Leontief production function

In economics, the Leontief production function or fixed proportions production function is a production function that implies the factors of production will be used in fixed (technologically pre-determined) proportions, as there is no substitutability between factors. It was named after Wassily Leontief and represents a limiting case of the constant elasticity of substitution production function.

Two input Leontief Production Function with isoquants

For the simple case of a good that is produced with two inputs, the function is of the form

where q is the quantity of output produced, z1 and z2 are the utilised quantities of input 1 and input 2 respectively, and a and b are technologically determined constants.

Example

Suppose that the intermediate goods "tires" and "steering wheels" are used in the production of automobiles (for simplicity of the example, to the exclusion of anything else). Then in the above formula q refers to the number of automobiles produced, z1 refers to the number of tires used, and z2 refers to the number of steering wheels used. Assuming each car is produced with 4 tires and 1 steering wheel, the Leontief production function is

Number of cars = Min{1⁄5 times the number of tires, 1 times the number of steering wheels}.
gollark: THAT would destroy the sun, if you have high enough speed.
gollark: Oh, *or* launch a gas giant at relativistic speeds from the next solar system along somehow.
gollark: Maybe just put the black hole into the sun.
gollark: So how much do you think adding 0.002% more mass to the sun will do?
gollark: > The principal component of the Solar System is the Sun, a G2 main-sequence star that contains 99.86% of the system's known mass and dominates it gravitationally.[18] The Sun's four largest orbiting bodies, the giant planets, account for 99% of the remaining mass, with Jupiter and Saturn together comprising more than 90%. The remaining objects of the Solar System (including the four terrestrial planets, the dwarf planets, moons, asteroids, and comets) together comprise less than 0.002% of the Solar System's total mass.[h]

See also

References
  • Allen, R. G. D. (1968). Macro-economic Theory: A Mathematical Treatment. London: Macmillan. p. 35.
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