Question

If a firm is producing in the long run using capital and labor inputs, how the least cost
combination of the inputs will be determined? Show graphically and mathematically

Answer 1

Here, we want to find out a combination of inputs which should cost the least. i.e. minimization of cost. The tangency of the isocost and the isoquant curves will give the least cost combination of capital($X_1$) and labor($X_2$).

The slope of the isoquant should be equal to the slope of the isocost.

The least cost combination is given mathematically as follows:

$MRS_{X_1 X_2}=\frac { \Delta X_1}{\Delta X_2}=\frac {P_{X}{ 2}}{P_{X }{1}}$

This is graphically represented as: