Production possibility frontier

In economics, the production possibility frontier (the PPF, also called the production possibilities curve (PPC) or the “transformation curve”) is a graph that depicts the trade-off between any two items produced. It indicates the opportunity cost of increasing one item's production in terms of the units of the other forgone. An additional trade-off exists between the reward (i.e. sales) of the produced good and the opportunity cost of that good. A choice is non-improvable if the direct reward is higher than the opportunity cost. There is an equilibrium between these two. The rules can be changed by changing the rewards however, which can lead to a Nash equilibrium.

It shows the maximum obtainable amount of one commodity for any given amount of another commodity, given the availability of factors of production and the society's technology and management skills. 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: resources are 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 -- for increasing the production of any good. All resources are used as completely as possible (without the situation becoming unsustainable) and appropriately.

An economy may have productive efficiency, but not allocative efficiency: the market 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.

Point A in the diagram for example, shows that F_A of food and C_A of computers can be produced when production is run efficiently. So can F_B of food and C_B of computers (point B).

All points to the right of (or above) the curve are technically impossible (or cannot be sustained for long). Most real-world economies and firms are operating well inside the curve (i.e., inefficiently). In a situation where more than two commodities are being produced this two sector model is not adequate. It would show firms and economies well to the left of the curve for statistical reasons.

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 management techniques) and available factor endowments since they define the resources available and the most efficient combination of these resources to employ. If the technology or management know-how improves or the supplies of factors of production increases, 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 describing this frontier is not straight, but is concave to the origin (that is, curved inward toward the axes). This is due to a disparity in the factor intensities and technologies of the two sectors. The concavity reflects the higher marginal costs that become inevitable due to diminishing marginal returns in the production of each good as output of the other good approaches zero (that is, at either extreme of the curve). 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 loss will increase as more better and more specialised food manufacturs are attracted.

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.

See also

• production, costs, and pricing
• production theory basics
• production functionsk:Hranica produkèných možností