Production-possibility frontier

In economics, a production-possibility frontier (PPF), sometimes called a production-possibility curve or product transformation curve, is a graph that shows the different rates of production of two goods and/or services that an economy can produce efficiently during a specified period of time with a limited quantity of productive resources, or factors of production. The PPF shows the maximum amount of one commodity that can be obtained for any specified production level of the other commodity (or composite of all other commodities), given the society's technology and the amount of factors of production available.

Though they are normally drawn as concave (bulging out) from the origin, PPFs can also be represented as linear (straight) or bulging in toward the origin, depending on a number of factors. A PPF can be used to represent a number of economic concepts, such as scarcity of resources (i.e., the fundamental economic problem all societies face), opportunity cost (or marginal rate of transformation), productive efficiency, allocative efficiency, and economies of scale. In addition, an outward shift of the PPF results from growth of the availability of inputs such as physical capital or labor, or technological progress in our knowledge of how to transform inputs into outputs. Such a shift allows economic growth of an economy already operating at full capacity (on the PPF), which means that more of both outputs can be produced during the specified period of time without reducing the output of either good. Conversely, the PPF will shift inward if the labor force shrinks, the supply of raw materials is depleted, of a natural disaster decreases the stock of physical capital. However, most economic contractions reflect not that less can be produced, but that the economy has started operating below the frontier—typically both labor and physical capital are underemployed. The combination represented by the point on the PPF where an economy operates shows the priorities or choices of the economy, such as the choice between producing relatively more capital goods and relatively fewer consumer goods, or vice versa.

Contents

Indicators

Efficiency

An example PPF with illustrative points marked

A PPF shows all possible combinations of two goods that can be produced simultaneously during a given period of time, ceteris paribus. Commonly, it takes the form of the curve on the right. 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 in order to produce more guns. PPFs represent how much of the latter must be sacrificed for a given increase in production of the former.[1]

Such a two-good world is a theoretical simplification, necessary for graphical analysis. If one good is of primary interest, all others can be represented as a composite good.[2][3] In addition, the model can be generalised to the n-good case using mathematics.[4]

Assuming that the supply of the economy's factors of production does 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 an intermediate mix is required, and so forth.[1]

Hence, all points on the curve are points of maximum productive efficiency (i.e., no more output can be achieved from the given inputs); all points inside the frontier (such as A) are feasible but productively inefficient; all points outside the curve (such as X) are infeasible with the given resources and thus unattainable in the short run. [5] A point on the curve satisfies allocative efficiency, also called Pareto efficiency, if, for given preferences and distribution of income, no movement along the curve or redistribution of income there could raise utility of someone without lowering the utility of someone else.[6]

Opportunity cost

Increasing butter from A to B carries little opportunity cost, but for C to D the cost is great.
Main article: Opportunity cost

If there is no increase in productive resources, increasing production of a first good entails 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 forgone for one or more units of the first good.[1]

In the context of a PPF, opportunity cost is directly related to the shape of the curve (see below). Unless a straight-line PPF is used, opportunity cost will vary depending on the start and end point. In the diagram on the right, producing 10 more packets of butter, at a low level of butter production, costs the opportunity of 5 guns (as with a movement from A to B). At point C, the economy is already close to its maximum potiential butter output. To produce 10 more packets of butter, 50 guns must be sacrificed (as with a movement from C to D). The ratio of opportunity costs is determined by the marginal rate of transformation.

Marginal rate of transformation

Marginal rate of transformation increases when the transition is made from AA to BB.

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 from the origin 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.[7]

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 packet 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 packets of butter, and the opportunity cost of guns in terms of butter is 4.

Shape

The production-possibility frontier can be constructed from the contract curve in an Edgeworth production box diagram of factor intensity.[8] The example used above (which demonstrates increasing opportunity costs, with a curve concave from the origin) is the most common form of PPF.[9] It represents a disparity in the factor intensities and technologies of the two production sectors. That is, as an economy specialises more and more into one product (e.g., moving from point B to point D), the opportunity cost of producing that product increases, because we are using more and more resources that are less efficient in producing 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 be transferred into making more butter, and moving these workers has little impact on the opportunity cost of increasing butter production: the loss in gun production will be small. But the cost of producing successive units of butter will increase as resources that are more and more specialised in gun production are moved into the butter industry.[10]

If opportunity costs are constant, a straight-line (linear) PPF is produced.[11] This case reflects a situation where resources are not specialised and can be substituted for each other with no added cost.[10] Products requiring similar resources (bread and pastry, for instance) will have an almost straight PPF, hence almost constant opportunity costs.[10] 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.[12]

With economies of scale, the PPF would appear bowed in ("inverted") toward the origin, with opportunity costs falling as more is produced of each respective product. Here greater specialization in producing successive units of a good drives down its opportunity cost (say from mass production methods or specialization of labor).[13]

A common PPF: increasing opportunity cost
A straight line PPF: constant opportunity cost
An inverted PPF: decreasing opportunity cost

Position

An unbiased expansion in a PPF

The two main determinants of the position of the PPF at any given time are the state of technology and management expertise (which are reflected in the available production functions) and the available quantities and productivity of factors of production. Only points on or within a PPF are actually possible to achieve in the short run. In the long run, if technology improves or if the productivity or supply of factors of production increases, the economy's capacity to produce both goods increases, i.e., economic growth occurs. This increase is shown by a shift of the production-possibility frontier to the right (outward). Conversely, a natural, military or ecological disaster might move the PPF to the left (inward), reflecting a reduction in an economy's total productive capacity.[1] Thus all points on or within the curve are part of the production set, i.e., combinations of goods that the economy could potentially produce.

If the two production goods depicted are capital investment (to increase future production possibilities) or current consumption goods, the PPF can represent, how the higher investment this year, the more the PPF would shift out in following years.[14] It can also represent how a technological progress that more favors production possibilities of one good, say Guns, shifts the PPF outwards more along the Gun axis, "biasing" production possibilities in that direction. Similarly, if one good makes relatively more use of say capital and if capital grows faster than other factors, growth possibilities might be biased in favor of the capital-intensive good.[15][16]

Other applications

In microeconomics, the PPF shows the options open to an individual, household, or firm in a two-good world. By definition, each point on the curve is productively efficient, but, given the nature of market demand, some points will be more profitable than others. Equilibrium for a firm will be the combination of outputs on the PPF that is most profitable. [17]

From a macroeconomic perspective, the PPF illustrates the production possibilities available to a nation or economy during a given period of time for broad categories of output. However, an economy may achieve productive efficiency without necessarily being allocatively efficient. Market failure (such as imperfect competition or externalities) and some institutions of social decision-making (such as government and tradition) may lead to the wrong combination of goods being produced (hence the wrong mix of resources being allocated between producing the two goods) compared to what consumers would prefer, given what is feasible on the PPF.[18]

See also

References

  1. ↑ 1.0 1.1 1.2 1.3 Lipsey, Richard G.. An introduction to positive economics (fourth ed.). Weidenfeld & Nicolson. pp. 57–8. ISBN 0297768999. 
  2. ↑ Samuelson, Paul A. (1947). Foundations of Economic Analysis. Cambridge, Massachusetts: Harvard University Press. ISBN 0-674-31300-3. 
  3. ↑ Chacholiades, Miltiades (1986). Microeconomics. New York: Macmillan. pp. 97. ISBN 0-02-320560-1. 
  4. ↑ Ferguson, C. E. (1972). Microeconomic Theory (3rd ed.). Homewood, Illinois: Richard D. Irwin, Inc.. pp. 458–465. ISBN 0256021570. 
  5. ↑ Standish, Barry. Economics: Principles and Practice. South Africa: Pearson Education. pp. 13–15. ISBN 978-1-86891-069-4. 
  6. ↑ Samuelson, Paul A.; William D. Nordhaus (2004). Economics. McGraw-Hill. ch. 1, sect. C,"The Production-Possibility Frontier," pp. 9–15; ch. 8, Section D, "The Concept of Efficiency"}. ISBN 0-07-287205-5. 
  7. ↑ Pindyck, Robert S.; Rubinfeld, Daniel L. (2005). Microeconomics. Pearson Education. ISBN 0137133359. http://books.google.com/?id=V4hAQBB5Qn4C&pg=PA597. 
  8. ↑ Stolper, W. F.; Samuelson, P. A. (1941). "Protection and Real Wages". Review of Economics Studies (The Review of Economic Studies, Vol. 9, No. 1) 9 (1): 58–74. doi:10.2307/2967638. http://jstor.org/stable/2967638. 
  9. ↑ Barthwal, R. R. (2007). Industrial Economics: An Introductory Text Book. p. 31. 
  10. ↑ 10.0 10.1 10.2 Anderson, David. Cracking the AP Economics Macro Micro Exam. Princeton Review. pp. 37–8. ISBN 978-0-375-76384-7. 
  11. ↑ Hall, Robert Ernest; Lieberman, Marc (2008). Macroeconomics: principles and applications. Mason, OH: Thomson/South-Western. p. 466. ISBN 0-324-42146-X. 
  12. ↑ Choi, Eun Kwan; Harrigan, James (2003). Handbook of international trade. Malden, MA: Blackwell Pub.. pp. 192–3. ISBN 0-631-21161-6. 
  13. ↑ Kemp, Murray C.; Herberg, Horst; Long, Ngo van (1993). Trade, welfare, and economic policies: essays in honor of Murray C. Kemp. Ann Arbor: University of Michigan Press. pp. 3. ISBN 0-472-10364-4. 
  14. ↑ Samuelson, Paul A., and William D. Nordhaus (2004). Economics. Ch. 1, "Figure 1-5. Investment for Future Consumption Requires Sacrificing Current Consumption."
  15. ↑ Krugman, Paul R. (2004). International economics: theory and policy (sixth ed.). 清华大学出版社. pp. 100–1. ISBN 9787302078890. http://books.google.com/?id=L5DaCeXtNq0C&pg=PA100. 
  16. ↑ Gillespie, Andrew (2007). Foundations of Economics, ch. 2, "The production possibility frontier (curve): the PPF or PPC" (press +). Oxford University Press. Access date 6 January 2010 .
  17. ↑ Coelli, Time; Prasada Rao, D. S.; Battese, George E. (1998). An Introduction to Efficiency and Productivity Analysis. Springer. pp. 59–60. ISBN 9780792380627. http://books.google.com/?id=HILg4zH6SZ8C&lpg=PA60&dq=production%20possibility%20curve&pg=PP1#v=onepage&q=production%20possibility%20curve. 
  18. ↑ Farrell, M. J. (1957). "The Measurement of Productive Efficiency". Journal of the Royal Statistical Society (Journal of the Royal Statistical Society. Series A (General), Vol. 120, No. 3) 120 (3): 253–290. http://www.jstor.org/stable/2343100.