Marginal Rate of Technical Substitution
The following production table gives 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
|
Do the two inputs exhibit the characteristics of constant, increasing, or decreasing marginal rates of technical substitution? How do you know? Assuming that output sells for $3 per unit, complete the following tables: 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? 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? What is the nature of the returns to scale for this production system if the optimal input combination requires that X = Y?