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Economic Output Variables

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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?

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Solution Preview

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 ...

Solution Summary

Economic output variables are examined.

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Economics: Cost Analysis

An economist estimated that he cost function of single-prodcut firm is
C(Q) = 100 + 20Q + 15Q2 + 10Q3
Based on this information, determine:

a. The fixed cost of producing 10 units of output
b. The variable cost of producing 10 units of output
c. The total cost of producing 10 units of output
d. The average fixed cost of producing 10 units of output
e. The average variable cost of producing 10 units of output
f. The average total cost of producing 10 units of output
g. The marginal cost when Q = 10


A firm's fixed costs for producing 0 units of output and its average total cost of producing different output levels are summarized in the tale below.

Complete the table to find the fixed cost, variable cost, total cost, average fixed cost, average variable cost, and marginal cost at all levels of output.

0 $15,000 -----
100 $300
200 200
300 175
400 225
500 325
600 400


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