Task: PRODUCTION ANALYSIS AND COMPENSATION POLICY / COST ANALYSIS AND ESTIMATION
Marginal Rate of Technical Substitution. The following production table provides estimates of the maximum amounts of output possible with different combinations of two input factors, X and Y. (Assume that these are just illustrative points on a spectrum of continuous input combinations.)
|
Units of
Y Used
|
Estimated Output per Day
|
|
5
|
210
|
305
|
360
|
421
|
470
|
|
4
|
188
|
272
|
324
|
376
|
421
|
|
3
|
162
|
234
|
282
|
324
|
360
|
|
2
|
130
|
188
|
234
|
272
|
305
|
|
1
|
94
|
130
|
162
|
188
|
210
|
|
|
1
|
2
|
3
|
4
|
5
|
|
|
Units of X used
|
Q1. Do the two inputs exhibit the characteristics of constant, increasing, or decreasing marginal rates of technical substitution? How do you know?
Q2. Assuming that output sells for $3 per unit, complete the following tables:
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|
X Fixed at 2 Units
|
|
Units of
Y Used
|
Total
Product
of Y
|
Marginal
Product
of Y
|
Average
Product
of Y
|
Marginal
Revenue
Product
of Y
|
|
1
|
|
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|
|
|
2
|
|
|
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|
|
3
|
|
|
|
|
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4
|
|
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5
|
|
|
|
|
|
Units of
X Used
|
Total
Product
of X
|
Marginal
Product
of X
|
Average
Product
of X
|
Marginal
Revenue
Product
of X
|
|
1
|
|
|
|
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2
|
|
|
|
|
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3
|
|
|
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|
|
4
|
|
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5
|
|
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Q3. Assume that the quantity of X is fixed at 2 units. If output sells for $3 and the cost of Y is $120 per day, how many units of Y will be employed?
Q4. Assume that the company is currently producing 162 units of output per day using 1 unit of X and 3 units of Y. The daily cost per unit of X is $120 and that of Y is also $120. Would you recommend a change in the present input combination? Why or why not?
Q5. What is the nature of the returns to scale for this production system if the optimal input combination requires that X = Y?