Maths for Social Sciences by Lorenzo Peccati & Mauro D’Amico & Margherita Cigola

Author:Lorenzo Peccati & Mauro D’Amico & Margherita Cigola
Language: eng
Format: epub
ISBN: 9783030023362
Publisher: Springer International Publishing

or:

(2.3.12)

Note that the first m equations require the respect of the constraints, so that it is true that brings us back to .

Any solution of the system (2.3.12) is an -vector:

at which the gradient of L is the null vector:

could identify an extremum.

Let’s look at a numerical example:

Example 2.3.15

The function to be maximized is:

under the constraints:

The Lagrangean for the problem is:

Its gradient turns out to be:

The FOCs boil down to the following linear system:

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