# Question about Marginal Rate of Technical Substitution

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.)
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
Y Fixed at 3 Units
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?
What is the nature of the returns to scale for this production system if the optimal input combination requires that X = Y?
Question 7.1 Is use of the least-cost input combinations (technical efficiency) a necessary condition for profit maximization? Is it a sufficient condition? Explain.

Question 7.5 Explain why the MP/P relation is deficient as the sole mechanism for determining the optimal level of resource employment.

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• Q7-1-7-2.doc
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The solutions provides answers to questions that deal with marginal rate of technical substitution, marginal product, Marginal Revenue Product, returns to scale, optimal level of resource employment

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Extracted Content from Question Files:

single plant muncie Normal Dayton
monthly capacity 300000 120000 100000 80000
monthly fixed cost 262500 120000 110000 95000
variable cost per case 3.25 3 3 3
demand 200000 80000 70000 50000
price per case 5 5 5 5
breakeven output 150000 60000 55000 47500
profit 40000 30000 5000
87500 75000
sales equal capacity: profit 120000 90000 65000
262500 275000

• Q7-1-7-2.doc

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

X Fixed at 2 Units

Marginal
Units of Total Product Marginal Product Average Product Revenue Product
Y Used of Y of Y of Y of Y

1
2
3
4
5

Y Fixed at 3 Units

Marginal
Units of Total Product Marginal Product Average Product Revenue Product
X Used of X of X of X of X
1
2
3
4
5
2

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

Question 7.1 Is use of the least-cost input combinations (technical efficiency) a
necessary condition for profit maximization? Is it a sufficient condition? Explain.

Question 7.5 Explain why the MP/P relation is deficient as the sole mechanism for
determining the optimal level of resource employment.