Answer to Question #228104 in Macroeconomics for Emy

Question #228104
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
1
Expert's answer
2021-08-24T14:09:12-0400

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:





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