Marginal Rate of Technical Substitution

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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

A. Do the two inputs exhibit the characteristics of constant, increasing, or decreasing marginal rates of technical substitution? How do you know?

B. Assuming that output sells for $3 per unit, complete the following tables:

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

2

3

4

5

Y Fixed at 3 Units

Units of
X Used

Total
Product
of X

Marginal
Product
of X

Average
Product
of X
Marginal
Revenue
Product
of X

1

2

3

4

5

C. 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?

D. 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?

E. What is the nature of the returns to scale for this production system if the optimal input combination requires that X = Y?