Shephard's lemma

The accompanying this so-called value function is given by the initially minimized function, in which one uses the now preserved. They are called output function:

Shephard's lemma in the Financial Theory: The Hick'sche demand for a commodity j is given by the partial derivative of the output function according to the price of the goods:

It is initially based on a cost minimization problem by

Is given, in which continuous, differentiable and strictly quasikonkav was. The total expenditure is minimized for the factors of production, but a certain amount of output to be produced (the production function ). The solution of such a cost minimization problem is intended a function that indicates what quantity should be sought from the relevant factors in order to achieve the given production target as inexpensively as possible. It is therefore a function of the factor price vector and the specified output levels. This is referred to as given as conditional factor demand.

The accompanying this so-called value function is given by the initially minimized function, in which one uses the now preserved. They are called cost function:

It provides the actual costs incurred in the minimum cost for a given amount of output.

Shephard's lemma in the theory of the firm: The conditional factor demand for a factor of production j is given by the partial derivative of the cost function according to the price of the production factor:

Derivation

The lemma is a direct application of the envelope theorem.