Value & Capital, CHAPTER XVI -- PRICES AND THE PRODUCTION PLAN

In this first section of Chapter XVI, the author, Sir John Hicks gives an overview of the discussion the chapter will contain.  He starts by observing that the equilibrium and stability conditions worked out in the previous chapter for a dynamic plan of production "have of course identically the same role as the parallel conditions in static theory."  The current chapter will examine how a production plan changes when prices or price-expectations change.   The following chapter will look at the effects of changes in interest.  The parallelism between the dynamic problem of the production plan and the corresponding static problem will simplify the discussion, so that "the purely formal properties of technical substitution and technical complementarity" can be taken for granted, and the discussion can simply describe these properties "in dynamic terms."

Value & Capital, CHAPTER XV, Section 7

In this section, the final one of the chapter, the author discusses one additional characteristic of the dynamic production plan -- one that, he suggests, "ought perhaps to be reckoned among the stability conditions."  In addition to having a positive net present value initially, the investment plan must also have a positive net present value "at all future dates within the period for which he is planning."  If this were not the case, the planner would recognize that he would lose money by continuing, and he would cut the plan short.  The author notes that "The importance of this condition will emerge fully at a later stage."

He then discusses the ratio of the present value of a stream of capitalized values of a production plan at regular intervals (weeks, in his example) to the present value of the plan itself.  He notes that this ratio "is what we have called the average period of the stream of surpluses."  In an earlier section, he explained that this ratio can be thought of as the weighted average of lengths of times that payments are deferred from the present, with the times of deferment weighted by the discounted values of the payments.  He closes the section by noting that "The significance of this average period will come out when we discuss the effect of changes in interest on the production plan."

Value & Capital, CHAPTER XV, Section 6

This section begins by pointing out that the three categories of equilibrium conditions identified in the previous section are necessary conditions.  In other words, a production plan that fails to satisfy one of these types of conditions cannot maximize profits.  But these conditions are not sufficient to achieve to equilibrium;  "stability conditions have to be satisfied too."  The text identifies three types of stability conditions.

There must be (1)  an increasing marginal rate of substitution between outputs;  (2)  a diminishing marginal rate of substitution between inputs;  (3)  a diminishing marginal rate of transformation of an input into an output.

The author points out that these conditions have the same form as those found for the static equilibrium case.  In addition, there is an analogous condition to the static one that requires a positive surplus;  in the dynamic case, the condition is that "the present value of the stream of surpluses must be positive."

The latter part of this section addresses the conditions needed to ensure the stability of equilibrium under perfect competition.  In the static case, these involved postulating the existence of limitations on increasing the capacity of certain factors of production, such that overall returns were diminishing.  The author then asks what the situation looks like in the dynamic case.  His answer to this question covers two cases

(1) where the entrepreneur, at the date in question, has an already established business, (2) where he is a potential entrepreneur considering whether to set up a business, and, if so, what sort of a business to set up.

In the first case, the author concludes that the "fixity" (or fixed nature) of the resources required for setting up the business is sufficient for providing the necessary diminishing returns.  In the case of the new firm, the author identifies both the difficulties of management and control in the absence of "standing rules" for running the business, as well as the element of risk.

Overall, the author concludes that "we need have rather less compunction" in assuming perfect competition in the dynamic case than in the static case.  This is because "The elements which limit the size of firms in practice are very largely dynamic elements."
 

Value & Capital, CHAPTER XV, Section 5

This section continues explaining some of the details of how "the problem of maximizing the present value of the production plan is formally identical with the problem of maximizing the surplus of receipts over costs in the static problem of the firm."  For given interest rates, future costs enter into the analysis as discounted costs.  Outputs at different dates are treated as different outputs.  "With these adjustments," the author states, "the whole static theory of the firm still holds.  We have nothing to do but translate."

For conditions of equilibrium, the author identifies three kinds of conditions, "corresponding to the three 'elementary' forms of variation."  These are as follows:
(1)  For any two dates, the marginal rate of substitution between an output at those two dates must equal the ratio of the discounted prices.
(2) For any two dates, the marginal rate of substitution between an input at those two dates must equal the ratio of the discounted prices.
(3)  The marginal rate of transformation between any input and output pair must equal the ratio of their discounted prices.

The author goes on to explain that certain other equilibrium conditions stated by other writers are special cases of these three.  In particular, he notes that "the often stated rule that the current rate of wages equals the discounted value of the marginal product of current labour is a special case of our third condition."  Similarly, a rule noted by Wicksell -- that the interest rate equals the relative marginal productivity of waiting -- is a special case of the first condition.

Also, Keynes's statement that "short-period supply price is the sum of marginal factor cost and marginal user cost" corresponds to a combination of the first and third conditions.  Finally, another rule from Keynes, that the marginal cost of a unit of input equals "the present value of the stream of output increments made possible by the marginal input" appears to be (although not stated explicitly in the text) a combination of the second and third conditions.

The author concludes the section by noting briefly that in some cases, groups of inputs or outputs must be chosen in fixed proportions, but "little is to be gained by paying a great deal of attention to these cases ... at this stage of our inquiry."

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.

Value & Capital, CHAPTER XV, Section 3

In this section the author sketches a simple model of a production plan of the sort that an entrepreneur would seek to determine at some hypothetical date.  The model is as follows:

A0, A1, A2, A3, … , An

B0, B1, B2, B3, … , Bn

·    · ·    · · ·  

X0, X1, X2, X3, … , Xn

Y0, Y1, Y2, Y3, … , Yn

·    · ·    · · ·  

where "A, B, ... are different kinds of inputs, X, Y, ... are different kinds of outputs, and the entrepreneur is supposed to make his plan for a period of n future weeks." Inputs to the production process are simply things that the entrepreneur buys for his enterprise, and outputs are those things that he sells. The author points out that the model is general enough to handle the case in which the entrepreneur plans to shut down the enterprise and sell off all the equipment at some future date. In this case, "the plant he plans to have left over ... [is] a particular kind of output (say Zn), a kind which is only produced in the last week." All outputs are then zero for all time periods after the enterprise is sold.

The general dynamic problem for the enteprise is to select the optimal production plan from among all those that are technically feasible. The author points out the similarity of this problem to the static problem of choosing the set of quantities of factors of production and products. He explains that the technical limitation on production plans (or the "production function") will give the maximum possible quantity of a given output on a given date, if all inputs, and all outputs but the given one, are fixed in magnitude. Similarly, "if all outputs, and all inputs but one, are given in magnitude, [the production function] will give the minimum input necessary on the remaining date." Given this limitation, all changes between production plans reduce to (1) "substituting some amount of one output for some amount of another, (2) ... substituting [some amount of] one input for another," or (3) "increasing or diminishing one input and one output simultaneously" or some combination of these "elementary variations." The author concludes the section by noting that this is "exactly as in statics."

Value & Capital, CHAPTER XV, Section 2

In this section the author notes that "the dynamic theory of production has been the occasion of a great controversy" in economic dynamics.  He identifies the "great name in this department of economics" as being Böhm-Bawerk, whose theory of production he terms the "Austrian theory."

The definition of capitalistic production as time-consuming production; of the amount of capital employed as an indicator of the amount of time employed; of the effect of a fall in interest on the structure of production as consisting in an increase in the amount of time employed; all these ideas give to the subject an apparent clarity which is, at first sight, irresistable.  The theory stands up very well to the more obvious objections which can be made against it; yet, as one goes on, difficulties mount up.

The author notes some of the criticisms that have been made against Böhm-Bawerk's theory by Knight and Kaldor but claims that "the main issue is still left unsettled."  He previews the discussion in upcoming sections by saying "I hope to show, that when we transcend ... artificially simple cases ... the central propositions change their character rather markedly."  In a satisfactory general theory of capital,  Böhm-Bawerk's theory is "valid as a limiting case, though not a very important case.  The general theory differs from Böhm-Bawerk's in some important respects."