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Analyzing increasing and decreasing marginal returns

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A firm's product sells for $2 per unit. The firm produces output using capital (which it rents for $75 per hour) and labor (which is paid a wage of $15 per hour under a contract for 20 hours or labor services). Complete the following table.

For table please refer attached Excel file.

a) Identify the fixed and variable cost
b) What are the firm's fixed costs
c) What is the variable cost of producing 475 units of output
d) How many units of the variable input should be used to max profits
e) What are max profits firm can earn
f) Over what range of the variable input usage do increasing marginal
returns exist
g) Over what range of input usage do decreasing marginal returns exist
h) Over what range of input usage do negative marginal returns exist

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Solution Summary

Solution describes the steps for calculating variable, fixed costs and maximium profit. It also indentifies the variable input range over which increasing/decreasing and negative marginal returns take place.

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Please refer attached file for better understanding of tables and formulas.

Solution:

Table :1

K L Q MPk APk APl VMPk at P=2
0 20 0 0 0 0
1 20 50 50 50 2.5 100
2 20 150 100 75 7.5 200
3 20 300 150 100 15 300
4 20 400 100 100 20 200
5 20 450 50 90 22.5 100
6 20 475 25 79.16 23.75 50
7 20 475 0 67.85 23.75 0
8 20 450 -25 56.25 22.5 -50
9 20 400 -50 44.44 20 -100
10 20 300 -100 30 15 -200
11 20 150 -150 13.36 7.5 -300

a) Identify the fixed and variable cost
The firm has two input costs, namely captial costs and labor costs. Firm uses
a wage of $15 per hour under a contract for 20 hours or labor services. This is a fixed cost in this case.
Firm rents for $75 per hour, It is a variable cost in the given case.
Table 2
Fixed and Variable costs are calculated as under ...

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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