Marginal Analysis and Efficiency

Prof. Dohan, Economics 207, Lecture Notes
Simple model of decision-making, information and motivation:
The self-sufficient peasant and the need for marginal analysis
The Robinson Crusoe Economy
Every economic system has “decision making systems”. To understand a “decision making
systems”, as an information system and as motivation structure, let’s examine how the actual economic
processes and decisions that might be made in the simplest model: the self-sufficient peasant
In the simplest model, let us start to understand what we mean by each of these concepts, by
using the simplest model possible, namely an isolated farmer or peasant who is producing only private
type goods. grain and cloth.
We are going to assume that he is initially that the farmer is isolated from the market. The
farmer is assumed to have perfect information about his resources, his production function, and his
utility function. We are assuming that he owns all his resources and has the goal of maximizing his
household utility over time.
What type of information does he need to have and what decisions does he have to make?
First, he determines what are his current resources which, in the case of a peasant, might be his
land, his labor, and farm equipment which in peasant times may have consisted only of an ox, a plow
and a scythe. He produced only private-type goods, has only a limited amount of private-type resources
and he does not interact with the market. That is to say, he is isolated from a market system (for the
moment). This allows us to concentrate on the importance of relative opportunity costs in decision
making. Unlike the serf on a Manor, this peasant is free to produce whatever maximizes his utility.
Second, he determines from his production function what his production possibility frontier is
which is determined by the individual production functions of each of the individual goods he could
produce. Each production function exhibited diminishing marginal returns as you increased the ratio of
one input compared to the other input that is to say, in the simplest model, the capital labor ratio. And
that his utility function obeys the law of diminishing marginal utility as you increase the proportion of
one good and decrease the proportion of the other good.
As you know a production possibility frontier is an economist’s shorthand for describing relative
opportunity costs of producing different types of goods, given that that (opportunity) cost of producing
each one is minimized. MPPlf/MPPlc = MPPkf/MPPkc
For example, he could use his land and labor to produce food or cloth spun from the wool of
sheep which graze on land which could be used for growing crops or grazing sheep.
Third, the farmer then decides what to produce depending on his (private or internal) utility
function, generating his own internal map of indifference curves. His goal is to maximize his utility over
time, given the risks of various choices.
He adjusts his production of food and cloth so that:
MRT fc = MCf/MCc = ∆C/∆F = MUf/MUc = MRSfc
It also turns out , at his best point Max that he allocates his capital
and labor so that:
MPPlf/MPPlc = MPPkf/MPPkc = MUf/MUc
Prof. Dohan, Economics 207, Lecture Notes
Simple model of decision-making, information and motivation:
The self-sufficient peasant and the need for marginal analysis
The Robinson Crusoe Economy
The fifth decision is actually quite complex. The farmer can decide to consume a variety of goods today
from his current output or he could decide to save part of it to use in the future either as consumption
or investment in capital goods to increase his resources for future periods. A similar law of diminishing
marginal product holds as the farmer allocates more current output to investment because the amount
of land and labor he has is fixed. . Similarly the law of diminishing marginal utility of future output falls
as he allocates more of current output towards future output.
To illustrate this, we used above a production possibility frontier for food and clothing that
depends on his resources. We can then impose upon that same diagram his utility function for cloth and
food where he chooses a combination of cloth and food on the PPF which maximizes his utility. We have
to draw another set of curves namely the relationship between current output and future output and
his evaluation of the desirability of current output versus future output, namely another utility curve.
Believe it or not even for the simple peasant, there were many ways of converting grain output
into capital of a very different nature. For example, the peasant could accumulate enough grain so that
he would not have to spend his labor growing grain one year and could use his labor and the labor of his
family to either clear off more land (a frequent activity in medieval time, or he could feed it to cattle to
increase the number of cattle he has or he could build irrigation ditches to water his crops better during
the dry seasons. Presumably this accumulation of capital through saving and production of investment
goods would shift the production possibility outward. Capital has a net productivity so that he has to
choose between less consumption now in exchange for more consumption later.
Let us call this decision to allocate consumption between current consumption and savings a
macro type decision and it assumes that the farmer has enough output above subsistence (to live on) to
set aside a portion of it.
For those of you who remember your micro, you will see how many types of decisions are
involved here. Basically the farmer has to consider the contribution of each input in increasing his
utility. You can intuitively understand that if the farmer considers both current use and the benefits of
saving for future use that has influenced his overall utility of producing one type of good versus another
type of good. Even the simplest peasant, knew that he had to set aside a portion of his crop to use for
seed for the next growing season and that he could not kill off all his cattle for meat because they were
needed to breed more cattle in the future.
To summarize, we have the following types of decisions. The allocation of private type resources
among various types of output so as to maximize the utility the farmer is getting from those resources in
the current year and the allocation of current output between current consumption and current
We can express the equilibrium condition necessary for the allocation of resources and output
to maximize the utility of this peasant over time without consult prices. He looks at the relative
opportunity cost of using his capital and labor to producing grain versus making cloth.
Prof. Dohan, Economics 207, Lecture Notes
Simple model of decision-making, information and motivation:
The self-sufficient peasant and the need for marginal analysis
The Robinson Crusoe Economy
One of the benefits of this model is that since the model is self-contained, we do not have to
worry about the sources of decision making authority nor do we have to worry about how the farmer
actually uses the output within his family. We assume that the farmer (you can substitute central
planner) arbitrarily determines what the marginal utility is of distributing additional units of goods to
each of the members of his household and most importantly what weight he gives to the welfare of the
other members of his family. Note also that there are no prices in here and no money is involved.
By definition this single head of household farm is an authoritarian model and because the
farmer determines the utility of different outputs to his household.
Even though there are no prices in terms of money, there is the similar concept
of the ratios of opportunity costs and ratios of marginal products
marginal utility, etc.
in this system, we actually can see all the marginal conditions that
must be met for the efficient allocation of resources to maximize the farmer’s utility. These are called
the Pareto Optimum Conditions. See
This model of economy is called the Robinson Crusoe economy
See Wikipedia
Marginal product of labor in producing grain over the marginal product of labor in producing
cloth has to equal marginal utility grain of over the marginal utility of cloth. The same is true for all the
other inputs. That is to say the concept of efficient allocation of resources is independent of the type of
economic system that exists.
Because everything is a “private type” input or “private type” output, there are no public goods
where you have the problem of a high initial cost with a low marginal cost of using the public good.
The importance of this conclusion is that it will enable you to examine an economic system for
possible inefficiencies.
Let’s go now to the Soviet system from 1935 to 1990. There in essence you had the Politburo
making decisions about the structure of output of the entire economy as well as the allocation of
resources to each specific type of good. The Politburo determined in essence what to produce, how to
produce and also the allocation of output between consumption and investment. Furthermore, they did
not rely on market prices to make these decisions and for many years, they didn’t even use interest
rates to allocate capital among various uses. This was an authoritarian economy with a very strict
hierarchy. We will discuss in a later lecture, the problems they had with information gathering and
Prof. Dohan, Economics 207, Lecture Notes
Simple model of decision-making, information and motivation:
The self-sufficient peasant and the need for marginal analysis
The Robinson Crusoe Economy
The manorial system, which we assume is a self-contained village or enterprise or producing
unit, is actually quite similar to the Soviet system in so far as the Lord of the manor determined how to
allocated the land among various crops and uses, and sometimes determined what crops and
agricultural products should be raised or how some of the labor should be used to make non-agricultural
products such as cloth, furniture, leather processing, construction, etc.
At once, you see, that the Lord of the Manor had to have an information system and a
motivation system which enable him to make these decisions as well as to collect his share of the output
and to make sure that the peasant was following his orders.
Placing the peasant in a market economy.
If you remember the conclusion about the condition for efficient allocation of resources above,
you will see that a peasant in a fully monetized market economy each peasant will allocate his privately
owned capital, labor and other private type resources to meet the same efficiency conditions as
determined above.