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Solve production function using excel and optimization procedure

Given the following production function:
Q = 42L + 18L2 -2L3 WHERE Q= TP (TOTAL PRODUCT) or quantity of output in units and L(labor) in units
FIND THE FOLLOWING: First solve this problem using an spreadsheet approach and then do the problem using the optimization procedure; compare the answers for the two methods. Show your work to receive credit.
A: The amount in units of labor when diminishing returns to labor sets in and then explain why this happens.
B. The amount in units of labor used when the average product curve is at its highest point.
C. What amount of labor in units should be used to get maximum output?

Solution Preview

Please find my response attached,

So, I'll run through normal optimization first. It looks like you've got three different powers of labour. If these are different variables, please let me know so I can correct my calculation.

Q= 42L + 18L2-2L3

Where "Q" is an expression for total product. We're going to need an expression for marginal product to perform a future calculations, so let's take the first derivative of the total product curve.

MP=42+36L-6L2

We're also going to find ...

Solution Summary

A production function is analyzed using a spreadsheet approach. The amount of units of labor when diminishing returns to labor sets in is explained.

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