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    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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    Marginal Rate of Technical Substitution is considered.

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