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In long run production, using isoquant-isocost analysis, what marginal condition must be true concerning the MPL...

In long run production, using isoquant-isocost analysis, what marginal condition must be true concerning the MPL per $ of Labor Cost and the MPK per $ of Capital Cost along the optimal expansion path for production? When this marginal condition is met, what is true about the total cost of production? Why would this result be of interest to a rational production manager?

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Answer #1

To find the optimal inout combination using the isoquant-isocost analysis, the condition that must be satisfied in order to attain the optimal is:

Slope of isoquant = slope of isocost

The slope of isoquant is given by the marginal rate of technical substitution or the MRTS.

MRTS= marginal productivity of labour/marginal productivity of capital

i.e. MRTS = MPL/MPK

The slope of the isocost is given by wages/rent i.e. the cost of labour relative to the cost of capital.

Therefore, slope of isocost = w/r

Combining all the above equations we get,

MRTS=w/r

= or

At this level the cost of additional output is equal across inputs.

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