A small company that shovels sidewalks and driveways has 100 homes signed up for its services this winter. It can use various combinations of capital and labor: intensive labor with hand shovels, less labor with snow blowers, and still less labor with a pickup truck that has a snowplow on front. To summarize, the method choices are:Method 1: 50 units of labor, 10 units of capitalMethod 2: 20 units of labor, 40 units of capitalMethod 3: 10 units of labor, 70 units of capitalQuestionIf hiring labor for the winter costs $100/unit and a unit of capital costs $400, what is the best production method? What method should the company use if the cost of labor rises to $200/unit?

Question
Asked Nov 17, 2019
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A small company that shovels sidewalks and driveways has 100 homes signed up for its services this winter. It can use various combinations of capital and labor: intensive labor with hand shovels, less labor with snow blowers, and still less labor with a pickup truck that has a snowplow on front. To summarize, the method choices are:

Method 1: 50 units of labor, 10 units of capital

Method 2: 20 units of labor, 40 units of capital

Method 3: 10 units of labor, 70 units of capital

Question

If hiring labor for the winter costs $100/unit and a unit of capital costs $400, what is the best production method? What method should the company use if the cost of labor rises to $200/unit?

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Expert Answer

Step 1

A small company use various combinations of capital and labor in production. These combinations are given in the table.

Capital
10
40
Labor
50
20
Method 1
Method 2
Method 3
10
70
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Capital 10 40 Labor 50 20 Method 1 Method 2 Method 3 10 70

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Step 2

If the cost of hiring labor is $100 per unit and a unit of capital costs $400. Then the cost of production is:

Cost of Capital
labor
Labor
Cost of
Cost of production
capital per
unit
per unit
$100
10
40
Method 1
50
20
Method 2
Method 3
10
50x100 10x400 = 9000
20x100+ 40x400 = 18000
10x100 70x400 = 29000
$400
$400
$400
$100
s100
70
Therefore, method 1 should be selected, because this method minimizes the cost of production.
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Cost of Capital labor Labor Cost of Cost of production capital per unit per unit $100 10 40 Method 1 50 20 Method 2 Method 3 10 50x100 10x400 = 9000 20x100+ 40x400 = 18000 10x100 70x400 = 29000 $400 $400 $400 $100 s100 70 Therefore, method 1 should be selected, because this method minimizes the cost of production.

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Step 3

If the cost of labor rises to $200 per uni...

Cost of Capital
Cost of production
Labor
Cost of
capital per
unit
labor
per unit
$200
10
$200
40
50x20010x400 = 14000
Method 1
$400
$400
50
Method 2
20
20x200 40x400 20000
Method 3
10
$200
70
$400
10x20070x400 = 30000
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Cost of Capital Cost of production Labor Cost of capital per unit labor per unit $200 10 $200 40 50x20010x400 = 14000 Method 1 $400 $400 50 Method 2 20 20x200 40x400 20000 Method 3 10 $200 70 $400 10x20070x400 = 30000

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