I. We need a quantity to maximize. This objective function has to be a function of the quantities of all the different goods (and services) produced by our economic system.
Here “objective” is used in the sense of “goal”, not in the sense of “factual”. In Kantorovich’s world, the objective function is linear, just a weighted sum of the output levels. Those weights tell us about trade-offs: we will accept getting one less bed-sheet (queen-size, cotton, light blue, thin, fine-weave) if it lets us make so many more diapers (cloth, unbleached, re-usable), or this many more lab coats (men’s, size XL, non-flame-retardant),or for that matter such-and-such an extra quantity of toothpaste. In other words, we need to begin our planning exercise with relative weights. If you don’t want to call these “values” or “prices”, I won’t insist, but the planning exercise has to begin with them, because they’re what the function being optimized is built from.
It’s worth remarking that in Best Use of Economic Resources, Kantorovich side-stepped this problem by a device which has “all the advantages of theft over honest toil”. Namely, he posed only the problem of maximizing the production of a “given assortment” of goods—- the planners have fixed on a ratio of sheets to diapers (and everything else) to be produced, and want the most that can be coaxed out of the inputs while keeping those ratios. This doesn’t really remove the difficulty: either the planners have to decide on relative values, or they have to decide on the ratios in the “given assortment”.
Equivalently, the planners could fix the desired output, and try to minimize the resources required. Then, again, they must fix relative weights for resources (cotton fiber, blue dye #1, blue dye #2, bleach, water [potable],water [distilled], time on machine #1, time on machine #2, labor time [unskilled], labor time [skilled, sewing], electric power…). In some contexts these might be physically comparable units. (The first linear programming problem I was ever posed was to work out a diet which will give astronauts all the nutrients they need from a minimum mass of food.) In a market system these would be relative prices of factors of production. Maintaining a “given assortment” (fixed proportions) of resources used seems even less reasonable than maintaining a “given assortment” of outputs, but I suppose we could do it.