The Leontief Produktionsfunktion is a type (type B) of the micro-economic production function. It is called linear limitational, there the factors of production in a firm relationship to each other and in firm relation to the output (output) of an enterprise or a plant to stand. The yield quantity reaches a Limitation, if a factor of production is not available in sufficient measure.

In formal way of writing applies to the function

\ mathbb {R} ^n \ longmapsto \ mathbb {R} ^1, n \ geq1, f (v) = a_0 \ min \ left \ {\ frac {v_1} {a_1}, \ frac {v_2} {a_2}, \ dots, \ frac {v_n} {a_n} \ right \} ^ {r}

The Leontief Produktionsfunktion is a CES Produktionsfunktion with the substitution elasticity 0. It is homogeneous with the homogeneity degree of R.

Example

Each "prescription-moderate" production in the kitchen or in the laboratory is example of the Leontief Produktionsfunktion. If one needs e.g. for a cake after prescription a_1=2 eggs, a_2=100g flour and a_3=0,1 litre milk, then one can with v_1=4 eggs, v_2=300g flour and v_3=0,3 litres of milk f (v) = \ min \ left \ {\ frac {4} {2}, \ frac {300} {100}, \ frac {0.3} {0.1} \ right \} =2Kuchen to produce. Limitational are in this case the eggs, with 6 eggs one 3 cakes have produced could.

The production function goes back on Wassily Leontief. It forms the basis of the input-output analysis.

See also

• Production
• Good mountain production function

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