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hours
coal
true MPL
.
hrs
coal
'
'
5
.
0
.
hrs
'
.
hrs
coal
'
'
1
.
hrs
'
0
0
infinite
–
–
0.5
0.71
0.71
1.41
–
1.0
1.00
0.50
0.59
1
1.5
1.22
0.41
0.45
–
2.0
1.41
0.35
0.38
0.41
2.5
1.58
0.32
0.33
–
3.0
1.73
0.29
0.30
0.32
3.5
1.87
0.27
0.28
–
4.0
2.00
0.25
0.26
0.27
Notice also what happens when we sum the last two columns of the table above (i.e. the columns of
.
hrs
coal
'
'
). The column listing a time interval of one hour sums to 2, which is exactly how many tons
of coal are produced. The area under the marginal product curve equals total product because increasing
the number of hours from zero to one yields one additional ton of coal per hour, increasing the number of
hours from one to two yields 0.41 additional tons of coal per hour, etc.
The column listing a time interval of half an hour sums to 4, which when multiplied by 0.5 hours also
equals 2 (tons of coal), so once again the area under the marginal product curve equals total product.
The column listing the true marginal product of labor sums to 3.1 plus infinity, which at first glance
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 Fall '10
 willis

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