Question

For a firm operating in a perfectly competitive market which of the following statements is CORRECT?

• A. Profit function is convex and homogeneous of degree 1 in prices
• B. Profit function is concave and homogeneous of degree 1 in prices
• C. Profit function is convex but not homogeneous in prices
• D. Profit function is neither concave nor convex in prices

Answer 1

The Correct Option is A

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.

1. 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.
2. 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.
3. 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.
4. 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.