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Finding least-cost input-combination of labor and capital

Name: Production functions
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Use the following data for a firm's output at various levels of employment (L) to calculate:

Number of Workers (L) Output (Q)
1 100
2 300
3 600
4 850
5 1000
6 1100

a) Its marginal physical product of labor (MPPL) schedule;

(b) Its (MPPL/MRCL) schedule, given a fixed wage (W = MRCL) of $25 per hour per worker.

(c) Assuming that capital (K) is held constant at 2 machines and MPPK/MRCK = 10, what is the least-cost input-combination of labor and capital and how much output is produced with that set of resources?

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Solution describes the steps to calculate least-cost input-combination of labor and capital.

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Please refer attached file for better clarity of formulas and tables.
Solution:

Use the following data for a firm's output at various levels of employment (L) to calculate:

No. of workers (L) Output MPPL MPPL/MRCL MPPK/MRCK
L Q Change in Q/change in L MMPL/$25
1 100 100 ...

Solution provided by:

Lokesh Jain, MSc

Education

BEng (Hons) , Birla Institute of Technology and Science, India
MSc (Hons) , Birla Institute of Technology and Science, India

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