Production-possibility frontier
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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 individual or group can efficiently produce with limited productive resources. The PPF shows the maximum obtainable amount of one commodity for any given amount of another commodity or composite of all other commodities, given the society's technology and the amount of factors of production available.
[edit] Productive efficiency, allocative efficiency, and opportunity cost
Here is an example using the two goods, food and computers.
The move from point A to point B indicates an increase in the number of computers produced, but it also indicates a decrease in the amount of food produced. Assuming that productive resources do not increase, making more computers requires that resources be redirected from making food to making computers. If production is efficient, FA of food and CA of computers could be made (as Point A shows), or FB of food and CB of computers could be made (as Point B shows).
All points on the curve are points of maximum productive efficiency; all points inside the frontier are feasible but productively inefficient; all points outside the curve are infeasible for given resources.
If there is no increase in productive resources, increasing production of a first good has to entail 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" (so-called because the opportunity to increase the first good entails the cost of decreasing the second). Opportunity cost is measured in the number of units of the second good that are foregone if an additional unit of the first good is made.
In microeconomics, the PPF shows the options open to an individual, household, or firm for a 2-good world (but the 2-good case easily generalizes to the n-good world that we live in). For example: by definition each point on the curve is productively efficient. But, given market demand, one point might be less profitable than another. Equilibrium for a firm will be the point on the PPF that is most profitable.
In macroeconomics, the PPF illustrates the production possibilities available to a nation or economy for broad categories of output. An economy 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.
As the opening paragraph notes, the two main determinants of the curve are available production functions (reflecting the state of 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 (outward), raising the amount of each good that can be produced. A military or ecological disaster might move the PPF to the left (inward).
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-possibility 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 the 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-possibility 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).
[edit] 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.
