Tootmisfunktsioon

Tootmisfunktsioon, in economics, is a mathematical representation of the technological relationship between inputs used in production and the maximum quantity of output that can be produced with those inputs, given available knowledge and efficiency. It summarizes how different amounts of inputs translate into goods or services.

A typical production function maps input quantities, usually capital (K) and labor (L), to output (Q): Q = F(K, L). It embodies the idea that more of a useful input can raise output, up to technological limits. The function implies marginal products, such as the marginal product of capital MPK = ∂F/∂K and the marginal product of labor MPL = ∂F/∂L, which often diminish as input levels rise.

Returns to scale describe how output changes when all inputs are scaled by the same factor. Constant returns to scale satisfy F(tK, tL) = tF(K, L); increasing or decreasing returns to scale occur when the equality is respectively greater or less than tF(K, L). Isoquants, the set of input combinations that yield a given output, are typically drawn from a production function and are convex, reflecting substitutability between inputs and diminishing marginal rates of technical substitution.

Common functional forms include Leontief, Cobb-Douglas, and CES functions, each capturing different substitutability and elasticity properties between inputs. In the short run, some inputs may be fixed, limiting production, while in the long run all inputs are variable.

Used in microeconomic analysis, tootmisfunktsioon underpins cost and profit optimization, input demand, and assessments of technological change. It provides a framework for understanding efficiency, resource allocation, and the trade-offs involved in production decisions.