Production and cost theories

Production theory asks how inputs become output; cost theory asks what that output costs. The short run has at least one fixed input (say, the factory), so adding more of the variable input first raises output faster, then slower, then reduces it — the law of variable proportions. Worked example: with a fixed workshop, adding workers raises output by 20, then 15, then 8, then −3 units: the marginal product first rises, then falls, then turns negative.