# 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?

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#### Solution Summary

Marginal Rate of Technical Substitution is considered.