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Slope and Shape of Isoquant and Isocost curve

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The following production table provides estimates of the maximum amounts of output possible with different combinations of two input factors, X and Y. Assume for purposes of this problem that inputs X and Y cannot be used in partial units, so, for example, 1.5 units of X cannot be combined with 3.75 units of Y, etc.
Units of Y
Used Estimated Output per Day
5 184 265 334 395 440
4 176 248 303 352 395
3 164 216 264 303 334
2 128 176 216 248 265
1 88 128 164 176 184
1 2 3 4 5
Units of X Used

a. List the different combinations of inputs X and Y that, if graphed, would define an isoquant for an output of exactly 248.
b. Assuming that output sells for $5 per unit and input X is fixed at 3 units, complete the following table:
See attached document for table.
c. Assuming still that X is fixed at 3 units, the output of the production process sells for $5, and the cost of a unit of Y is $245 per day, how many units of Y will be employed? Explain how you reached your answer.
d. Suppose that the cost of units of both input X and input Y are the same and are $200 per input unit. Describe how isocost curves for a cost of $200 and also for a cost of $400 would look. How would you describe the shape and slope of the isocost curves? What is the numeric slope of the isocost lines?

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Solution Summary

This problem helps students to understand the concepts related to production function in economics and business. Specifically, they will understand how to analyze the isocost and isoquant curves given the production table for a combination of inputs. The problem here deals with two inputs. This also describes the shape and slope of the isocost curves.

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See the attached file. The text here may not print correctly for tables and symbols. Thanks

8. The following production table provides estimates of the maximum amounts of output possible with different combinations of two input factors, X and Y. Assume for purposes of this problem that inputs X and Y cannot be used in partial units, so, for example, 1.5 units of X cannot be combined with 3.75 units of Y, etc.
Units of Y
Used Estimated Output per Day
5 184 265 334 395 440
4 176 248 303 352 395
3 164 216 264 303 334
2 128 176 216 248 265
1 88 128 164 176 184
1 2 3 4 5
Units of X ...

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