Production Theory and Indivisible Commodities. (PSME-3) by Charles Raphael Frank

Production Theory and Indivisible Commodities. (PSME-3) by Charles Raphael Frank

CHAPTER 1
INTRODUCTION
1.1 Indivisible Commodities
Economic theory, if it is to be useful at all, must be abstract. That is,
some postulates may not conform completely to all the facts. This may be
necessary to engage in logical analysis and arrive at specific conclusions,
but postulates should emphasize those facts which are particularly relevant

to the problem at hand. The conclusions reached on the basis of such
postulates must be meaningful or valid with respect to any policy decisions

which have to be made. Although the economic theorist may make
simplifying postulates and ignore certain variables, he must guard against
the tendency to choose his postulates solely on the basis of building a
model which is easily manipulated.
One of the usual assumptions in economic theory is that commodities
can be measured by real numbers. Production functions, demand curves,
and cost functions are assumed to be defined for real number arrays and
to behave properly with respect to various criteria of continuity. Assumptions

of this sort simplify economic analysis. They imply, however, an
acceptance of commodity divisibility and ignore the difficulty or even
impossibility, in practice, of using or producing fractional units of a commodity.

In many instances indivisible rather than divisible commodities
are the more relevant with which to deal.
This book incorporates the notion of indivisibility in a limited way
into an analysis of production and allocation in the belief that there is a
large class of problems for which this type of analysis is important. In
some instances we make drastically simple assumptions to provide a basis
for meaningful analysis.
1.2 Efficiency and Pareto Optimality
Frequently it is useful to divide an economy into two sectors—the
production sector and the consumption sector. In the production sector,
inputs of various commodities may be combined to produce outputs of
various other commodities. A set of numbers specifying the amount of
each input and each output is called an input-output combination. If we

ignore resource limitations, then an input-output combination is called a
possible input-output combination if it is compatible with a given state of
technology. If an input-output combination is compatible with the known
state of technology and also with any resource restrictions, then it is called
an attainable input-output combination. A possible (or attainable) inputoutput

combination is an efficient input-output combination only if there
is no other possible input-output combination which (a) results in more
of one output with no less of any other output or with no more of any

input or which [b) uses less of any input with no more of any other input or
with no less of any output. Our definition of efficiency refers only to
efficiency within the production sphere.
Each commodity is assigned a price. Associated with each possible
input-output combination is a unique profit. A profit-maximizing inputoutput

combination is one which gives the maximum profit over all
possible input-output combinations.
In the consumption sector of the economy, there is a given number of
consumers, each with a set of preferences (a partial ordering) for all

commodity combinations. An input-output combination is Pareto optimal if
there is no other attainable input-output combination which could make
at least one consumer "better off" with no other consumer "worse off."
Given some easily acceptable assumptions, one can show that every
Pareto optimal input-output combination is efficient. In a sense one
might say that every efficient input-output combination is a candidate as
a point of Pareto optimality.
We can illustrate this in a simplified way in terms of Figure 1.1. Let
RR' represent an indifference curve for Robinson Crusoe. Let the heavy
dots in the shaded area represent the attainable combinations of the two
indivisible goods X and Y. Then the point E is the most preferred

combination from Robinson's point of view.
For any efficient point such as B, C, or F, one can draw a conceivable
indifference curve for Robinson which would make such an efficient
point the most preferred point from Robinson's point of view. Thus,
every efficient point may possibly be socially desirable.
On the other hand, consider a point which is not efficient, such as G.
Only a very strange preference pattern for Robinson would make such a
point socially desirable. Only if Robinson were completely satiated with
respect to one or the other of the commodities or if Robinson had a
positive dislike for one of the commodities would such a point be a most

Production Theory and Indivisible Commodities. (PSME-3) by Charles Raphael Frank