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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 Preview

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 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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Fixed and Variable costs

A firm has fixed costs of $60 and varable costs as indicated in the table below. Complete the table.

(a) Graph total fixed cost, total varable cost, and total cost. Explain how the law of diminishing returns influences the shapes of the variable-cost and total-cost curves.

(b) Graph AFC, AVC ATC and MC. Explain the derivation and shape of each of these four curves and their relationshops to one another. Specifically, explain in non-technical terms why the MC curve intersects both the AVC and the ATC curves at their minimum points.

(c) Explain how the location of each curve graphed in Question 7(b) would be altered if (1) total fixed cost had been $100 rather than $60 and (20 total variable cost had been $10 less at each level of output.

Total Total Total Variable Total Average Fixed Average Variable Average Marginal
Product FixedCost Cost Cost Cost Cost Cost
0 $0
1 45
2 85
3 120
4 150
5 185
6 225
7 270
8 325
9 390
10 465

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