An Optimal Plan


This is the planning problem: how many machines should Economia plan to produce, and how much food? This may sound like two questions, but it is really only one. Because the economy of Economia is so simple -- with only two goods to produce -- we really need to decide only one of them, and then devote all of our leftover resources to producing the other. Accordingly we ask: how many machines should Economia plan to produce? We know that production of machines will have costs and benefits and (as I said before) we will use cost-benefit analysis to answer the question.

By definition, benefits are good and costs are bad. In cost-benefit analysis, we assume that the good results from production of machines (or from any other activity) can be measured in numerical terms. We also assume the bad results, the costs, can be measured in numerical terms, and that the benefits and costs are measured on the same scale, so that we may subtract the costs from the benefits. This difference -- the benefits minus the costs -- we call the net benefit from producing machines. But the net benefit will depend on how many machines we produce. Economists expect that the net benefits will increase at first, as machine production increases, and then level off, and then decrease, as shown in Figure 2. In Figure 2, net benefits are measured from bottom to top, and the production of machines is shown from left to right. The idea is to find the quantity of production marked off by the vertical gray line -- where the net benefit of machine production is greatest. (We can see from the picture that that's about 580 machines). This is the optimum output of machines. Economia should plan to produce that output -- according to cost-benefit analysis.

Figure 2. Maximum Net Benefit

Of course, there is a lot more to it than that. How can we find that optimum quantity of production, in general? And where do these costs and benefits come from? How are they defined? How can they be measured? In short, we need to get behind the curve and learn a little more about what it means and how to use cost-benefit analysis in more realistic examples where we do not have pretty pictures to look at. We'll go forward a bit at a time. The first step will be to take a closer look at costs.

Mathematical Details

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