The derivation of a firm’s supply curve explains how much a firm chooses to produce as the market price changes, based on its production costs.

Short-Run Firm Supply:

• Profit maximization: A firm produces where Marginal Revenue (MR) equals Marginal Cost (MC). In perfect competition, this means the firm produces where Price equals MC (P = MC).
• Finding the curve: By identifying the output level where P = MC for every possible price, we map out the supply curve.
• Shutdown condition: If the price falls below the Average Variable Cost (AVC), the firm loses more money by operating than by closing. Therefore, the firm will produce zero output if P is below the minimum AVC.
• Key rule: In the short run, the firm’s supply curve is the portion of its MC curve that lies above the minimum point of its AVC curve.

Long-Run Firm Supply:

• In the long run, firms will stay in the market only if the price is greater than or equal to the Long-Run Average Cost (LAC).
• The long-run supply curve is the portion of the MC curve that lies above the minimum point of the LAC curve.

Market Supply:

• The total market supply is the horizontal sum of all individual firms’ supply curves at every given price.