prices."
- This perfectly aligns with the nature of firms in a perfectly competitive market.
Thus, the correct choice is the first option: Profit function is convex and homogeneous of degree 1 in prices.
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