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Productionpossibility frontier

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In economics, a productionpossibility frontier (PPF), sometimes called a productionpossibility curve, production-possibility boundary or product transformation curve, is a

graph that compares the production rates of two commodities that use the same fixed total of the

factors of production. The PPF curve shows a possible specified production level of onecommodity that results given the production level of the other. By doing so, it defines productive

efficiency, such that production of one commodity is maximised given the production level of

the other commodity. A period of time is specified as well as the production technologies. The

commodity compared can either be agoodor aservice.

PPFs are normally drawn as bulging upwards ("concave") from the origin but can also berepresented as bulging downward or linear (straight), depending on a number of factors. A PPF

can be used to represent a number of economic concepts, such as scarcityof resources (i.e., the

fundamental economic problem all societies face), opportunity cost (or marginal rate of

transformation), productive efficiency,allocative efficiency, andeconomies of scale. In addition,an outward shift of the PPF results from growth of the availability of inputs such as physical

capital or labour, 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 its fullproductivity (on the PPF), which means that more of both outputs can be produced during the

specified period of time without sacrificing the output of either good. Conversely, the PPF will

shift inward if the labor force shrinks, the supply of raw materials is depleted, or a natural

disaster decreases the stock of physical capital. However, most economic contractions reflect notthat less can be produced, but that the economy has started operating below the frontiertypically 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 more capital goods and fewer consumer goods, or vice

versa.

[edit] Indicators

[edit] Efficiency
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An example PPF with illustrative points marked

See also:Productive efficiencyandPareto efficiency

A PPF shows all possible combinations of two goods that can be produced simultaneously duringa 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 goodmust 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, due to the difficulty of graphical analysisof multiple goods. If we are interested in one good, a composite score of the other goods can be

generated using different techniques.[2][3]Furthermore, the production model can be generalised

using higher-dimensional techniques such as Principal Component Analysis (PCA) and others.[4]

For example, assume that the supply of the economy's factors of production does not change

over time, in order to produce more butter, producing "guns" needs to be sacrificed. If production

is efficient, the economy can choose between combinations (i.e. points) on the PPF:B if guns areof interest, Cif more butter is needed,D if an equal mix of butter and guns is required.

[1]

In the PPF, all points on the curve are points of maximumproductive efficiency(i.e., no moreoutput can be achieved from the given inputs); all points inside the frontier (such as A) can be

produced but productively inefficient; all points outside the curve (such asX) cannot be produced

with the given, existing resources.[5]

Not all points on the curve are Pareto efficient, however;

only in the case where themarginal rate of transformation is equal to all consumers' marginal

rate of substitutionand hence equal to the ratio of prices will it be impossible to find any tradethat will make no consumer worse off.[6]

[edit] Opportunity cost
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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 entailsdecreasing 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 thesecond). 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).

If the shape of the PPF curve is straight-line, the opportunity cost is constant as production of

different goods is changing. But, opportunity cost usually 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 ofbutter production, costs the opportunity of 5 guns (as with a movement from A toB). At point C,

the economy is already close to its maximum potential butter output. To produce 10 more

packets of butter, 50 guns must be sacrificed (as with a movement from C to D). The ratio ofopportunity costs is determined by the marginal rate of transformation.

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

The slope of the productionpossibility frontier (PPF) at any given point is called the marginal

rate of transformation (MRT). Theslopedefines the rate at whichproductionof one good can beredirected (by re-allocation of production resources) into production of the other. It is also called

the (marginal) "opportunity cost" of a commodity, that is, it is the opportunity cost ofXin terms

ofYat 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 a PPF is commonly drawn as concave from the origin to representincreasing 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 pointBB in the

diagram is equal to 2, then, in order to produce one more packet of butter, the production of 2guns 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. Therefore Opportunity cost plays a major role insociety,

[edit] Shape

The productionpossibility 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 productionsectors. That is, as an economy specializes 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 areusing 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 haslittle impact on the opportunity cost of increasing butter production: the loss in gun production
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will be small. But the cost of producing successive units of butter will increase as resources that

are more and more specialized 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 almoststraight 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 ofproductionto 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]

Witheconomies of scale, the PPF would appear inward, with opportunity costs falling as more is

produced of each respective product. Specialisation in producing successive units of a good

determines its opportunity cost (say frommass productionmethods orspecialization of labor).[13]

A common PPF: increasing opportunity

cost

A straight line PPF: constant opportunity

cost

An inverted PPF: d

cost

[edit] Position
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An unbiased expansion in a PPF

The two main determinants of the position of the PPF at any given time are the state oftechnologyand management expertise (which are reflected in the availableproduction functions)

and the available quantities andproductivityoffactors 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 ifthe 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. Conversely, a natural, military or ecological disastermight move the PPF to the left, in response to a reduction in an economy's productivity.[1]Thus

all points on or within the curve are part of theproduction set, i.e., combinations of goods that

the economy could potentially produce.

If the two production goods depicted are capital investment (to increase future productionpossibilities) 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 atechnological 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 more use of say capital and if capital grows faster than otherfactors, growth possibilities might be biased in favor of the capital-intensive good.[15][16]

[edit] Other applications

In microeconomics, the PPF shows the options open to an individual, household, or firm in atwo-good world. By definition, each point on the curve is productively efficient, but, given the

nature ofmarket demand, some points will be moreprofitablethan others. Equilibrium for a firmwill be the combination of outputs on the PPF that is most profitable.[17]

From amacroeconomicperspective, the PPF illustrates the production possibilities available to anation or economyduring a given period of time for broad categories of output. However, an

economy may achieve productive efficiency without necessarily being allocatively efficient.
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where w represents the wage rate of labour, r represents the rental rate of capital, K is the amount

of capital used, L is the amount of labour used, and C is the total cost of acquiring those

quantities of the two inputs.

The absolute value of the slope of the isocost line, with capital plotted vertically and labourplotted horizontally, equals the ratio of unit costs of labour and capital. The slope is:

The isocost line is combined with theisoquantmap to determine the optimal production point at

any given level of output. Specifically, the point of tangency between any isoquant and an

isocost line gives the lowest-cost combination of inputs that can produce the level of outputassociated with that isoquant. Equivalently, it gives the maximum level of output that can beproduced for a given total cost of inputs. A line joining tangency points of isoquants and isocosts

(with input prices held constant) is called theexpansion path.[3]

[edit] The cost-minimization problem

The cost-minimization problem of the firm is to choose an input bundle (K,L) feasible for the

output level y that costs as little as possible. A cost-minimizing input bundle is a point on theisoquant for the given y that is on the lowest possible isocost line. Put differently, a cost-

minimizing input bundle must satisfy two conditions:

1. it is on they-isoquant2. no other point on they-isoquant is on a lower isocost line.

[edit] The case of smooth isoquants convex to the origin

If they-isoquant is smooth and convex to the origin and the cost-minimizing bundle involves apositive amount of each input, then at a cost-minimizing input bundle an isocost line is tangent to

they-isoquant. Now since the absolute value of the slope of the isocost line is the input cost ratio

, and the absolute value of the slope of an isoquant is the marginal rate of technicalsubstitution(MRTS), we reach the following conclusion: If the isoquants are smooth and convexto the origin and the cost-minimizing input bundle involves a positive amount of each input, then

this bundle satisfies the following two conditions:

It is on they-isoquant (i.e. F(K,L) =y where Fis theproduction function), and the MRTS at (K,L) equals w/r.

The condition that the MRTS be equal to w/rcan be given the following intuitive interpretation.We know that the MRTS is equal to the ratio of the marginal products of the two inputs. So the

condition that the MRTS be equal to the input cost ratio is equivalent to the condition that the
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marginal product per dollar is equal for the two inputs. This condition makes sense: at a

particular input combination, if an extra dollar spent on input 1 yields more output than an extradollar spent on input 2, then more of input 1 should be used and less of input 2, and so that input

combination cannot be optimal. Only if a dollar spent on each input is equally productive is the

input bundle optimal.

[4]==References==

Isoquant

From Wikipedia, the free encyclopedia


An isoquant map where Q3 > Q2 > Q1. A typical choice of inputs would be labor for input Xand capital for input Y. More of input X, input Y, or both is required to move from isoquant Q1

to Q2, or from Q2 to Q3.

A) Example of an isoquant map with two inputs that are perfect substitutes.
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B) Example of an isoquant map with two inputs that are perfect complements.

Ineconomics, an isoquant (derived from quantity and the Greek word iso, meaning equal) is acontour linedrawn through the set of points at which the same quantity of output is producedwhile changing the quantities of two or more inputs

.

[1][2]

While anindifference curvemappinghelps to solve the utility-maximizing problem of consumers, the isoquant mapping deals with thecost-minimization problem of producers. Isoquants are typically drawn on capital-labor graphs,

showing the technological tradeoff between capital and labor in the production function, and the

decreasing marginal returns of both inputs. Adding one input while holding the other constanteventually leads to decreasing marginal output, and this is reflected in the shape of the isoquant.

A family of isoquants can be represented by an isoquant map, a graph combining a number of

isoquants, each representing a different quantity of output. Isoquants are also called equalproduct curves.

Production Isoquant/IsocostCurve

An isoquant shows the extent to which the firm in question has the ability to substitutebetween the two different inputs at will in order to produce the same level of output. An

isoquant map can also indicate decreasing or increasing returns to scalebased on increasing or

decreasing distances between the isoquant pairs of fixed output increment, as output increases. If

the distance between those isoquants increases as output increases, the firm's production functionis exhibiting decreasing returns to scale; doubling both inputs will result in placement on an
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isoquant with less than double the output of the previous isoquant. Conversely, if the distance is

decreasing as output increases, the firm is experiencing increasing returns to scale; doubling bothinputs results in placement on an isoquant with more than twice the output of the original

isoquant.

As with indifference curves, two isoquants can never cross. Also, every possible combination ofinputs is on an isoquant. Finally, any combination of inputs above or to the right of an isoquant

results in more output than any point on the isoquant. Although the marginal product of an inputdecreases as you increase the quantity of the input while holding all other inputs constant, the

marginal product is never negative in the empirically observed range since arationalfirm would

never increase an input to decrease output.

[edit] Shapes of Isoquants

If the two inputs are perfect substitutes, the resulting isoquant map generated is represented infig. A; with a given level of production Q3, input X can be replaced by input Y at an unchanging

rate. The perfect substitute inputs do not experience decreasing marginal rates of return whenthey are substituted for each other in the production function.

If the two inputs are perfect complements, the isoquant map takes the form of fig. B; with a level

of production Q3, input X and input Y can only be combined efficiently in the certain ratiooccurring at the kink in the isoquant. The firm will combine the two inputs in the required ratio

to maximize profit.

Isoquants are typically combined with isocost lines in order to solve a cost-minimization

problem for given level of output. In the typical case shown in the top figure, with smoothly

curved isoquants, a firm with fixed unit costs of the inputs will have isocost curves that are linear

and downward sloped; any point of tangency between an isoquant and an isocost curverepresents the cost-minimizing input combination for producing the output level associated with

that isoquant. A line joining tangency points of isoquants and isocosts (with input prices held

constant) is called theexpansion path.[3]

The only relevant portion of the isoquant is the one that is convex to the origin, part of the curve

which is not convex to the origin implies negative marginal product for factors of production.Higher isoQuant higher the production.

[edit] See also

Wikimedia Commons has media related to:Isoquants

Microeconomics xpansion path From Wikipedia, the free encyclopedia
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In economics, an expansion path (also called a scale line[1]) is a line connecting

optimal input combinations as the scale of production expands.[2]

A producer

seeking to produce the most units of a product in the cheapest possible way attempts

to increase production along the expansion path.[3]

Economists Alfred Stonier and Douglas Hague defined expansion path as "that linewhich reflects least cost method of producing different levels of output, when factor

prices remain constant."[4]The points on an expansion path occur wherebudget level

and the purchaser's indifference curve are tangents. As a producer's budget level

increases, each of these points can be connected in a line. A line joining tangency pointsof isoquants and isocosts (with input prices held constant).

[5] If an expansion pathforms a straight line, the production technology is considered homothetic (or

homoethetic).[6]In this case, theratiois always the same, and the inputs can be adjusted

based on this ratio for any budget. A CobbDouglas production function has an

expansion path which is a straight line through the origin
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