Isoquant

An isoquant is a curve that represents all combinations of inputs that produce a fixed level of output in a production technology. In the most common two-input setting, inputs are capital (K) and labor (L), and an isoquant corresponds to a production function F(K, L) = Q, where Q is a specified output level.

Along an isoquant, the rate at which one input can be substituted for the other while keeping output constant is described by the slope dK/dL = - MP_L / MP_K, where MP_L and MP_K are the marginal products of labor and capital, respectively. The absolute value of this slope is the marginal rate of technical substitution (MRTS). It measures how much of one input a firm is willing to give up to gain an additional unit of the other input without changing output.

Isoquants are typically downward sloping and convex to the origin under standard neoclassical assumptions. Convexity reflects a diminishing MRTS: as more labor is used and capital is reduced, the ease of substituting labor for capital falls. Special production technologies yield non-typical isoquants: L-shaped isoquants arise with perfect complements, while straight-line isoquants appear with perfect substitutes.

An isoquant map is a family of isoquants for different output levels and is used with an isocost line to analyze cost-minimizing input bundles for a given output. This framework parallels consumer theory, with isoquants playing a role analogous to indifference curves but oriented around production rather than utility.

Limitations arise from real-world departures from smooth, convex production functions, such as discontinuities or fixed input requirements. Isoquants remain a central tool in production analysis, illustrating input substitution and technological constraints.