# The quantity, q, of a product manufactured depends on the number of workers, W , and the amount of capital

## Question:

The quantity, q, of a product manufactured depends on the number of workers, W , and the amount of capital invested, K, and is given by the Cobb-Douglas function q = 6W3∕4K1∕4.

In addition, labor costs are \$10 per worker and capital costs are \$20 per unit and the budget is \$3000.

(a) What are the optimum number of workers and the optimum number of units of capital?

(b) Re compute the optimum values of W and K when the budget is increased by \$1. Check that increasing the budget by \$1 allows the production of λ extra units of the product, where λ is the Lagrange multiplier.

## This problem has been solved!

Related Book For

## Applied Calculus

ISBN: 9781119275565

6th Edition

Authors: Deborah Hughes Hallett, Patti Frazer Lock, Andrew M. Gleason, Daniel E. Flath, Sheldon P. Gordon, David O. Lomen, David Lovelock, William G. McCallum, Brad G. Osgood, Andrew Pasquale

Question Details
Chapter # 8
Section: problem 8.6
Problem: 25
View Solution