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?
Perhaps the first thing that should be understood is that the firm will be producing in the most efficient manner when the marginal products are set equal to one another. In this case, you've been saved the calculus.
So, we simply set:
(1) (Y / X) = (4X / Y)
We have other information we need to make use of, including the prices of inputs. We should construct the budget set:
This says the ...
Economic output variables are examined.