# Production possibility frontier

In

economics, the

**production possibility frontier** (also called “transformation curve”) is a

graph that depicts the opportunity cost between any two items produced.
It shows the maximum obtainable amount of one commodity for any given amount of another commodity. The concept is used in

macroeconomics to show the production possibilities available to a nation or economy, and also in

microeconomics to show the options open to an individual firm. All points on a production possibilities curve are points of maximum efficiency: resources are allocated such that it is impossible to increase the output of one commodity without reducing the output of the other.

*Production Possibilities Curve*

Point A in the diagram for example, shows that “Fa” of food and “Ca” of computers can be produced efficiently. So can “Fb” of food and “Cb” of computers (point B). All points to the right of the curve are technically impossible. Most real world economies and firms are operating well inside the curve (ie. - 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 shift 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.

The two main determinants of the curve are production functions and factor endowments since they define the resources available and the most efficient combination of these resources to employ. In practice production possibility frontiers can easily be constructed from the contract curves in Edgeworth box diagrams of factor intensity.

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 of the two sectors. The concaveture reflects the higher marginal costs that become inevitable due to inefficiencies in the production of each good as output 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.

*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.

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.

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.

*Marginal Rate of Transformation*

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.

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