Introduction:
Perfect competition is a market structure where there are a large number of buyers and sellers, a homogeneous product, and free entry and exit. In such a market, the supply curve is derived from the cost curves of the firms operating in the market.

Cost Curves:
There are three types of cost curves:
1. Marginal Cost (MC) Curve
2. Average Cost (AC) Curve
3. Total Cost (TC) Curve

Derivation of Supply Curve:
Under perfect competition, the firms are price takers, i.e., they cannot influence the market price. Therefore, the price is given and constant for all the firms in the market. In such a scenario, the firms produce at a level where their marginal cost is equal to the market price.

Thus, in the short run, the supply curve of an individual firm is the portion of its marginal cost curve that lies above the average variable cost curve. This is because, in the short run, the firm needs to cover its variable costs, and any production below that level would result in losses.

In the long run, the supply curve of the firm becomes its marginal cost curve, as all costs become variable in the long run, and the firm needs to cover all its costs to stay in the market.

The market supply curve is derived by horizontally summing the individual supply curves of all the firms operating in the market.

Conclusion:
Therefore, under perfect competition, the supply curve is derived from the cost curves of the firms. The individual supply curve of a firm is its marginal cost curve above the average variable cost curve in the short run, and its marginal cost curve in the long run. The market supply curve is derived by horizontally summing the individual supply curves of all the firms in the market.

A). The individual supply curve shows how much output a firm in a perfectly competitive market will supply at any given price. Provided that a firm is producing output, the supply curve is the same as marginal cost curve.