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Question

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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?

Explanation / Answer

a) The rational producer wants to minimize the cost of production which only can be

possible if the input combination is optimal which is implied maximum returns of factor
to the producers. Thus a ration firm would combine the various factor of production in
such a way that the minimum input and the maximum output is obtained at minimum
cost. Such a combination is know as least cost combination of inputs for producing a
given rate of output. We know in the Least cost point MPx/MPy=Py/Px
Or,Y/X/4X/Y=10/40
Or,Y2/4X2=1/4
Or,X2=Y2
Or,X=Y

b) It is using 200 hours of X and 100 hours of Y

so X is not equal Y

so the number of hours should be same

for e.g 200 hours of X and 200 hours of Y

per day.

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