We can get a more exact answer by looking at a picture or tinkering with the program example a bit. Here is a picture of the profit-maximizing hiring in this example:
The picture suggests that the exact amount is a bit less than 500 units of labor. If you tinker with the program example enough, you will see that the exact profit maximizing labor input is 454.54545454545 ... units of labor -- a repeating decimal fraction.
Notice the shaded area between the VMP curve and the price (wage) line. n the picture, the area of the shaded triangle is the total amount of payments for profits, interest, and rent -- in other words, everything the firm pays out for factors of production other than labor. The rectangular area below the wage line and left of the labor=454 line is shows the wage bill. Thus, the John Bates Clark model provides us with a visualization of the division of income between labor and property. We'll make use of this fact in exploring the economics of income distribution in the last Part of this chapter.
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