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(X1X_1) and labor(X2X_2).

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

The least cost combination is given mathematically as follows:

MRSX1X2=ΔX1ΔX2=PX2PX1MRS_{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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