Production-possibility frontier

In economics, a production-possibility frontier (PPF) or “transformation curve” is a graph that shows the different rates of production of two goods that an economy (or agent) could efficiently produce with limited productive resources. Points along the curve describe the trade-off between the two goods, that is, the opportunity cost. Opportunity cost here measures how much an additional unit of one good costs in units forgone of the other good. The curve illustrates that increasing production of one good reduces maximum production of the other good as resources are transferred away from the other good.

Productive efficiency, opportunity cost, and allocative efficiency

The production possibilities curve shows the maximum feasible (obtainable) amount of one commodity for any given amount of another commodity, as of the society's technology and the amount of factors of production available. The concept is used to show the options open to a firm, individual, household, or economy for a 2-good world. In microeconomics, the 2-good case readily generalizes to the n-good case. In macroeconomics, it illustrates the production possibilities available to a nation or economy (corresponding roughly to macroeconomic notions of potential output at a given point on the curve) for broad categories of output. 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".

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).

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-possibiliity 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.

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.

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-possibiliity 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 possibility frontier (PPF) at any given point is called the marginal rate of transformation (MRT). 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. It measures how much of good Y is given up for one more unit of good X or vice versa. The shape of PPF is commonly drawn as concave downward 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.

"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.

ee Also

* Production, costs, and pricing
* Production theory basics
* Production function