In economics, a production–possibility frontier, sometimes called a production–possibility
curve, production-possibility boundary or product transformation curve, is a graph representing
production tradeoffs of an economy given fixed resources.
The graph shows the various combinations of amounts of two commodities that an economy
can produce using a fixed amount of each of the factors of production.
Graphically bounding the production set for fixed input quantities, the PPF curve shows
the maximum possible production level of one commodity for any given production level of
the other, given the existing state of technology.
By doing so, it defines productive efficiency in the context of that production set: a point
on the frontier indicates efficient use of the available inputs, while a point beneath
the curve indicates inefficiency.
A period of time is specified as well as the production technologies and amounts of inputs
available.
The commodities compared can either be goods or services.
PPFs are normally drawn as bulging upwards from the origin but can also be represented
as bulging downward or linear, depending on a number of factors.
A PPF can be used to illustrate a number of economic concepts, such as scarcity of resources,
opportunity cost, productive efficiency, allocative efficiency, and economies of scale.
In addition, an outward shift of the PPF results from growth of the availability of inputs
such as physical capital or labour, or technological progress in our knowledge of how to transform
inputs into outputs.
Such a shift allows economic growth of an economy already operating at its full productivity,
which means that more of both outputs can be produced during the specified period of
time without sacrificing the output of either good.
Conversely, the PPF will shift inward if the labor force shrinks, the supply of raw materials
is depleted, or a natural disaster decreases the stock of physical capital.
However, most economic contractions reflect not that less can be produced, but that the
economy has started operating below the frontier—typically both labor and physical capital are underemployed.
The combination represented by the point on the PPF where an economy operates shows the
priorities or choices of the economy, such as the choice of producing more capital goods
and fewer consumer goods or vice versa.
Indicators Efficiency
A PPF typically takes the form of the curve on the right.
An economy that is operating on the PPF is said to be efficient, meaning that it would
be impossible to produce more of one good without decreasing production of the other
good.
In contrast, if the economy is operating below the curve, it is said to be operating inefficiently
because it could reallocate resources in order to produce more of both goods.
For example, assuming that the economy's available quantity of factors of production does not
change over time and that technological progress does not occur, then if the economy is operating
on the PPF production of guns would need to be sacrificed in order to produce more butter.
If production is efficient, the economy can choose between combinations on the PPF: B
if guns are of interest, C if more butter is needed, D if an equal mix of butter and
guns is required.
In the PPF, all points on the curve are points of maximum productive efficiency; all points
inside the frontier can be produced but are productively inefficient; all points outside
the curve cannot be produced with the given, existing resources.
Not all points on the curve are Pareto efficient, however; only in the case where the marginal
rate of transformation is equal to all consumers' marginal rate of substitution and hence equal
to the ratio of prices will it be impossible to find any trade that will make no consumer
worse off.
Any point that lies either on the production possibilities curve or to the left of it is
said to be an attainable point, meaning that it can be produced with currently available
resources.
Points that lie to the right of the production possibilities curve are said to be unattainable
because they cannot be produced using currently available resources.
Points that lie within the curve are said to be inefficient, because existing resources
would allow for production of more of at least one good without sacrificing the production
of any other good.
An efficient point is one that lies on the production possibilities curve.
At any such point, more of one good can be produced only by producing less of the other.
Such a two-good world is a theoretical simplification, due to the difficulty of graphical analysis
of multiple goods.
If we are interested in one good, a composite score of the other goods can be generated
using different techniques.
Furthermore, the production model can be generalised using higher-dimensional techniques such as
Principal Component Analysis and others.
Opportunity cost
If there is no increase in productive resources, increasing production of a first good entails
decreasing production of a second, because resources must be transferred to the first
and away from the second.
Points along the curve describe the trade-off between the goods.
The sacrifice in the production of the second good is called the opportunity cost.
Opportunity cost is measured in the number of units of the second good forgone for one
or more units of the first good.
In the context of a PPF, opportunity cost is directly related to the shape of the curve.
If the shape of the PPF curve is straight-line, the opportunity cost is constant as production
of different goods is changing.
But, opportunity cost usually will vary depending on the start and end point.
In the diagram on the right, producing 10 more packets of butter, at a low level of
butter production, costs the opportunity of 5 guns.
At point C, the economy is already close to its maximum potential butter output.
To produce 10 more packets of butter, 50 guns must be sacrificed.
The ratio of opportunity costs is determined by the marginal rate of transformation.
Marginal rate of transformation
The slope of the production–possibility frontier at any given point is called the
marginal rate of transformation.
The slope defines the rate at which production of one good can be redirected into production
of the other.
It is also called the "opportunity cost" of a commodity, that is, it is the opportunity
cost of X in terms of Y at the margin.
It measures how much of good Y is given up for one more unit of good X or vice versa.
The shape of a PPF is commonly drawn as concave from the origin to represent increasing opportunity
cost with increased output of a good.
Thus, MRT increases in absolute size as one moves from the top left of the PPF to the
bottom right of the PPF.
The marginal rate of transformation can be expressed in terms of either commodity.
The marginal opportunity costs of guns in terms of butter is simply the reciprocal of
the marginal opportunity cost of butter in terms of guns.
If, for example, the slope at point BB in the diagram is equal to 2, then, in order
to produce one more packet of butter, the production of 2 guns must be sacrificed.
If at AA, the marginal opportunity cost of butter in terms of guns is equal to 0.25,
then, the sacrifice of one gun could produce four packets of butter, and the opportunity
cost of guns in terms of butter is 4.
Therefore opportunity cost plays a major role in society.
Shape The production–possibility frontier can
be constructed from the contract curve in an Edgeworth production box diagram of factor
intensity.
The example used above is the most common form of PPF.
It represents a disparity in the factor intensities and technologies of the two production sectors.
That is, as an economy specializes more and more into one product, the opportunity cost
of producing that product increases, because we are using more and more resources that
are less efficient in producing it.
With increasing production of butter, workers from the gun industry will move to it.
At first, the least qualified gun workers will be transferred into making more butter,
and moving these workers has little impact on the opportunity cost of increasing butter
production: the loss in gun production will be small.
But the cost of producing successive units of butter will increase as resources that
are more and more specialized in gun production are moved into the butter industry.
If opportunity costs are constant, a straight-line PPF is produced.
This case reflects a situation where resources are not specialised and can be substituted
for each other with no added cost.
Products requiring similar resources will have an almost straight PPF, hence almost
constant opportunity costs.
More specifically, with constant returns to scale, there are two opportunities for a linear
PPF: firstly, if there was only one factor of production to consider, or secondly, if
the factor intensity ratios in the two sectors were constant at all points on the production-possibilities
curve.
With varying returns to scale, however, it may not be entirely linear in either case.
With economies of scale, the PPF would curve inward, with the opportunity cost of one good
falling as more of it is produced.
Specialisation in producing successive units of a good determines its opportunity cost.
Position
The two main determinants of the position of the PPF at any given time are the state
of technology and management expertise and the available quantities of factors of production.
Only points on or within a PPF are actually possible to achieve in the short run.
In the long run, if technology improves or if the supply of factors of production increases,
the economy's capacity to produce both goods increases; if this potential is realized,
economic growth occurs.
This increase is shown by a shift of the production-possibility frontier to the right.
Conversely, a natural, military or ecological disaster might move the PPF to the left, in
response to a reduction in an economy's productive capability.
Thus all points on or within the curve are part of the production set, i.e., combinations
of goods that the economy could potentially produce.
If the two production goods depicted are capital investment and current consumption goods,
the higher is investment this year, the more the PPF would shift out in following years.
Shifts of the curve can represent how technological progress that favors production possibilities
of one good, say guns, more than the other shifts the PPF outwards more along the favored
good's axis, "biasing" production possibilities in that direction.
Similarly, if one good makes more use of say capital and if capital grows faster than other
factors, growth possibilities might be biased in favor of the capital-intensive good.
Other applications In microeconomics, the PPF shows the options
open to an individual, household, or firm in a two-good world.
By definition, each point on the curve is productively efficient, but, given the nature
of market demand, some points will be more profitable than others.
Equilibrium for a firm will be the combination of outputs on the PPF that is most profitable.
From a macroeconomic perspective, the PPF illustrates the production possibilities available
to a nation or economy during a given period of time for broad categories of output.
It is traditionally used to show the movement between committing all funds to consumption
on the y-axis versus investment on the x-axis.
However, an economy may achieve productive efficiency without necessarily being allocatively
efficient.
Market failure and some institutions of social decision-making may lead to the wrong combination
of goods being produced compared to what consumers would prefer, given what is feasible on the
PPF.
Notes
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