costminimizing

Cost minimization, in economics, is the process by which a decision-maker seeks to achieve a specific outcome at the lowest possible cost. It is a central problem in firm theory and is closely linked to the concept of the cost function. In a typical production setting, a firm with given input prices and a production technology aims to produce a target output while minimizing total expenditure on inputs such as labor and capital. The structure of a cost-minimization problem produces input demand functions and a corresponding cost function that shows the minimum cost to produce any given level of output.

In standard analysis, the problem is solved by choosing the least-cost combination of inputs that satisfies the production constraint. Under regularity conditions, the optimal solution often equates the rate at which inputs can substitute for one another (the marginal rate of technical substitution) to the ratio of input prices. This yields relationships between input choices and cost, and gives rise to the dual concept of the cost function C(y, w), which maps a desired output y and input prices w to the minimum achievable cost.

Cost minimization contrasts with profit maximization, which also accounts for output price and revenue, and with expenditure minimization in consumer theory, which focuses on achieving a utility level at minimum spending. Real-world applications include budgeting, procurement, manufacturing planning, energy sourcing, and supply chain design, where firms seek the most economical input combinations under technology and price changes. Limitations include assumptions of certainty, static technology, and convexity of production possibilities, which may not hold in all contexts.