Figure 5: Marginal Productivity and Efficient Allocation
If you were a bug, you couldn't see much. Perhaps you couldn't see to the top of the hill. But you would be able to tell if you were going up, or down, or neither. So you would just keep going as long as you were going up, and stop when you were neither going up nor down. That's the way a bug gets to the top of a hill.
If you were a farmer with two fields, it's a little more complicated, but the same principles apply: take it step by step. However much you may be producing, ask yourself "What would happen if I were to take one worker away from the North Field and put her to work on the South Field? How much less will the North Field produce? The answer to that question is the marginal productivity of labor on the North Field. How much more will the South Field produce? The answer to that question is the marginal productivity of labor on the South Field. So the move of labor from the North Field will increase production if the marginal productivity on the North Field is less than the marginal productivity on the South Field. Like the bug, you want to keep moving in that direction as long as production keeps getting greater, that is, as long as the marginal productivity on the North Field is less than the marginal productivity on the South Field. And you stop when further movement won't get you any higher on the hill, that is, when the marginal productivities are equal on the two fields.
So now, let's visualize the marginal productivities for these two fields. But this time we will do it a slightly different way. We will measure the labor used on the infertile north field from left to right on the horizontal axis. Then, what's left is what's available for the north field, so we will measure the labor used on the south field from left to right -- from 1000 hours down to zero. The marginal product on the north field is shown with the green line, and the marginal product on the south field with the vertical-dashed purple line. (Remember, the marginal productivity on the south field decreases as the labor input on the south field gets bigger, so the marginal productivity on that field increases as labor used on the field gets smaller, as it does here). Here it is:
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