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.
Any given PPF can be used to illustrate a number of economic concepts, such as opportunity cost, productive efficiency and marginal rate of transformation. Though they are normally concave, PPFs can also be linear (straight) or convex, depending on a number of factors. When an economy grows or shrinks, its PPF will expand (more can be produced) or contract (less can be produced). Likewise, combinations can illustrate the relevant priorities of an economy, such as the choice between producing capital goods or consumer goods.
A PPF simultaneously shows all possible combinations of two goods that can be produced ceteris paribus; commonly it takes the form of the curve on the right. Invariably, in order for an economy to increase the quantity of one good produced, production of the other good must be sacrificed. Here, butter production must be sacrificed for production of guns. PPFs are most commonly used to predict how much of the latter must be sacrificed for a given increase in production of the former.
Assuming that the economy's factors of production do not increase, making more butter requires that resources be redirected from making guns to making butter. If production is efficient, the economy can choose between combinations (i.e. points) on the PPF: B if guns are to be prioritised, C if more butter is needed, D if a mix is required, and so forth.
Hence, all points on the curve are points of maximum productive efficiency (no more output can be achieved from the given inputs); all points inside the frontier are feasible but productively inefficient (such as A); all points outside the curve are infeasible for given resources and thus unattainable in the short run, such as X. In addition, a single point on the PPF represents perfect allocative efficiency, where the correct combination of both is produced to maximise social welfare.
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" (because increasing production of the first good entails losing the opportunity to produce some amount of the second). Opportunity cost is measured in the number of units of the second good that are forgone if an additional unit of the first good is made.
In the context of a PPF, opportunity cost is directly related to the shape of the curve. Unless a straight-line PPF is used, opportunity cost will vary depending on the start and end point. Thus, producing ten more packs of butter when only a little butter is being produced may carry with it small opportunity costs (as with a movement from A to B), but the same change once more is produced may seem more costly (as with C to D).
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 output of one good can be transformed (by re-allocation of production resources) into output of 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. Since the shape of a 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.
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 (absolute) slope at point BB in the diagram is equal to 2, then, in order to produce one more pack 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 packs of butter, and the opportunity cost of guns in terms of butter is 4.
The example used above (increasing opportunity costs, with a curve approaching a quarter-circle) is the most common form of PPF. It can represent an assumed disparity in the factor intensities and technologies of the two sectors. That is, as an economy specializes 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 butter, workers from the gun industry will move to it. At first, the least qualified (or most general) gun workers will help start making butter. The move of these workers has little impact on the opportunity cost of increasing butter production: the loss in gun production will be small. This cost of successive units will increase as more specialised gun manufacturers are attracted.
If opportunity costs are constant, a linear PPF is produced. Products requiring similar resources (bread and pastry, for instance) will have an almost straight PPF, and hence almost constant opportunity costs (when increasing production rates). 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. 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.
With varying returns to scale, in the long run the PPF would appear inverted with opportunity costs falling as more is produced of a particular product. This is caused by the diminishing marginal return issues such as labour immobility and skills mismatch all being resolvable in the long run, leaving only economies of scale to be achieved from the greater specialisation into a particular good to drive down opportunity cost. Under constant returns to scale, however, the Manning-Markusen-Melvin model and others predict a linear PPF.
The two main determinants of the position of the curve are available production functions (reflecting the state of technology and management) and available factors of production. Only points within a PPF are actually possible in the short run. In the long run, 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).
Virtually all such shifts have their own costs associated with them. By extension, PPFs can be used to show whether an economy is prioritising future development (capital goods) or present consumption (consumer goods). Likewise, the growth may be biased, that is, the PPF shifts outwards more in one direction than the other, usually caused by unequal technological improve or increase in the factors of production.
In microeconomics, the PPF shows the options open to an individual, household, or firm, in a 2-good world (the 2-good case easily generalizes to the n-good world in which we live). For example, by definition each point on the curve is productively efficient, but, given the nature 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.
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 B to point D) reflects the costs of using resources that are not well-specialized for the production of the good which is being produced in greater quantity.