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Ppf

This is a PowerPoint presentation on the concept of

of production possibilities or the transformation

function and alternative economic choices.

A left mouse click or the enter key will add an

element to a slide or move you to the next slide. The

backspace key will take you back one element or

slide. The escape key will get you out of the

presentation.

Principles of Microeconomics


Production and choices

Production and Choices

  • Production is the process of altering inputs so they will satisfy more wants.

    • Change in physical characteristics to increase inputs ability to satisfy wants {Utility}

    • Change in location

    • Change in time available for consumption (storage)

    • Change in ownership

  • Consider how Production might be measured.

Principles of Microeconomics


Factors of production or inputs

Factors of Production or inputs

  • Typical taxonomy of inputs

    • land [considered a “gift of nature”]

    • labour [human effort in production]

    • capital [inputs created by humans

    • entrepreneurial ability [innovation]

  • Alternative taxonomy

    • energy, matter, time & technology [knowledge]

Principles of Microeconomics


Ppf

Land

  • Natural resources which are considered as a “gift of Nature.”

  • Some natural resources are:

    • Flow [sunlight, use of solar does not diminish the solar power available]

    • Renewables [fish, trees, rivers, resources that can be renewed]

    • Stock or exhaustible [fossil fuels]

  • Return to land is “rent”

Principles of Microeconomics


Labour

Labour

  • Labour is any human effort used to produce goods and services

    • manual

    • mental

  • Return to labour includes wages, salaries, bonuses, commissions, etc.

  • Education and training is often referred to as “human capital”

Principles of Microeconomics


Capital kapital

Capital {Kapital}

  • Kapital is the buildings, equipment, tools, etc. that humans create to use in the further production of goods and services

  • The concept of Kapital was added during the early years of the industrial revolution

  • the return to kapital is interest

  • Usury and ethical judgment

Principles of Microeconomics


Entrepreneurial ability

Entrepreneurial Ability

  • The last factor of production added to out perspective [added by Richard Cantillon (1680-1734) and popularized by J.B. Say (1776-1832)]

  • Used to explain the distribution of a “surplus” in production

  • Entrepreneurial activity is the creation or innovation process in an economy. Not to be confused with business.

  • the return to the entrepreneur is “profit”

Principles of Microeconomics


Historical basis of factors of production

Historical basis of factors of production

  • During feudal era, the two inputs were regarded as land and labour. This was used to describe the allocation of the output among social classifications.

  • With the industrial revolution, a new social class was added, the capitalists. Capital was the justification for the share of output they received.

  • In the midst of the industrial revolution when productivity was high, there was often a surplus which was taken by the capitalist. Say’s addition of entrepreneurial ability justified this act.

Principles of Microeconomics


Production possibilities

Production Possibilities

  • The production alternatives open are determined by the availability and quality of the inputs, technology [our knowledge about how to use the physical world] and social institutions[such as traditions, customs, mores, laws, etc.]

  • At any given point in time inputs are finite (limited), the state of knowledge and the social institutions are fixed.

  • All of these can change over time

Principles of Microeconomics


Example ppf or transformation function

Example PPF or Transformation Function

  • Consider a small economy with a fixed amount of labour [L], kapital [K] and a given state of technology. For simplicity we shall assume all these are homogeneous

  • There are two fields that can be used to grow two crops [these are the only outputs]Wheat [X] and Peanuts [Y]

  • These two fields are of different soil types, so out putof Wheat [X] and Peanuts [Y] is different on each field

  • Field A is more productive in Wheat [X], Field B in [Y]

Principles of Microeconomics


Ppf

60

[Y]

50

40

T

30

20

M

10

[X]

10 20 30 40 50 60

These alternatives can

be plotted on the graph,

Field A is more productive in growing

Wheat [X] than peanuts [Y]

.

These alternatives

can be illustrated by a line

.

.

If no Wheat is produced

a maximum of 30 units of

peanuts can be produced.

If no peanuts are produced, 60 unit of wheat can be grown. This

is because the land is better suited to growing Wheat [X] than [Y].

If the production relationship is linear, we can interpolate an infinite

number of alternatives that lie along the line TM.

The equation that represents the production alternatives on Field

A is: Y = 30 - .5X This implies that 1 unit of X can be acquired by

sacrificing .5 units of Y

Principles of Microeconomics


Ppf

R

[Y]

80

70

60

50

40

30

20

10

S

[X]

10 20 30 40 50 60

Field B is more productive in

growing Y than X

These alternatives are

plotted

The estimated relationship of the trade off

between X and Y is: Y = 80 - 2.67X

This relationship is represented

by the line RS

This set of production alternatives implies that 1 unit of X requires a

sacrifice of 2.67 units of Y. Remember that on Field A an additional

unit of X cost .5Y.

If you were producing Y on both fields and wanted some X, which field

would you first grow X on?

Principles of Microeconomics


Ppf

Why?

Did you choose Field A?

If were producing all Y on both fields, you could produce 110 units of

peanuts with no wheat. If you wanted a unit of Wheat [X] you would

have to sacrifice [opportunity cost] 2.67 units of Y if you chose

Field B. On Field A you would only sacrifice .5 units of Y. Therefore,

X [wheat] would cost less if it were grown on Field A.

You can produceup to 60 units of X at a cost of .5 Y per unit of X.

To produce more than 60X, you will be required to sacrifice 2.67Y.

If we combine thetwo fields to evaluate the alternatives

we develop a “production possibilities frontier” [PPF] or

a Transformation function.

The PPF is a graphical representation [model] of the

production alternatives available to the community or

firm with the two fields, a given level of technology and

other inputs [labour, kapital, entrepreneurial ability].

Principles of Microeconomics


Ppf

60

R

50

80

40

70

T

30

60

[Y]

20

50

10

M

40

30

[Y]

110

20

100

10

S

90

[X]

10 20 30 40 50 60

80

70

60

50

40

30

20

10

S + M

  • 10 20 30 40 50 60 70 80 90 100 110 120 130

[X]

[Y]

Field A

Field B

Production alternatives

on Field A

Production alternatives

on Field B

[X]

10 20 30 40 50 60

[T+R]

On Field A, only .5Y

is sacrificed for each

unit of X [up to 60units]

When both fields are used to

produce Y, 110units of

output can be achieved.

30 on Field A & 80 on Field B

If more than 60 X is desired

you must sacrifice 2.67Y per unit of X while producing on Field B

Principles of Microeconomics


Ppf

[Y]

110

100

Production

on Field A

90

80

70

60

50

40

Production

on Field B

30

20

10

  • 10 20 30 40 50 60 70 80 90 100 110 120 130

[X]

The production possibilities on the two

fields are demonstrated as a PPF

As the number of fields increases,

or we break the two fields up into

smaller homogeneous fields, the

PPF will “smooth” out and can be

represented by a curve or

nonlinear function

This transformation function or PPF demonstrates all production

alternatives available given the inputs [L, K, E, Land and technology]

The fact that it is “bowed out” (convex from above) demonstrates the problem

that as we increase the output of X (or Y) we must sacrifice larger and larger

amounts of Y (or X). This is the “law” of “increasing relative costs.”

Principles of Microeconomics


Ppf

R

[Y]

110

100

S

90

80

T

70

60

V

50

40

30

20

W

10

H

  • 10 20 30 40 50 60 70 80 90 100 110 120 130

[X]

Because of some basic relationships, and the

fact that optimizers will choose alternatives

that have the lowest opportunity cost [i.e.the

lowest cost or sacrifice of other goods]

PPF is “bowed out” (concave to origin).

Definitely not

a good idea! This

requires that the initial

units of X be acquired at

their highest possible

sacrifice of Y [cost].

If an individual, firm or society

made choices that required the

greatest sacrifice, the PPF would

be “bowed in” (convex to origin).

If all inputs are “efficiently” employed the output

combination will fall on the PPF. Points R, S, T, V, W & H

are all equally “efficient.” Any point on the PPF is “efficient.”

“Efficiency” does not serve as a useful criteria to choose among

alternatives unless it is carefully specified as to what you mean!

Principles of Microeconomics


Efficiency

Value of output

Value of input

“Efficiency”

  • There are several types of “efficiency”

  • Technical efficiency is borrowed from physics, it is :

  • Allocative efficiency is :

.

ParetoEfficiency

Principles of Microeconomics


Technical efficiency

Technical Efficiency

  • Technical efficiency is defined as a ratio of output to input

  • concept is “borrowed” from physics

  • MPG, kPH as measures of efficiency

    • MPG or miles per gallon: miles is output, gallons of gas is the input

    • kPH or kilometers per hour: kilometers traveled is the output, time is an input

    • Which is the “better” measure of “efficiency?”

Principles of Microeconomics


Technical efficiency cont

Technical Efficiency [cont. . .]

  • To “maximize” efficiency

    • maximize the output while input is constant

    • minimize the input while output is constant

  • In a PPF, the attempt is to maximize the output [of two goods] while technology and the inputs are constant

Principles of Microeconomics


Ppf

.

corn

J

.

170

167

Any output

alternative that

falls in this yellow

area is possible given

the inputs and technology

100

H

wheat

100

60

90

It is not possible to produce 90X and 170Y.

Given a PPF which is determined by the technology

and inputs available to produce the goods. Any output

combination on the blue PPF is feasible or possible.

Any output alternative that lies outside the

PPF is not possible. There are not enough

resources or known technology that will permit

the production of those quantities of outputs.

An example of an impossible output combination

is point J.

Any output combination that lies “inside” the PPF is not technically efficient!

Consider the choice of a production alternative described by point H .

X = 60 and Y= 100.

More wheat can be produced without reducing the output of corn!

or more Y [corn] can be produced with no sacrifice of X [wheat] !

Principles of Microeconomics


Ppf

corn

K

.

167

F

100

H

wheat

60

100

Starting with the PPF model for corn and wheat, an output

choice that results in Y = 100 and X = 60 is not efficient.

More Y [corn] can be produced with no sacrifice of wheat.

F an K both describe output choices that are more

efficient than the output combination described at H

More wheat can be produced with no

reduction in the output of corn.

Any output choice that lies in the blue

area [triangle HFK] results in an

increase in output over point H,

this is called “Pareto Safe.”

At point H the output is 100Y and 60X. At point F the output

is Y = 100 and X = 100, output has increased with the same inputs

and technology. Increased technical efficiency.

Similar reasoning shows that K and all output combinations that

lie in the blue area are technically more efficient than that at H.

There is more X or Y or both with no less of either!

Principles of Microeconomics


Ppf

.

.

A

.

D

K

.

167

F

100

.

B

.

C

60

100

corn

The concept of technical

efficiency fails to offer infallible

criteria for making choices.

.

In the example, K & F are more

“efficient” than H. However, we have

no information about whether F or K is

more “valued” by individuals and society!

We have no information about which

alternative is preferred by which

individuals or classes of individuals.

H

wheat

All production alternatives on the blue PPF

are technically efficient. Points A, D, K, F, B, and C are alternatives that

satisfy the conditions of “technical efficiency.” However, there is no

information that tells us which alternative is “best.”

Neoclassical economics is a theory of market exchange and relative

prices which is used to evaluate which production alternative is best.

Principles of Microeconomics


Ppf

.

K

.

$574

167

F

$600

100

$580

60

100

The “value” of alternative B is : (50 x $2) + (120 x $4) = $580. so F is more

highly “valued” than alternative B.Later in the section on demand theory the

issue of income, income distribution, preferences and prices will be discussed in more detail.

.

.

corn

A

D

Market exchange is a transaction

between individuals. In a monetized

economy a “Price” reflects the a value

that the two parties agree on.

[Remember Oscar Wilde’s warning that a “Cynic is

someone who knows the price of everything and the

value of nothing!]

.

H

.

$440

In the example, let the price of

wheat be PX = $4 and the price of

corn be PY = $2.

50

B

.

PX = $4

PY = $2.

Then the “value” of alternative H is

(100 x $2) + (60 x $4) = $440.

120

wheat

The “value” of alternative F is: (100 x $2) + (100 x $4) = $600.

The “value” of alternative K is: (167 x $2) + (60 x $4) = $574.

Using neoclassical theory and market prices, F is preferred

over K and K is preferred over H.

Principles of Microeconomics


Allocative efficiency

Allocative Efficiency

  • allocative efficiency is the “highest valued” output possible given the market prices

  • This alternative must necessarily fall on the PPF

  • The location on the PPF depends on “relative prices” of the goods

    • relative prices depends on income distribution and the preferences of the individuals

Principles of Microeconomics


Allocative efficiency1

Allocative Efficiency

  • allocative efficiency is defined as:

where;

Principles of Microeconomics


Pareto efficiency

Pareto Efficiency

  • Pareto efficiency is the primary criteria used in Neoclassical economics to evaluate alternatives

  • Pareto efficiency is a condition such that there are no alternatives that will improve the welfare of any person(s) without making some one else (or others) “worse off”

Principles of Microeconomics


Pareto efficiency cont

Pareto Efficiency [cont. . . ]

  • Clearly, if there is an alternative that will improve the welfare of at least one person and no one is any worse off, that alternative would improve the welfare of society. This is a Pareto improvement

  • If the utility of at least one person can be increased, but some one else (or others) is made worse off, it is not a Pareto improvement

  • Benefit/cost analysis is based on the Pareto criterion {rate of return on investment and others are also based on the Pareto criterion

Principles of Microeconomics


Ppf

.

167

100

H

60

100

corn

Starting with the PPF model for corn and wheat,

an output choice [H] that results in Y = 100 and

X = 60 is not “Pareto Efficient.”

K

*

Individual’s preferences are not the same.

Some people like wheat “better” than corn.

Others prefer corn to wheat.

F

*

Irrespective of Price, a move to alternative F is

a Pareto improvement. People who prefer wheat

are “better off,“ people who like corn are

“no worse off.”

Any choice that lies in the blue triangle

HFK is a Pareto improvement

or is Pareto safe.

wheat

Irrespective of Price, a move to alternative K is a Pareto improvement.

People who prefer corn are “better off,“ people who like wheat are

“no worse off.”

Once on the PPF, there are no alternatives that are Pareto improvements.

Any increase in the output [which makes some one “better off”] of one good,

requires a decrease in the other[ which makes some one “worse off” ]

Principles of Microeconomics


Pareto efficiency and voluntary exchanges

Pareto Efficiency and Voluntary Exchanges

  • Market exchanges that are voluntary are said to be Pareto Optimal

  • It is believed that no one would voluntarily enter into a voluntary exchange and make themselves “worse off”

  • Therefore, one or both parties to a voluntary exchange is believed to be better off and no one is any worse off

Principles of Microeconomics


Opportunity cost ppf

Opportunity Cost & PPF

  • The PPF demonstrates all production alternatives available given inputs and technology

  • For each alternative represented by a point on the PPF, given an output of X there is an output of Y

  • If you change X, you change Y.

  • Consider a PPF

Principles of Microeconomics


Ppf

Y

6

C

5

slope = -.3

4

3

slope = -.7

2

1

X

1 2 3 4

Given a PPF,

A

B

If we were producing at point A,

5.7

C

the choice results in 0 units of X

and 6 units of Y.

DY = -.3

If we want to produce 1 unit of X,

the output of Y must decrease

to 5.7 at point B

DX=1

The cost of this first unit of X is -.3

units of Y. This is an approximation

of the slope of PPF between A and B. This is also the “Opportunity

Cost” of the first unit of X. Later we will call this the “Marginal Cost”

The second unit of X requires that the output of Y be reduced to 5.

This alternative [at point C] shows that the second unit of X

“costs” .7 units of Y. This is the |slope| of PPF between points

B and C.

Principles of Microeconomics


Ppf

Y

6

5.7

5

4

3

2

1

X

1 2 3 4

DY

DX

Given the PPF

A

B

The output of Y

decreased between

A&B, so the cost

of -.3 units of Y is

associated with

the first unit of X.

Problem of discrete

data!

C

From A to B

Slope = 6-5.7

From B to C

Slope = 5.7-5

-.3

D

3.8

From C to D

Slope = 5-3.8

-.7

-1.2

-3.8

E

Given the data above, the first unit of

X “costs” .3Y; the second X costs .7Y; the third unit of X costs

1.2 units of Y and the last [4] unit of X costs 3.8 Y.

The cost of each additional unit of X is defined by the absolute value

of the slope of the PPF,

Principles of Microeconomics


Ppf

Y

A

B

6

5.7

slope -3.8

C

5

slope -.3

D

4

slope -.7

3

2

6

5.7

slope -1.2

1

5

E

4

X

1 2 3 4

3

2

1

X

1 2 3 4 5 6

The opportunity cost of X, [in terms

of Y] is the absolute value of the

slope of the PPF. If the price of Y

is known, the opportunity cost can

be stated in $.

The PPF

Y given up for X

.

The 4rth unit

of X costs

3.8 Y.

opportunity cost

of X in terms of

Y sacrificed

.

.

.

The third unit of X costs 1.2 units of Y

The second X costs .7Y;

The first unit of X “costs” .3Y;

Principles of Microeconomics


Ppf and economic growth

PPF and Economic Growth

  • The PPF will shift if:

    • there is a change in technology

    • there is a change in the quantity or quality of inputs

  • If the PPF shifts “out,” we can produce more output. Increased output is a simplistic definition of economic growth. In a more complex sense, the output mix or quality of output may change.

Principles of Microeconomics


Ppf

corn

A

Economic growth can be imagined as

an outward shift of the PPF.

C2

Should the quantity or quality of

inputs diminish, the PPF would shift in.

We would have fewer alternatives and

wouldn’t be able to produce as much.

C1

B

W1

wheat

Given a set of inputs and a state of

technology, production function AB

is determined.

If there should be an improvement in the technology or an input that only

applied to the production of wheat, the PPF would shift out along the X axis.

Society might choose to produce the same amount of wheat [W1].

Even so, the output of corn could be increased as a result of an

improved ability to produce wheat!

Principles of Microeconomics


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