Step 1: Understanding the Concept:
Under perfect competition, a firm acts as a price taker and maximizes profit by setting the market price equal to its marginal cost of production.
The supply curve of a competitive firm represents the relationship between market price and the quantity of output the firm is willing to produce.
Step 3: Detailed Explanation:
For a perfectly competitive firm, the short-run profit maximization condition is:
\[ P = MC \]
However, this equilibrium is valid only if the following conditions are met:
The Marginal Cost (MC) must be rising at the point of intersection (meaning the curve must be positively sloped).
The market price must be at least equal to the minimum of the Average Variable Cost (AVC) curve.
If the price falls below the minimum point of the AVC curve, the firm cannot cover its variable costs and will minimize its losses by shutting down completely (producing zero output).
Therefore, for prices above the minimum AVC, the firm chooses its output level along the upward-sloping portion of its MC curve.
Thus, the short-run supply curve of a perfectly competitive firm is represented by the positively sloped portion of the marginal cost curve that lies above the minimum point of the average variable cost curve.
Step 4: Final Answer:
The supply function is represented by the positively sloped marginal cost curve.