# Variable inputs

Hernandez Corp. uses two variable inputs, X and Y, to produce its final product, canoes. Its engineering department has estimated the marginal product functions for inputs X and Y as follows:

MPx = Y/X

MPy = 4 X/Y

Where X and Y denote, respectively, the quantity in hours of inputs X and Y used.

At present Hernandez Corp. pays $40 per hour for input X and $10 per hour for input Y. It is using 200 hours of X and 100 hours of Y per day.

a. Write a paragraph explaining how the Hernandez Corp. finds the least cost combination of inputs for producing a given rate of output.

b. Using the data provided above, determine if the Hernandez Corp. is using a cost minimizing combination of inputs. Explain your answer/show your work. If your answer is no, how should the input combination be adjusted?

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#### Solution Preview

The ideal combination of inputs occurs where the marginal rate of substitution between the inputs equals the ratio of their prices. The marginal rate of substitution is the ratio of the marginal products. When we set this ratio equal to the ratio of the ...

#### Solution Summary

How to find the optimal combination of variable unit to minimize costs.