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Calculate inputs, calculate labor, production functions

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1. Could the isoquants corresponding to two different levels of output ever cross? Explain.

2. A firm uses the inputs of fertilizer, labor, and hothouses to produce roses. Suppose that when the quantity of labor and hothouses is fixed, the relationship between the quantity of fertilizer and the number of roses produced is given by the following table:
(attached)

a) What is the average product of fertilizer when 4 tons are used?
b) What is the marginal product of the sixth ton of fertilizer?
c) Does this total production function exhibit diminishing marginal returns? If so, over what quantities of fertilizer do they occur?

5. Suppose that a firm's production function is given by Q = KL + K, with MP_x = L + 1 and MP_L = K . At point A, the firm uses K = 3 units of capital and L = 5 units of labor. At point B, along the same isoquant, the firm would only use 1 unit of capital.

a) Calculate how much labor is required at point B.
b) Calculate the Marginal rate of technical substitution (MRTS) at point A and B respectively.

6. For the production function Q = 6L^2 — L^3, fill in the following table and state how much the firm should produce so that:
a) average product is maximized
b) marginal product is maximized
c) total product is maximized
d) average product is zero

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The expert calculates the inputs, calculates labor and production functions.

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Answer:
1) No, isoquants can never cross. For example, If we look at the diagram with two isoquants for two levels of output Q1 and Q2 where Q2>Q1. Let the ...

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Jayant Kumar, MBA
Education
  • MBA, Indian Institute of Finance
  • Bsc, Madras University
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