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Plotting the miner’s marginal product of labor against the amount of hours that he works shows the rate of
output change at each amount of working hours.
hours
coal
of
tons
hours
coal
hours
coal
'
'
0
0
–
1
1
1
2
1.41
0.41
3
1.73
0.32
4
2
0.27
We don’t need to measure the changes in the miner’s coal output in one hour increments however. In fact,
economists are usually more interested in a continuous rate of change. Those of you who have taken a
course in calculus should know that the continuous rate of change in output is simply the first derivative
of the total product function with respect to the number of hours worked.
For those of you who have not taken a course in calculus, imagine that we can measure the miner’s total
output at each second in time. If we look at how much the miner’s output increases from one second to
the next and divide that change by one second, we’ll have a good approximation of the first derivative.
For example, one second is
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This note was uploaded on 12/29/2011 for the course ECO 311 taught by Professor Willis during the Fall '10 term at SUNY Stony Brook.
 Fall '10
 willis

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