Production possibilities frontier
In economics, a production possibilities curve (PPC) or “transformation curve”
is a graph that shows the different quantities of two goods that an economy can
produce (if it uses its limited productive resources efficiently). Points along
the curve describe the trade-off between the two goods. In principle the curve
can apply to any two goods. In practice it is frequently used as a
simplification to illustrate a 2-good economy. The point it makes carries over
to the more realistic case of an economy with many goods.
A brief statement of the PPC is the following. Consider a 2-good economy,
producting Computers and Food with given labor, land, and capital that are
already being used efficiently. Then increasing production of Food requires
transferring some resources used in production of Computers. This reduces
production of Computers. More details see
Productive efficiency, opportunity cost, and allocoative efficiency
The production possibilities curve shows the maximum feasible (obtainable)
amount of one commodity for any given amount of another commodity, given the
availability of factors of production and the society's technology. The concept
is used in macroeconomics to show the production possibilities available to a
nation or economy (corresponding roughly to macroeconomic notions of potential
output), and also in microeconomics to show the options open to an individual
firm. All points on a production possibilities curve are points of maximum
productive efficiency or minimum productive inefficiency: allocated such that it
is impossible to increase the output of one commodity without reducing the
output of the other. That is, there must be a sacrifice, an opportunity cost
(given by the slope of the curve in absolute value), for increasing the
production of a good by one unit. Conversely, points inside the frontier are
feasible but productively inefficient.
alt text
Production Possibilities Curve
Point A in the diagram for example, shows that FA of food and CA of computers
can be produced when production is run efficiently. So can FB of food and CB of
computers (point B).
For a firm, a point on the curve is productively efficient but, given market
demand, could be less profitable than another point on the curve. Equilibrium
for the firm with given resources is at the most profitable and productively
efficient point on the PPF.
There is a parallel for an economy as well. It may have productive efficiency
but not allocative efficiency. Markets and other institutions of social
decision-making (such as government, tradition, and community democracy) may
lead to the wrong combination of goods being produced (and the wrong mix of
resources allocated) compared to what individuals would prefer, given what is
feasible on the PPF.
All points to the right of (or above) the curve are infeasible for given
resources. A move from point A to point B indicates an increase in the number of
Computers produced. But it also implies a decrease in the amount of Food
produced. This decrease is the opportunity cost of producing more computers.
As mentioned, the two main determinants of the curve are production functions
(reflecting the available technology and available factor endowments. If the
technology improves or the supplies of factors of production increase, the
production possibility frontier shifts to the right (upward), raising the amount
of each good that can be produced. A military or ecological disaster might move
the PPF inward and to the left.
In neoclassical economics, production possibility frontiers can easily be
constructed from the contract curves in Edgeworth box diagrams of factor
intensity. In other interpretations (often seen in textbooks), the concave
production possibilities frontier reflects the specialized nature of the
heterogeneous resources that any society uses: the opportunity cost of shifting
production from one mix to another (e.g., from point A to point B) reflects the
costs of using resources that are not well-specialized for the production of the
good which is being produced in greater quantity.
The line curve in Figure is not straight but is concave to the origin (that is,
curved inward toward the axes). This can represent an assumed disparity in the
factor intensities and technologies of the two sectors. That is, as we
specialize more and more into one product, the opportunity costs of producing
that product increase, because we are using more and more resources that are
poorly suited to produce it. With increasing production of computers, workers
from the food industry will move to it. At first, the least qualified (or most
general) food workers will help start making computers. The move of these
workers has little impact on the opportunity cost of increasing computer
production: the loss in food production will be small. This cost of successive
units will increase as more of specialised food manufacturers are attracted.
alt text
Production Possibilities Curve
For example, in the second diagram, the decision to increase the production of
computers from 5 to 6 (from point Q to point R) requires a minimum loss of food
output. However, the decision to add a tenth computer (from point T to point V)
has a much more substantial opportunity cost.
In the neoclassical interpretation, if the factor intensity ratios in the two
sectors were constant at all points on the production possibilities curve, the
curve would be linear and the opportunity cost would remain the same, no matter
what mix of outputs were produced. In other interpretations, a straight-line
production possibilities frontier reflects a situation where resources are not
specialized and can be substituted for each other with no cost. Products
requiring similar resources (bread and pastry, for instance) will have a nearly
straight PPF, hence constant opportunity costs (when increasing production
rates).
The marginal rate of transformation
The slope of the production possibilities curve at any given point is called the
marginal rate of transformation. It describes numerically the rate at which one
good can be transformed into the other. It is also called the “marginal
opportunity cost” of a commodity, that is, it is the opportunity cost of X in
terms of Y at the margin.
If, for example, the (absolute) slope at point "BB" in the diagram is equal to
2, then, in order to produce one more computer, 2 units of food production must
be sacrificed. If at "AA" for example, the marginal opportunity cost of
computers in terms of food is equal to 0.25, then, the sacrifice of one unit of
food could produce 4 computers.
The marginal rate of transformation can be expressed in terms of either
commodity. The marginal opportunity costs of computers in terms of food is
simply the reciprocal of the marginal opportunity cost of food in terms of
computers.
