Details

A Leontief production function of the form

has all its optimal solutions lying on the line

.

Factors and are perfect complements in the model. To shift from one optimal solution to another, a producer has to change both factors in the established proportion . If we take an arbitrary point lying outside the optimal direction, a redundancy (inefficiency) exists. On the three-dimensional plot, the size of the inefficiency corresponds to the length of the blue or red arrow. The blue arrow shows how much of resource can be saved without reducing . The red arrow shows the same thing for .

The Leontief function has no partial derivatives in kink points lying on the optimal direction . Nonetheless, it has directional derivatives in points along the vector , which are equal to .

We also show blue and red angles with tangents and , respectively. The angles show that the model is the result of the intersection of two planes and , and changes to or move their respective planes.

Use the "top view" button to see a classical two-dimensional representation of the model.

Note also that in the context of consumer theory, the same model can be interpreted as a utility function.