The Optimal Plan for Production of Machines

Now let's put what we have learned from neoclassical economics in the last two sections together and see what it can tell us about the optimal quantity of machines for Economia. Since we have expressed the costs and benefits in the same units -- units of food -- we can subtract the benefits from the costs to compute the net benefits. Similarly, marginal benefits and marginal costs are expressed in the same units: food per machine. Let's put the marginal cost and the marginal benefit together and see what we get.

Figure 6 does this. In the figure, the production of machines is measured from left to right as in Figures 4 and 5. Marginal cost and marginal benefit are measured from bottom to top.

Figure 6. The Optimal Plan

In Figure 6, the dark, downward-sloping line is marginal benefit, while the upward-sloping cross-hatched line is the marginal cost. Figure 6 illustrates a basic rule for the optimal allocation of resources. Notice the point at which the marginal cost line crosses the marginal benefit line. This point is indicated by the dark gray vertical line. This tells us that when machine production is 575 machines, marginal cost is equal to marginal benefit. And this is the machine output that gives Economia maximum net benefits. This is a general rule:

RULE: The output at which marginal benefit is equal to marginal cost is the output at which the net benefit of output is at its greatest. This is the optimal output, and when each industry has just enough resources to produce the optimal output (and the industries use the resources efficiently), that is the optimal allocation of resources.

This rule is another instance of the Equimarginal Principle, which we have seen several times in previous chapters.

Mathematical Details