Isocost

An isocost line is a concept in microeconomics that represents all combinations of two inputs that cost the same total amount for a given set of input prices. If a firm uses labor L and capital K with wage rate w and rental rate r, respectively, the total cost is C = wL + rK. The isocost is the set of input bundles (L, K) that satisfy this equation for a fixed C. The line has a negative slope, equal to -w/r, and intercepts where either input is zero: when L = 0, K = C/r; when K = 0, L = C/w.

In production analysis, the isocost is used together with isoquants (curves of equal output) to determine the least-cost combination of inputs for a given output level. The cost-minimizing point occurs where an isoquant is tangent to an isocost line, so the firm can produce the desired output at the lowest possible cost. At tangency, the marginal rate of technical substitution (MRTS) between inputs equals the ratio of input prices: MRTS = MP_L / MP_K = w/r, where MP_L and MP_K are the marginal products of labor and capital.

Isocosts respond to changes in input prices and total cost. A rise in w or r rotates the isocost line, changing the optimum input mix; a change in total cost C shifts the line outward or inward, preserving its slope. In models with more than two inputs, the isocost becomes a higher-dimensional hyperplane; in short-run analysis, some inputs may be fixed, restricting the feasible isocost sets. Isocost analysis aids in understanding cost minimization, budgeting, and input substitution decisions in competitive environments.