Marginal Rate of Technical Substitution

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See attached file for answers
Problem 7.1 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?

The two inputs exhibit the characteristics of decreasing marginal rates of technical substitution
This can be inferred from the fact that as per calculations below marginal product decreases in the direction of arrow

TABLE 1

Marginal product keeping X constant
Units of
Y Used
5 22 33 36 45 49

4 26 38 42 52 61

3 32 46 48 52 55

2 36 58 72 84 95

1 94 130 162 188 210
1 2 3 4 5
Units of X used

Marginal product decreases in the direction of arrow

TABLE 2

Marginal product keepingY constant
Units of
Y Used
5 210 95 55 61 49

4 188 84 52 52 45

3 162 72 48 42 36

2 130 58 46 38 33

1 94 36 32 26 22
1 2 3 4 5
Units of X used

Marginal product decreases in the direction of arrow

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