Value & Capital, CHAPTER XV, Section 4

Having sketched a simple model of a dynamic production plan in the previous section, the author turns in this section to the question of which among the various feasible production plans should be the preferred one.  In the static case, the problem was simple:  the entrepreneur would plan production so as to maximize the "surplus of receipts over costs."  For the dynamic case, there is no single instance of receipts and costs; instead, a given production plan will generate a stream of costs and receipts over time.  In the trivial case in which one stream has, at every step, a larger surplus than a second stream, the first stream is obviously preferred over the second.  In general, though, "we need some criterion to enable us to judge whether one stream [of surpluses] is to be reckoned larger than another."

The author makes the assumption (seemingly almost in passing) "that the entrepreneur can lend and borrow freely at given market rates" of interest.  This assumption is key to his being able to conclude that the preferred production plan must be the one that maximizes the capitalized value of the stream of surpluses.  If prices and price-expectations at each time step are known, then the surplus at each step "is determined as soon as the production plan is determined.  And its present value is determined if interest rates and interest-expectations are given."

The author examines a few other considerations of the model, including accounting for costs that the entrepreneur may face due to "contracts entered into in the past."  In this case the costs "are independent of his present decisions [and] cannot be modified by any change in the plan."  Therefore the capitalized value of his receipts, net of these costs, "only differs from the from the capitalized value of his prospective surpluses by a constant, and will be maximized when that is maximized."

He also notes that "any increase in the capital value of his prospective net receipts must always take the entrepreneur to a preferred position."  This is because the increased capital value "will enable him to plan the same expenditures as before ... and still to have something left over."

Finally, the author recalls that "a person's income can be regarded as the level of a standard stream whose present value is the same as the present value of his prospective receipts."  Once the type of standard stream is decided (which, as we saw in Chapter XIV, relates to the definition of income being used), and once "price- and interest-expectations are given," the values of surpluses and expenses are determined, and therefore "any increase in the present value of a stream must raise the level of the standard stream corresponding to it."  The author notes that net profit can be defined as net receipts plus the net effect of appreciation/depreciation (which may be negative).  He concludes this section by noting

We can either say that the entrepreneur maximizes his profits, or that he maximizes the present value of his prospective net receipts, or that he maximizes the present value of his prospective surpluses.  All these tests come to the same thing;  but it is the last of them (what we have called the present value of the plan) which is the most convenient analytically.