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If a production function is homogeneous of degree one, it is sometimes called "linearly homogeneous". A linearly homogeneous production function with inputs capital and labour has the properties that the marginal and average physical products of both capital and labour can be expressed as functions of the capital-labour ratio alone.
This is a list of production functions that have been used in the economics literature. Production functions are a key part of modelling national output and national income . For a much more extensive discussion of various types of production functions and their properties, their relationships and origin, see Chambers (1988) [ 1 ] and Sickles ...
Wire-grid Cobb–Douglas production surface with isoquants A two-input Cobb–Douglas production function with isoquants. In economics and econometrics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs (particularly physical capital and labor) and ...
Constant elasticity of substitution (CES) is a common specification of many production functions and utility functions in neoclassical economics.CES holds that the ability to substitute one input factor with another (for example labour with capital) to maintain the same level of production stays constant over different production levels.
Two input Leontief Production Function with isoquants. In economics, the Leontief production function or fixed proportions production function is a production function that implies the factors of production which will be used in fixed (technologically predetermined) proportions, as there is no substitutability between factors.
In lieu of the diminishing returns of capital implied by the usual parameterizations of a Cobb–Douglas production function, the AK model uses a linear model where output is a linear function of capital. Its appearance in most textbooks is to introduce endogenous growth theory. [1]
In economics, an expansion path (also called a scale line [1]) is a path connecting optimal input combinations as the scale of production expands. [2] It is often represented as a curve in a graph with quantities of two inputs, typically physical capital and labor , plotted on the axes.
The engine for growth can be as simple as a constant return to scale production function (the AK model) or more complicated set ups with spillover effects (spillovers are positive externalities, benefits that are attributed to costs from other firms), increasing numbers of goods, increasing qualities, etc. [citation needed]