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Product functions - Total, average & marginal product

Dimex Fabrication Co., a small manufacturer of sheet-metal body body parts for a major US automaker, estimates its long-run production to be
Q= -0.015625K3L3 + 10 K2 L2

where Q is the number of body parts producted daily, K is the number of sheet-, metal presses in its manufacturing plant, and L is the number of labor-hours per day of sheet-metal workers employed by Dimex. Dimex is currently operating with eight sheet-metal presses.

a. What is the total product function for Dimex? The average product function? The marginal product function?

b. Managers at Dimex can expect the marginal product of additional workers to fall beyond what level of labor employment?

c. Dimex plan to employ 50 workers. Calculate total product, average product, and marginal product.

Solution Preview

a) K=8
Total Product = Q=-0.015625*K^3*L^3+10*K^2*L^2=-0.015625*8^3*L^3+10*8^2*L^2=-8*L^3+640*L^2
Average Product = ...

Solution Summary

This post solves dimex fabrication co's production function problem. In simple steps it shows how to write the three functions from the long run production function, calculate the point of maxima and calculate the total, average and marginal product for a specific labor level.