Theory of production and costs

Production turns inputs into output, and the short run has at least one fixed input while in the long run all inputs can change. The law of variable proportions says that as more of a variable input is added to a fixed input, marginal product first rises and then falls, so total product rises at a falling rate and eventually falls. Costs follow from production: marginal cost is the cost of one more unit, and the marginal cost curve cuts average cost and average variable cost at their lowest points. Worked example: if total cost is TC = 100 + 10Q + Q^2, then marginal cost is MC = 10 + 2Q, so at Q = 10, MC = 30.