Take C = 20, then
A simple question: how much does cost change for a small (one unit) change in the driver, D?
This is the definition of the marginal cost.
For example, the driver D could be labor hours. If equals 1 then the equation is (anything to the power one is itself)
The left-hand side is measured in Dollars, D is measured in hours, so to make things balance C must be in dollars/hour, ie a wage rate.
Consider what happens if
,
so that
Find the marginal cost at D = 100.
First differentiate; bring down the power, knock the power down 1, to get:
What about the marginal cost at D = 200? You calculate to find that the marginal cost is 10.60.
Note how the marginal cost is decreasing as the driver increases.
Homework question: plot this marginal cost function for D = 50,100,150,200, 250, 300.