Structural

Change

and

Economic

Dynamics

47

(2018)

73–81

Contents

lists

available

at

ScienceDirect

Structural

Change

and

Economic

Dynamics

j

ourna

l

h

o

mepage:

www.elsevier.com/locate/sced

An

entropy

theory

of

value

School

of

Business,

University

of

Northern

British

Columbia,

Prince

George,

BC,

V2N

4Z9,

Canada

1

a

r

t

i

c

l

e

i

n

f

o

Article

history:

Received

9

June

2018

Accepted

30

July

2018

Available

online

7

August

2018

Keywords:

Value

Entropy

Information

Scarcity

Utility

Labor

a

b

s

t

r

a

c

t

From

the

properties

that

the

value

of

commodities

should

satisfy,

it

can

be

derived

that

the

only

mathe-

matical

formula

to

represent

value,

as

a

function

of

scarcity,

is

the

entropy

function.

From

this

function,

the

main

factors

that

influence

the

value

of

a

commodity

are

scarcity

of

the

commodity,

the

number

of

producers,

and

the

market

size.

In

particular,

monopolies

and

near

monopolies,

which

have

small

number

of

producers

or

service

providers,

have

high

valuations.

Many

of

the

important

institutional

structures,

such

as

religions,

governments,

unions,

patents

and

regulations,

obtain

high

valuation

through

monopoly.

I

thank

Kent

Klitgaard,

Dingkang

Wang

and

many

others

for

helpful

comments.

Extensive

editing

and

revision

from

Jamie

Galbraith

greatly

improves

the

quality

of

this

paper.

©

2018

Published

by

Elsevier

B.V.

1.

Introduction

Value

is

the

most

fundamental

concept

in

economics.

It

also

has

great

influence

in

broader

areas

of

social

theory

and

social

science.

A

good

understanding

of

value

should

shed

light

on

social

structures,

economic

policies

and

business

strategies.

There

are

three

main

theories

of

value:

utility

theory,

scarcity

theory

and

labor

theory.

,

the

chief

architect

of

the

neoclassical

economic

theory,

argued

that

value

is

a

function

of

scarcity.

He

said

that

it

is

too

broad

to

define

utility

as

value

since

many

things

with

high

utility,

such

as

oxygen,

are

of

no

economic

value.

Likewise

it

is

too

narrow

to

define

labor

as

value,

for

many

things

that

take

little

labor

have

high

value.

For

example,

although

oil

produced

in

Alberta

takes

much

more

labor

than

oil

produced

in

Saudi

Arabia,

Alberta

oil

is

not

more

expensive

than

Saudi

oil.

In

conventional

economic

theories,

additional

terminologies

are

created,

such

as

rent,

to

explain

this

phenomenon.

However,

this

makes

the

labor

theory

of

value

less

general.

In

this

paper,

we

present

an

entropy

theory

of

value.

Entropy

is

a

measure

of

scarcity

in

physics.

An

entropy

theory

of

value

is

a

scarcity

theory

of

value.

From

the

second

law

of

thermodynam-

ics,

or

the

entropy

law,

the

entropy

of

a

system

tends

to

increase.

A

display

of

low

entropy

state

is

the

universal

sign

of

attractive-

ness

for

animals,

which

include

human

beings.

This

explains

how

E-mail

address:

chenj@unbc.ca

1

http://web.unbc.ca/

∼

chenj/.

subjective

utilities

are

generally

entropy

related.

Since

all

human

activities

need

to

consume

low

entropy

sources

–

for

instance,

fresh

food

is

preferred

to

stale,

new

clothing

is

preferred

to

old,

an

entropy

theory

of

value

includes

the

labor

theory

of

value.

But

it

is

broader

than

the

labor

theory

of

value.

From

the

entropy

theory

of

value,

other

low

entropy

resources,

such

as

oil,

will

have

value

as

well.

Because

of

the

universality

of

the

entropy

law,

an

entropy

theory

of

value

has

been

suggested

before.

The

success

of

entropy

theory

of

information

stimulated

many

research

efforts

in

economics.

Since

information

is

the

reduction

of

entropy,

an

entropy

theory

of

value

is

inevitably

an

information

theory

of

value.

However,

the

information

theory

of

value,

or

the

entropy

theory

of

value,

was

not

developed

in

economics.

Very

often,

the

direction

of

scientific

research

is

shaped

by

the

thinking

of

an

authority.

In

an

often-cited

passage,

Arrow

wrote,

“the

well-known

Shannon

mea-

sure

which

has

been

so

useful

in

communications

engineering

is

not

in

general

appropriate

for

economic

analysis

because

it

gives

no

weight

to

the

value

of

the

information.

If

beforehand

a

large

manufacturer

regards

it

as

equally

likely

whether

the

price

of

his

product

will

go

up

or

down,

then

learning

which

is

true

conveys

no

more

information,

in

the

Shannon

sense,

than

observing

the

toss

of

a

fair

coin”

(Arrow,

1983

(

),

p.

138).

The

Shannon

measure

actually

measures

the

weight

of

infor-

mation.

For

example,

N

symbols

with

identical

Shannon

measure

carry

N

times

more

information

than

a

single

symbol

(

).

Similarly,

the

value

of

the

information

about

the

future

price

is

higher

to

a

large

manufacturer

than

to

a

small

manufacturer,

https://doi.org/10.1016/j.strueco.2018.07.008

0954-349X/©

2018

Published

by

Elsevier

B.V.

74

J.

Chen

/

Structural

Change

and

Economic

Dynamics

47

(2018)

73–81

other

things

being

equal.

Later,

we

show

that

information

as

an

economic

commodity

shares

most

of

the

important

properties

of

physical

commodities.

Georgescu-Roegen

observed

that

“there

have

been

sporadic

suggestions

that

all

economic

values

can

be

reduced

to

a

com-

mon

denominator

of

low

entropy”

(

,

p.

283).

However,

he

thought

that

linking

economic

value

to

low

entropy

would

not

be

of

much

help

to

economists

because

“he

would

only

be

saddled

with

a

new

and

wholly

idle

task—to

explain

why

these

coefficients

differ

from

the

corresponding

price

ratios”

(

,

p.

283).

To

this

argument

we

may

reflect

on

Shannon’s

entropy

theory

of

information.

The

entropy

theory

of

information

does

not

resolve

all

problems

related

to

information.

But

it

does

resolve

many

important

problems

in

communication.

For

example,

the

entropy

theory

of

information

provides

a

mea-

sure

on

the

minimal

cost

of

information

transmission.

Very

often,

video

data

can

be

compressed

one

hundred

times

in

transmission

with

little

loss

of

quality.

The

entropy

theory

of

information

pro-

vides

a

theoretical

foundation

to

help

us

transmit

large

amount

of

information

at

low

cost,

which

is

extremely

important

in

today’s

society.

Similarly,

the

entropy

theory

of

value

will

not

resolve

all

problems

in

economic

activities.

But

it

greatly

simplifies

our

under-

standing

on

a

broad

range

of

social

and

economic

phenomena.

It

provides

a

simple

mathematical

relation

to

understand

how

scarcity,

the

number

of

producers

or

service

providers,

and

market

size

affect

values.

In

the

entropy

theory

of

value,

economic

value

is

defined

as

a

logarithm

function,

just

as

information

is

defined

as

a

logarithm

function.

In

information

theory,

the

base

of

the

loga-

rithm

function

is

2,

as

the

information

is

transmitted

in

a

binary

system

{

0,

1

}

.

In

the

entropy

theory

of

value,

the

base

of

the

loga-

rithm

function

represents

the

number

of

suppliers

of

a

product

or

a

service.

When

the

base

approaches

1,

the

value

of

the

product

or

service

approaches

infinity.

This

indicates

that

monopoly

and

near

monopoly

are

the

most

important

ways

to

increase

value.

Governments

have

monopoly

in

violence,

legal

actions

and

tax-

ation.

Patents,

intellectual

property

rights,

regulation,

industry

standards

and

market

dominance

help

businesses

establish

and

maintain

monopolies.

Unionization

achieves

monopolies

in

bar-

gaining.

Monotheistic

religions

hold

monopolies

to

reach

heaven.

Indeed,

many

of

the

most

important

functions

in

human

societies

are

structured

in

monopoly

or

near

monopoly.

The

mainstream

value

theory

is

represented

by

the

classical

book,

Theory

of

value;

an

axiomatic

analysis

of

economic

equilibrium

by

.

Debreu’s

theory

of

value

is

used

to

construct

a

rigorous

foundation

of

equilibrium

theory,

according

to

which

wealth

is

maximized

in

an

equilibrium

state.

In

equilibrium,

many

competitors

are

assumed

to

operate

in

the

market.

From

practical

experience,

we

know

that

valuation

is

low

in

a

market

with

many

competitors.

Market

participants,

as

individuals

or

organizations,

will

actively

seek

opportunities

to

gain

and

maintain

monopolies.

This

feature

is

ignored

by

the

Debreu

model

but

accurately

captured

by

the

entropy

theory

of

value.

This

entropy

theory

of

value

is

largely

unchanged

since

its

early

development

(

),

but

the

applications

have

greatly

expanded.

The

rest

of

the

paper

is

structured

as

follows.

In

Sec-

tion

2

,

we

formally

develop

the

mathematical

theory

of

value

as

entropy.

The

influence

on

value

of

factors

such

as

scarcity,

the

num-

ber

of

producers

and

market

size

of

a

commodity

can

be

understood

naturally

from

the

logarithm

function

of

value.

Since

scarcity

of

resources,

including

human

resources,

is

often

regulated

by

insti-

tutional

measures

such

as

immigration

laws

and

patent

laws,

the

value

of

economic

commodities

is

in

great

part

a

reflection

of

insti-

tutional

structures.

In

Section

3

,

we

apply

this

theory

to

trade,

regulation

and

competition.

In

Section

4

,

we

utilize

the

results

from

information

theory,

statistical

physics

and

the

theory

of

evolution

to

discuss

the

relation

between

physical

entropy

and

economic

value.

We

discuss

how

the

entropy

theory

of

value

offers

a

unifying

understanding

of

the

objective

and

subjective

theories

of

value.

In

Section

5

,

we

discuss

how

informational

and

physical

commodi-

ties

share

common

properties

in

the

light

of

this

entropy

theory

of

value.

By

resolving

the

conceptual

difficulties

that

have

confounded

us

for

many

years,

we

offer

a

unified

understanding

of

physical

entropy,

information

and

economic

value.

In

Section

6

,

we

discuss

the

relation

between

economic

value

and

social

welfare.

Section

7

concludes.

2.

Main

properties

Value

is

a

function

of

scarcity.

Scarcity

can

be

defined

as

a

prob-

ability

measure

P

in

a

certain

probability

space.

The

value

of

any

product

shall

satisfy

the

following

properties:

(a)

The

value

of

two

products

should

be

higher

than

the

value

of

each

of

them.

(b)

If

two

products

are

independent,

that

is,

if

the

two

products

are

not

substitutes

or

partial

substitutes

of

each

other,

then

the

total

value

of

the

two

products

will

be

the

sum

of

two

products.

(c)

The

value

of

any

product

is

non-negative.

The

only

mathematical

functions

that

satisfy

all

of

the

above

properties

are

of

the

form

V

(

P

)

=

−

log

b

P

(1)

Where

b

is

a

positive

constant

(

).

In

information

theory,

the

base

of

the

logarithm

function

is

usually

chosen

to

be

two

because

there

are

two

choices

of

code

in

information

trans-

mission,

namely,

0

and

1

(

).

In

economics,

the

base

b

can

be

understood

as

the

number

of

producers.

In

general,

if

the

scarcity

of

a

service

or

product,

X

,

can

be

estimated

by

the

proba-

bility

measure

{

p

1,

p

2,

.

.

.

p

n

}

,

the

expected

value

of

this

product

is

the

average

of

the

value

of

each

possibility,

that

is

V

(

X

)

=

n

∑

i

=

1

p

i

(

−

log

b

p

i

)

Therefore,

value

–

just

as

information

–

in

its

general

form

can

be

defined

as

entropy,

given

that

they

are

the

same

mathemati-

cally.

In

the

following,

we

will

discuss

the

properties

of

this

simple

analytical

theory

of

value-as-scarcity.

2.1.

Scarcity

and

value

Fig.

1

is

a

graph

of

Formula

(1)

,

which

shows

that

value

is

an

increasing

function

of

scarcity.

That

is

why

diamonds

are

worth

more

than

water

in

most

circumstances.

In

extreme

abundance,

i.e.,

when

P

=

1,

−

log

P

=

0,

the

value

of

a

given

commodity

is

equal

to

zero,

even

if

that

commodity

is

very

useful.

For

example,

food

is

essential

for

survival.

Most

countries

subsidize

food

production

in

various

ways

to

guarantee

the

abundance

of

food,

which

causes

its

low

economic

value.

This

shows

that

economic

value

and

social

value

can

diverge.

Gold

is

mined

on

average

at

low

concentrations

and

it

takes

much

energy

to

grind

up

the

rocks.

Likewise

silver,

as

compared

to

copper.

In

general,

a

scarce

commodity

takes

more

energy

and

labor

to

mine

than

an

abundant

commodity.

The

scarcity

theory

of

value

is

highly

consistent

with

the

energy

theory

of

value

and

the

labor

theory

of

value.

An

advantage

of

the

scarcity

theory

of

value

is

that

it

can

be

formulated

as

a

mathematical

theory

easily.

J.

Chen

/

Structural

Change

and

Economic

Dynamics

47

(2018)

73–81

75

Fig.

1.

Value

and

scarcity.

2.2.

Value

and

the

number

of

producers

or

consumers

From

Formula

(1)

,

value

is

inversely

related

to

the

number

of

producers

of

a

given

product.

Fig.

2

displays

the

relation

between

value

and

the

number

of

producers.

When

the

number

of

producers

is

small,

the

value

of

a

product

is

high.

That’s

why

the

products

of

monopolies

and

oligopolies

are

valued

highly.

If

the

base

becomes

one,

i.e.,

absolute

monopoly

without

substitution,

value

approaches

infinity.

Governments

have

the

monopoly

on

violence,

legal

decisions

and

taxation.

Democratic

societies

maintain

multiparty

system

and

elections.

This

is

to

reduce

the

power,

or

the

value,

of

governments.

But

monarchy

or

one

party

rule

are

more

common

in

most

of

human

history.

Even

in

democratic

societies,

the

power

of

governments,

as

monopolies,

tend

to

grow

over

time.

Today,

governments’

powers

over

citizens

and

businesses

are

much

broader

than

(say)

in

the

19

th

century.

Many

important

social

activities,

such

as

education

and

(in

most

countries)

medicine,

are

under

government

control

or

influence.

In

many

countries,

education

is

mostly

funded

by

the

govern-

ment.

Students

can

only

go

to

one

school

for

their

elementary

and

secondary

education.

This

lack

of

choice

in

education

for

students

greatly

increases

the

power

and

hence

the

value

of

edu-

cators.

The

medical

systems

in

some

countries,

such

as

Canada,

don’t

allow

patients

to

choose

doctors

and

the

types

of

treatments

they

can

have.

Instead,

patients

can

only

go

to

see

one

doctor,

who

decides

what

treatment

a

patient

can

get

and

who

the

patients

can

see.

With

this

monopoly

over

patients,

doctors

gain

extraordinary

power

and

hence

enjoy

high

incomes.

Fig.

2.

Value

and

the

number

of

producers.

Successful

religions,

such

as

Judaism,

Christianity

and

Islam,

are

monotheistic,

while

polytheistic

religions,

such

as

Buddhism,

have

difficulties

withstand

the

advance

of

monotheistic

religions.

Monotheism,

with

only

one

god,

exerts

much

greater

control

over

its

believers

than

polytheism.

The

number

of

providers

of

most

economic

goods

depends

on

many

factors.

In

the

following,

we

give

a

brief

discussion

about

the

institutional

structures

that

affect

market

entry

and

the

number

of

suppliers

for

a

given

product.

Anti-trust

regulations

aim

to

prevent

price

fixing

by

existing

providers

of

a

service

or

product.

They

also

intend

to

lower

barri-

ers

to

potential

entry.

By

increasing

the

number

of

choices,

both

measures

reduce

the

value

of

products,

and

hence

the

cost

to

con-

sumers.

For

this

reason,

the

value

of

a

product

will

in

general

be

lower

in

a

more

competitive

market.

Patent

rights

and

commercial

secrets

legislation,

on

the

other

hand,

grant

monopoly

power

and

discourage

the

diffusion

of

knowledge.

Patent

rights

and

monopoly

power

allow

the

holders

to

maintain

high

product

prices.

The

IT

industry

has

less

strict

patent

protection

than

the

biotech

industry.

As

a

result,

IT

develops

much

faster

than

biotech.

In

general,

indus-

tries

with

more

patent

protection

develop

slower

than

industries

with

less

patent

protection.

Technology

often

progresses

very

fast

during

war

time,

when

patent

laws

are

often

ignored.

The

quota

system

in

trade

policy

forces

the

transfer

of

produc-

tion

technology

from

the

dominant

producer

to

other

countries.

Ultimately,

the

diffusion

of

technology

and

the

increase

of

the

num-

ber

of

producers

will

reduce

the

value

of

the

imported

goods.

This

will

benefit

the

importing

countries

over

the

long

term,

instead

of

the

loss

suggested

in

standard

literature.

The

value

of

consumers

is

also

negatively

related

to

their

num-

bers.

When

there

is

only

one

dominant

customer,

it

can

mostly

dictate

the

terms

of

trade

and

hence

would

like

to

keep

its

monopoly

power.

Producers,

on

the

other

hand,

would

like

to

increase

the

number

of

their

customers.

The

relation

between

number

of

producers

and

value

can

help

understand

many

commercial

and

social

phenomena.

Each

printer

manufacturer

designs

printers

in

a

way

that

printer

ink

from

other

firms

cannot

operate

well.

Customers

who

buy

printers

from

one

company

can

use

ink

from

only

the

same

company.

By

restricting

the

choice

from

customers,

producers

can

sell

ink

at

higher

price

and

obtain

higher

profits.

Unions

form

a

monopoly

of

bargaining.

With

only

a

single

unit

of

bargaining,

a

trade

union

is

in

a

much

stronger

position

than

many

individuals

in

bargaining

with

management.

Unions

are

often

formed

in

many

stable

professions,

such

as

government

employees

and

teachers.

Professions

such

as

physicians,

often

are

certified

by

a

single

organization,

which

increases

their

monopoly

value.

Doctors’

notes

are

famously

illegible.

When

fewer

peo-

ple,

especially

patients,

are

informed,

the

value

of

the

profession

increases.

Household

machines

are

often

designed

that

they

can

only

be

repaired

with

specialized

tools.

Once

a

mixer

in

our

home

broke

down.

I

watched

a

YouTube

video

to

figure

out

how

to

have

the

mixer

repaired.

When

I

opened

the

mixer,

I

found

the

design

of

the

mixer

had

been

changed.

With

the

new

design,

specialized

tools

are

needed

to

repair

the

machine.

A

customer

has

to

buy

a

new

mixer

or

have

the

mixer

repaired

by

an

expensive

technician.

Since

the

value

of

a

product

depends

very

much

on

the

number

of

producers,

the

attempt

to

gain

monopoly

is

often

the

most

impor-

tant

business

strategy

and

political

strategy

(

).

It

is

often

difficult

to

determine

the

exact

number

of

providers

of

a

service

empirically.

Air

travel

in

vast

and

thinly

populated

coun-

tries,

such

as

Canada,

where

alternative

modes

of

transportation

are

often

very

time

consuming,

provides

a

good

testing

ground.

On

March

10,

2005,

Jetsgo,

a

Canadian

airline,

declared

bankruptcy.

76

J.

Chen

/

Structural

Change

and

Economic

Dynamics

47

(2018)

73–81

There

are

three

major

operators

in

the

air

travel

industry

in

Canada.

They

are

Air

Canada,

WestJet

and

Jetsgo.

There

are

regional

carriers

and

international

airlines

competing

for

many

routes.

Most

of

the

profits

of

airlines

come

from

regional

routes

where

competition

is

not

intense.

We

can

assume

four

providers

for

the

air

travel

service

for

typical

regional

routes

before

Jetsgo

declared

bankruptcy.

From

(1)

,

the

value

of

each

airline

can

be

represented

as

−

log

4

P

and

−

log

3

P

before

and

after

Jetsgo

declare

bankruptcy.

The

change

of

value

is

therefore

(

−

log

3

P

)

/

(

−

log

4

P

)

−

1

=

log

3

4

−

1

=

0

.

262

Jetsgo

declared

bankruptcy

at

the

evening

of

March

10,

2005,

after

the

market

close.

The

closing

prices

of

stocks

of

WestJet

and

Air

Canada

at

March

10

and

11

are

11.17,

15.6

and

32.19,

37

respec-

tively.

The

price

changes

are

15

.

6

/

11

.

17

−

1

=

0

.

397

for

WestJet

and

37

/

32

.

19

−

1

=

0

.

149

for

Air

Canada

respectively.

The

average

change

of

price

is

(0

.

397

+

0

.

149)

/

2

=

0

.

273

which

is

very

close

to

the

theoretical

prediction

of

0.

262.

Some

theoretical

and

empirical

results

can

be

further

refined.

For

example,

this

theory

does

not

distinguish

the

sizes

of

different

providers

of

a

service.

The

refinement

of

the

theory

is

left

to

the

future

research.

2.3.

Market

size,

product

life

cycle

and

product

value

Suppose

the

potential

market

size

of

a

product

is

M

.

The

per-

centage

of

people

who

already

have

the

product

is

P

.

Then

the

unit

value

of

the

product

is

−

log

P

(2)

Since

the

number

of

people

who

have

bought

the

product

is

MP

,

The

total

value

of

the

product

is

MP

(

−

log

P

)

(3)

From

(3)

,

the

value

of

a

product

is

higher

with

a

larger

market

size.

Fig.

3

is

the

graph

of

unit

value

and

total

value

of

a

product

with

respect

to

its

abundance.

From

Fig.

3

,

we

can

explore

the

relation

between

the

value

of

a

product

and

the

product

life

cycle.

When

a

product

is

new

and

scarce,

the

unit

value

is

high.

Its

total

value

is

low.

As

the

production

increases,

the

total

value

will

increase

as

the

unit

value

decreases.

When

the

production

quantity

is

over

a

certain

level,

however,

the

total

value

of

a

product

will

start

to

decrease

as

well.

Intuitively,

this

is

easy

to

understand.

The

market

values

of

manufacturers

of

mature

products

are

generally

low,

although

the

production

processes

are

very

efficient.

This

observation

shows

that

efficiency

is

not

equivalent

to

value.

The

above

discussion

shows

that

the

implications

of

identify-

ing

value

with

the

scarcity

are

highly

consistent

with

our

intuitive

understanding

of

economic

value.

It

should

be

noted

that

in

eco-

nomic

processes,

a

final

product

embodies

many

different

kind

of

scarcities:

labor,

raw

materials

and

equipment.

A

detailed

analysis

of

the

value

of

a

particular

product

will

be

much

more

involved.

For

example,

black

and

white

television

sets

are

less

common

than

color

television

sets

and

yet

they

have

less

economic

value.

This

is

because

the

process

of

making

color

TV

takes

more

scarce

resources

such

as

labor.

The

value

of

a

final

product

is

the

combination

of

total

scarcity.

Fig.

3.

The

unit

value

and

total

value

of

a

product

with

respect

to

scarcity.

3.

Several

applications

This

value

theory

can

be

applied

to

many

different

areas.

We

will

present

several

applications

on

the

impacts

of

trade

policies

and

regulatory

policies

3.1.

On

the

impact

of

trade

policies

and

trade

barriers

Trade

policies

can

be

open

or

restricted.

Access

to

the

market

can

be

easy

or

difficult.

What

are

their

effects?

In

general,

trade

occurs

between

regions

with

differential

abundance

of

a

commod-

ity,

which

could

be

due

to

differential

concentration

of

natural

resources

or

the

capacity

of

some

manufacturing

technology.

Most

oil

exports

occur

in

several

countries.

High

tech

industries

are

highly

concentrated

in

Silicon

Valley.

To

examine

the

quantitative

impacts

of

a

trade

policy,

we

will

look

at

a

two

region

case

and

calcu-

late

a

numerical

example.

(The

proof

of

the

general

case

is

available

from

the

author.)

Let

the

market

sizes

of

two

regions

be

100

and

1000

respectively,

with

resource

concentration

of

0.9

and

0.2.

This

indicates

that

the

smaller

region

is

abundant

in

a

particular

com-

modity.

Suppose

two

regions

are

segregated.

Then

the

commodity

prices

at

two

regions

are

−

ln

(0

.

9)

=

0

.

11

and

−

ln(0

.

2)

=

1

.

61

The

commodity

price

in

the

abundant

area

is

much

cheaper.

The

total

values

of

the

commodity

in

two

regions

are

100

∗

0

.

9

∗

(

−

ln(0

.

9))

=

9

.

48

and

1000

∗

0

.

2

∗

(

−

ln(0

.

2))

=

321

.

89

The

global

total

value

of

the

commodity

is

9

.

48

+

321

.

49

=

331

.

37

When

two

regions

are

integrated

into

a

free

trade

zone,

the

global

scarcity

of

the

commodity

is

(100

∗

0

.

9

+

1000

∗

0

.

2)

/

(100

+

1000)

=

0

.

26

The

new

price

of

the

commodity

is

−

ln(0

.

26)

=

1

.

33

The

global

value

of

the

commodity

is

1100

∗

0

.

26

∗

(

−

ln(0

.

26))

=

386

.

62

The

total

value

of

the

commodity

in

the

resource

rich

region

is

100

∗

0

.

9

∗

(

−

ln(0

.

26)

=

119

.

99

The

total

value

of

the

commodity

in

the

resource

poor

region

is

1000

∗

0

.

2

∗

(

−

ln(0

.

26)

=

266

.

64

J.

Chen

/

Structural

Change

and

Economic

Dynamics

47

(2018)

73–81

77

Table

1

Summary

of

value

changes

with

market

integration.

Segregated

market

Integrated

market

Resource

poor

region

Resource

rich

region

Market

size

1000

100

1100

Scarcity

0.2

0.9

0.26

Unit

price

1.61

0.11

1.33

Value

in

segregation

321.89

9.48

331.37

(sum

in

segregation)

Value

in

integration

266.64

120

386.62

Difference

in

value

−

55.25

55.25

In

the

following,

we

analyze

the

winners

and

the

losers

in

a

free

trade

economy.

First,

the

global

value

of

the

commodity

in

a

free

trade

environment

is

386.62,

which

is

higher

than

331.37,

the

global

value

in

a

segregated

economy.

In

general,

free

trade

increases

the

total

value

of

a

product.

Second,

the

total

value

from

the

resource

rich

region

in

the

free

trade

environment

is

119.99,

which

is

higher

than

9.48,

the

total

value

in

a

segregated

economy.

That

is

why

producers

from

the

resource

rich

region

will

promote

free

trade.

The

total

value

from

the

resource

poor

region

in

the

free

trade

environment

is

266.64,

which

is

lower

than

321.89,

the

total

value

in

a

segregated

economy.

That

is

why

producers

from

the

resource

poor

region

will

resist

free

trade.

Third,

the

magnitude

of

impact

to

small

and

large

regions

are

dif-

ferent.

For

the

small

region,

the

change

of

commodity

value

is

from

9.48

to

119.99,

which

is

very

high.

For

the

large

region,

the

change

of

commodity

value

is

from

321.89

to

266.64,

which

is

moderate.

As

a

result,

small

regions

have

stronger

incentive

to

influence

trade

policies,

although

large

regions

are

often

more

powerful.

For

exam-

ple,

Canada

charges

270%

tariff

on

import

dairy

products

to

deter

US

dairy

imports.

By

comparison,

US

charges

27%

tariff

on

Canadian

lumber

imports.

In

general,

small

social

groups

often

have

stronger

internal

cohesion

than

large

social

groups.

Fourth,

the

unit

value

of

the

commodity

in

a

free

trade

envi-

ronment

is

1.33,

which

is

higher

than

0.11,

the

unit

value

of

the

commodity

in

the

resource

rich

region

and

lower

than

1.61,

the

unit

value

of

the

commodity

in

the

resource

poor

region

in

a

segre-

gated

economy.

So

ordinary

consumers

in

a

resource

rich

country

who

do

not

receive

income

from

the

resource

industry

will

resist

free

trade.

Ordinary

consumers

in

a

resource

poor

country

who

do

not

receive

income

from

the

resource

industry

will

welcome

free

trade.

The

main

results

are

summarized

in

Table

1

.

There

are

two

major

price

indices

in

the

crude

oil

market:

WTI

and

Brent.

Historically,

WTI

and

Brent

crude

oil

prices

were

very

close.

However,

WTI

traded

at

a

deep

discount

to

Brent

in

recent

years

as

Alberta

increased

its

oil

output,

most

of

which

was

sold

in

the

US.

In

an

attempt

to

sell

more

oil

at

the

international

price,

proposals

were

made

to

build

or

expand

several

oil

pipelines

to

the

coastal

area

so

Alberta

oil

can

be

supplied

to

the

international

mar-

ket.

This

would

increase

the

value

of

Alberta

oil

products.

Canada

produces

about

three

million

barrels

of

crude

oil

per

day.

Canadian

oil

is

often

sold

several

dollars

per

barrel

below

the

international

price.

Every

year

the

Canadian

oil

industry

loses

several

billion

dollars

from

this

price

differential;

equivalently,

customers

of

the

Canadian

oil

gain

several

billion

dollars

per

year

from

the

cur-

rent

situation.

From

the

above

analysis,

it

is

easy

to

understand

why

there

is

so

much

negative

publicity

and

disruption

around

the

pipeline

projects.

Next,

we

will

analyze

how

trade

tariff

affects

import

and

export

countries.

From

our

value

theory,

product

value

is

a

function

of

scarcity.

Tariff

policy

can

often

significantly

influence

output

quan-

tity

and

hence

product

value,

especially

when

a

certain

commodity

has

one

big

producer

and

one

big

consumer.

For

example,

Canada

is

a

big

producer

of

softwood

lumber

while

USA

is

a

big

consumer.

From

value

theory,

the

value

of

lumber

market

is

represented

by

VP(

−

ln

P),

where

P

is

the

proportion

of

lumber

that

is

on

the

market.

Assume

V

,

the

total

volume

of

the

forest,

is

10,000.

A

con-

sumer

country

will

benefit

from

a

trade

policy

that

increases

the

production

of

lumber

since

it

will

reduce

the

value

of

imported

lumber.

Suppose

the

cost

structure

of

the

lumber

industry

is

the

fol-

lowing.

The

total

fixed

cost

in

lumber

production

in

country

C

is

100.

The

variable

cost

is

55%

of

product

value.

The

total

value

of

the

lumber

products

is

VP(

−

ln

P)

and

the

total

cost

of

production

is

100

+

0.55*V*P*(

−

lnP).

Suppose

every

year,

1%

of

the

all

lumber

is

harvested.

The

profit

on

lumber

production

is

equal

to

revenue

minus

total

cost

−

VP

ln

P

−

(100

+

0

.

55

∗

(

−

VP

ln

P

))

=

−

10000

∗

0

.

01

∗

ln(0

.

01)

−

(100

+

0

.

55

∗

(

−

10000

∗

0

.

01

∗

ln(0

.

01)))

=

107

In

2001,

the

USA

imposed

a

27%

import

duty

on

lumber

from

Canada.

If

the

volume

of

production

remained

at

the

same

level,

the

profit

for

lumber

production

would

be

−

VP

ln

P

∗

(1

−

0

.

27)

−

(100

+

0

.

55

∗

(

−

VP

ln

P

))

=

−

10000

∗

0

.

01

∗

ln(0

.

01)

∗

(1

−

0

.

27)

−

(100

+

0

.

55

∗

(

−

10000

∗

0

.

01

∗

ln(0

.

01)))

=

−

17

which

means

that

the

lumber

industry

will

lose

money.

Production

of

lumber

has

to

be

increased

to

avoid

loss.

If

the

production

level

is

increased

to

P

=

1.5%,

the

profit

for

the

lumber

industry

will

become

−

VP

ln

P

∗

(1

−

0

.

27)

−

(100

+

0

.

55

∗

(

−

VP

ln

P

))

=

−

10000

∗

0

.

015

∗

ln(0

.

015)

∗

(1

−

0

.

27)

−

(100

+

0

.

55

∗

(

−

10000

∗

0

.

015

∗

ln(0

.

015)))

=

13

As

the

production

is

increased

from

1.0%

of

the

total

reserve

to

1.5%,

the

unit

value

of

lumber

is

decreased

from

–ln(0.01)

=

4.6

to

–ln(0.015)

=

4.2.

USA

collects

27%

tariff

on

lumber

import

and

enjoy

lower

price

on

lumber.

Table

1

gives

a

summary

of

softwood

lum-

ber

futures

prices,

annual

production

from

Canada,

revenues

and

profits

from

Canfor,

Canada’s

largest

softwood

producer,

in

2000

and

2002,

one

year

before

and

after

USA

imposed

the

27%

tariff

on

softwood

lumber

import

from

Canada.

The

data

confirm

the

theoretical

prediction

that

after

the

tariff,

production

increased,

prices

dropped,

and

corporate

profits

from

lumber

producers

tumbled.

This

shows

that

tariffs

are

an

effective

way

to

shift

wealth

from

producing

countries

to

consuming

coun-

tries,

and

contradicts

the

standard

theory

that

tariffs

hurt

importing

countries

by

imposing

higher

prices

for

consumers.

From

the

theoretical

analysis,

as

well

the

data

in

Table

2

,

trade

policies

have

huge

effects

on

the

distribution

of

wealth

across

bor-

ders,

and

this

also

greatly

influences

the

distribution

of

jobs

across

78

J.

Chen

/

Structural

Change

and

Economic

Dynamics

47

(2018)

73–81

Table

2

Summary

statistics

of

softwood

lumber

futures

price,

annual

production

from

Canada,

revenues

and

profits

from

Canfor.

Sources

of

data:

CME,

indexmundi,

Canfor

annual

reports.

2000

2002

Softwood

lumber

futures

price

(January

closing)

346.6

268.7

Production

(thousands

of

cubic

meters)

68557

71989

Canfor

revenue

(millions

of

dollars)

2265.9

2112.3

Canfor

profit

(millions

of

dollars)

125.6

11.5

borders.

This

is

why

trade

policies

are

such

an

emotional

issue

over

history.

The

scarcity

of

a

commodity

is

influenced

by

the

market

size.

For

Canadian

lumber,

the

market

size

is

very

much

determined

by

the

US

housing

market,

which

is

much

larger

than

the

Canadian

market.

The

market

size

is

also

greatly

affected

by

transportation

costs.

For

example,

petroleum

is

relatively

light

compared

with

coal

for

the

same

amount

of

energy.

Therefore,

petroleum

is

a

global

commodity

while

coal

is

much

less

so.

Lumber

is

six

times

heavier

than

coal

as

a

fuel.

Hence

the

market

for

wood

as

a

fuel

is

highly

localized.

But

the

market

for

wood

as

lumber,

which

is

higher

priced

than

fuel,

is

much

larger.

Still,

the

increasing

cost

of

oil

decreases

the

size

of

the

lumber

market.

Not

only

do

transportation

costs

increase,

but

also

higher

energy

prices

can

make

constructing

a

home

more

expensive.

3.2.

Regulations

and

other

entry

barriers

in

market

competition

Regulations

and

other

entry

barriers

increase

fixed

costs.

Higher

fixed

cost

reduces

the

number

of

businesses

in

an

industry,

which

increases

the

value

of

their

products

or

services.

We

will

analyze

how

the

increase

of

fixed

cost

affects

the

return

of

an

industry.

Sup-

pose

the

market

size

of

an

industry

is

M,

scarcity

is

p,

the

number

of

businesses

in

the

industry

is

b.

Then

the

unit

value

for

the

product

is

−

log

b

p

The

fixed

cost

for

each

business

is

K,

variable

cost

is

C.

Assume

each

business

gets

the

same

amount

of

revenue.

The

revenue

and

total

cost

for

each

business

are

Mp

b

(

−

log

b

p

)

and

K

+

C

Mp

b

(

−

log

b

p

)

respectively.

The

return

for

each

business

is

Mp

b

(

−

log

b

p

)

K

+

C

Mp

b

(

−

log

b

p

)

−

1

(4)

Suppose

M

=

1000,

p

=

0.4,

b

=

3.

The

fixed

cost

of

each

business

is

35

and

the

variable

cost

of

each

business

is

60%

of

the

revenue.

The

rate

of

return

for

each

business

is

1000

×

0

.

4

3

(

−

log

3

0

.

4

)

35

+

0

.

6

1000

×

0

.

4

3

(

−

log

3

0

.

4

)

−

1

=

0

.

09

This

rate

of

return

is

not

very

high.

Now

a

business

persuades

the

government

to

increase

regulatory

measure

on

this

industry.

As

a

result,

the

fixed

cost

is

increased

to

50.

Assume

other

parameters

remain

the

same.

The

new

rate

of

return

for

each

business,

cal-

culated

from

(4)

,

becomes

negative.

If

the

rate

of

return

becomes

negative,

one

business,

usually

the

financially

weak

one,

will

drop

off

the

market.

Suppose

now

there

are

only

two

businesses

in

the

industry.

Assume

other

parameters

remain

the

same.

The

new

rate

of

return

for

each

remaining

business

is

1000

×

0

.

4

2

(

−

log

2

0

.

4

)

50

+

0

.

6

1000

×

0

.

4

2

(

−

log

2

0

.

4

)

−

1

=

0

.

27

This

is

much

higher

than

the

previous

rate

of

return.

Financially

strong

companies

can

use

regulatory

tools

to

increase

fixed

cost.

It

can

reduce

the

number

of

competitors

and

help

remaining

players

achieve

high

rate

of

return.

In

neoclassical

economics,

regulation

is

justified

when

there

is

a

“market

failure”.

From

the

above

analysis,

we

see

instead

that

regulation

is

largely

driven

by

industries

themselves

to

keep

a

high

rate

of

return.

The

theory

also

explains

why

biological

and

chem-

ical

weapons

are

banned

by

international

treaties

while

nuclear

weapons,

which

can

cause

much

more

destruction

than

chem-

ical

weapons,

are

not.

Biological

and

chemical

weapons,

which

are

sometimes

called

poor

men’s

nuclear

weapons,

are

cheap

to

make.

If

these

weapons

are

not

banned,

many

people

can

make

them,

which

will

reduce

the

value

of

weapons

of

mass

destruc-

tion.

To

maintain

the

high

value

of

such

weapons,

international

treaties,

which

are

generally

initiated

by

leading

political

pow-

ers,

banned

those

weapons

of

mass

destruction

that

are

cheap

to

make.

4.

Physical

entropy,

subjective

utility

and

economic

value

Living

organisms

need

to

extract

low

entropy

from

the

envi-

ronment,

to

defend

their

low

entropy

sources

and

to

reduce

the

diffusion

of

the

low

entropy.

The

struggle

to

stay

in

low

entropy

states

is

called

natural

selection.

In

human

societies,

the

purpose

of

agriculture

is

to

obtain

low

entropy

sources

of

food.

Part

of

health

care

systems

aim

to

defend

our

own

low

entropy

sources

from

viruses

and

bacteria.

The

military

forces

are

established

to

extract

low

entropy

from

others

and

to

defend

one’s

own

low

entropy

sources.

Clothing

and

housing

reduce

the

diffusion

of

low

entropy.

Sexual

selection

is

the

struggle

between

the

individuals

of

one

sex,

generally

the

males,

to

communicate

their

attractiveness

to

the

other

sex

in

order

to

form

a

partnership

for

reproduction.

Since

the

entropy

law,

which

states

that

closed

systems

tend

towards

states

of

higher

entropy,

is

the

most

universal

law

of

nature,

it

is

natural

that

the

display

of

low

entropy

has

evolved

as

the

universal

signal

of

attractiveness

in

the

process

of

sexual

selection.

Both

natural

selection

and

sexual

selection

indicate

that

human

beings

favor

low

entropy

sources

(

).

This

observa-

tion

offers

a

connection

between

the

entropy

theory

of

value

and

the

subjective

utility

theory

of

value.

“Mind

is

an

organ

of

com-

putation

engineered

by

natural

selection”

(

,

p.

429).

It

calculates

the

entropy

level

and

sends

out

signals

of

pleasure

for

accumulating

and

displaying

low

entropy

and

signals

of

pain

for

dissipation

of

low

entropy.

Jevons

“attempted

to

treat

economy

as

a

calculus

of

pleasure

and

pain”

(

,

p.

vi).

Pleasure

is

gen-

erally

associated

with

the

accumulation

or

display

of

low

entropy

level,

such

as

the

accumulation

of

wealth,

and

conspicuous

con-

sumption.

Pain

is

associated

with

dissipation

of

low

entropy,

such

as

work

and

the

loss

of

money.

So

value

in

subjective

utility

theory,

as

a

measure

of

pleasure

and

pain,

is

intrinsically

linked

to

the

level

of

entropy.

Mainstream

economic

theory

states

that

the

value

of

a

com-

modity

is

determined

in

exchange

and

is

a

function

of

supply

and

demand.

From

the

theory

of

natural

and

sexual

selection,

the

demand

of

an

economic

commodity

is

driven

by

its

level

of

entropy.

The

supply

of

an

economic

commodity

is

constrained

by

its

scarcity,

with

entropy

as

the

unique

measure

of

scarcity.

The

level

of

entropy

offers

a

natural

measure

of

economic

value.

J.

Chen

/

Structural

Change

and

Economic

Dynamics

47

(2018)

73–81

79

Since

the

entropy

level

of

a

system

increases

spontaneously,

the

reduction

of

entropy

in

a

system

represents

effort

that

has

been

expended

and

therefore

“value-added”.

Entropy

level

may

thus

be

the

closest

to

an

invariant

measure

of

the

value

of

labor

and

other

commodities.

While

economic

values

of

commodities

are

highly

correlated

with

the

level

of

physical

entropy,

they

are

not

identical

for

sev-

eral

reasons.

In

the

following,

we

will

discuss

two,

one

from

the

perspective

of

information

theory

and

another

from

the

institutional

structures

that

regulate

scarcity

and

number

of

pro-

ducers.

First,

the

entropy

level

we

perceive

of

a

commodity

is

differ-

ent

from

its

objective

entropy

level.

From

information

theory,

the

amount

of

information

one

can

receive,

R

,

is

equal

to

the

amount

of

information

sent

minus

the

average

rate

of

conditional

entropy.

R

=

H

(

x

)

−

H

y

(

x

)

(5)

The

conditional

entropy

H

y

(x)

is

called

the

equivocation,

which

measures

the

average

ambiguity

of

the

received

signal

(

).

Equivocation

arises

because

receivers

don’t

have

complete

background

knowledge

of

signals.

For

example,

gold,

a

scarce

com-

modity,

is

highly

valuable.

Another

commodity

could

be

as

scarce

as

gold,

but

unlike

shiny

and

stable

gold,

it

could

be

very

difficult

to

identify.

Most

people

will

not

invest

much

effort

to

gain

knowledge

needed

to

identify

this

commodity

because

the

cost

outweighs

the

potential

benefit.

Thus,

it

registers

less

attention

and

is

valued

less

by

human

beings.

Second,

scarcity

of

a

commodity

is

regulated

by

the

institutional

structures

that

enforce

property

rights.

For

example,

the

value

of

an

invention

is

influenced

by

how

long

and

how

broad

patent

pro-

tection

is

granted.

The

value

of

a

patent

is

higher

in

a

system

where

patents

are

valid

for

twenty

years

than

one

where

patents

are

valid

for

ten

years.

If

patent

protection

is

defined

more

broadly,

the

mar-

ket

is

larger

and

the

value

of

an

invention

is

higher.

Economic

value,

as

a

function

of

scarcity,

is

to

a

great

extent

regulated

by

institutional

structures.

Among

all

the

institutional

measures

that

regulate

scarcity,

the

most

important

regulation

is

the

immigra-

tion

laws

that

regulate

the

scarcity

of

the

labor

force,

which

makes

persistent

large

wage

differentials

across

regions

possible.

Wage

differentials

can

persist

for

other

reasons

such

as

relocation

costs,

or

differences

in

cost-of-living.

Wages

in

the

cities

are

higher

than

in

the

countryside

in

the

same

country,

with

no

legal

barriers

to

migration.

But

these

wage

differentials

are

relative

minor

com-

pared

with

wage

differentials

where

legal

barrier

to

migration

is

high.

5.

The

entropy

theory

of

value

and

information

The

discussion

about

the

relation

between

information

and

physical

entropy

began

with

the

Maxwell’s

demon

(

).

In

1870s,

Boltzmann

defined

the

mathematical

function

of

entropy,

which

identified

as

information

many

years

later.

Because

of

the

equivalence

of

entropy

and

information,

an

entropy

theory

of

value

is

inevitably

an

information

theory

of

value.

Information

is

often

regarded

as

a

rather

unusual

commod-

ity.

In

this

section,

we

will

show

that

informational

and

physical

commodities

share

most

of

the

same

fundamental

properties

from

the

perspective

of

entropy

theory.

Since

offered

an

authoritative

description

about

the

special

characteristics

of

infor-

mation

as

an

economic

commodity,

our

discussion

is

based

on

his

writing.

The

algebra

of

information

is

different

from

that

of

ordinary

goods.

.

.

.

Repeating

a

given

piece

of

information

adds

noth-

ing.

On

the

other

hand,

the

same

piece

of

information

can

be

used

over

and

over

again,

by

the

same

or

different

producer(s).

(

,

p.21)

From

Formula

(5)

,

the

amount

of

information

received

is

the

information

of

source

minus

equivocation.

Repeating

a

signal

of

information

helps

reduce

equivocation.

Different

types

of

coding

generally

maintain

a

certain

level

of

redundancy

to

reduce

error

in

transmission.

Repetition

is

the

most

important

method

in

learning.

Reciting

poems

is

one

of

the

most

effective

ways

to

study

a

lan-

guage

or

literature.

Important

genes

often

have

several

hundred

copies

in

genetic

codes

to

satisfy

heavy

work

demand

(

).

A

song

will

survive

only

if

people

repeat

it

over

generations.

A

theory

will

survive

only

if

researchers

continue

to

discuss

it

over

time.

Same

commercials

are

repeated

many

times

on

TV.

From

the

thermodynamic

theory,

all

low

entropy

sources

have

a

tendency

to

diffuse.

Repeating

the

same

piece

of

informa-

tion

is

essential

to

keep

it

alive

and

valuable.

The

essence

of

a

living

organism

is

to

repeat

and

spread

the

information

encoded

in

its

genes.

It

is

often

thought

that

the

use

of

information

does

not

involve

rivalry,

since

“the

same

piece

of

information

can

be

used

over

and

over

again,

by

the

same

or

different

producer(s)”.

This

property

is

not

confined

to

information.

The

same

hammer

“can

be

used

over

and

over

again,

by

the

same

or

different

producer(s)”.

However,

the

value

of

the

same

information

will

be

different

for

different

users

or

at

different

time.

For

example,

if

an

unexpected

surge

of

corporate

profit

is

known

by

very

few

people,

i.e.,

when

P

is

very

small

and

–log

P

is

very

high,

this

information

would

be

highly

valuable.

Huge

profit

could

be

made

by

trading

the

underlying

stocks.

But

when

it

is

known

to

many

people,

the

value

of

such

information

is

very

low.

In

general,

when

some

knowledge

is

mastered

by

many

people,

its

market

value

is

very

low.

The

peculiar

algebra

of

information

has

another

important

implication

for

the

functioning

of

the

economic

system.

Infor-

mation,

once

obtained,

can

be

used

by

others,

even

though

the

original

owner

has

not

lost

it.

Once

created,

information

is

not

scarce

in

the

economic

sense.

This

fact

makes

it

difficult

to

make

information

into

property.

It

is

usually

much

cheaper

to

repro-

duce

information

than

to

produce

it

in

the

first

place.

In

the

crudest

form,

we

find

piracy

of

technical

information,

as

in

the

reproduction

of

books

in

violation

of

copyright.

Two

social

inno-

vations,

patents

and

copyrights,

are

designed

to

create

artificial

scarcities

where

none

exists

naturally,

although

the

duration

of

the

property

is

limited.

The

scarcities

are

needed

to

create

incentives

for

undertaking

the

production

of

information

in

the

first

place.

(

,

p.

21)

Information

is

a

type

of

low

entropy

source.

Utilization

of

low

entropy

source

from

others

is

a

universal

phenomenon

of

living

systems.

Once

again

animals

discover

the

trick

first.

.

.

.

butterflies,

did

not

evolve

their

colors

to

impress

the

females.

Some

species

evolved

to

be

poisonous

or

distasteful,

and

warned

their

preda-

tors

with

gaudy

colors.

Other

poisonous

kinds

copied

the

colors,

taking

advantage

of

the

fear

already

sown.

But

then

some

nonpoisonous

butterflies

copied

the

colors,

too,

enjoying

the

protection

while

avoiding

the

expense

of

making

themselves

distasteful.

When

the

mimics

become

too

plentiful,

the

col-

ors

no

longer

conveyed

information

and

no

longer

deterred

the

predators.

The

distasteful

butterflies

evolved

new

colors,

which

were

then

mimicked

by

the

palatable

ones,

and

so

on.

(

,

p.

501)

The

perceived

uniqueness

of

copying

information

products

in

human

societies

is

actually

quite

universal

within

living

systems.

Once

we

look

at

the

living

world

from

the

entropy

perspective,

it

80

J.

Chen

/

Structural

Change

and

Economic

Dynamics

47

(2018)

73–81

can

hardly

be

otherwise.

In

human

societies,

the

attempt

to

copy

and

reproduce

valuable

assets,

whether

informational

or

physical

assets,

is

also

universal.

The

fashion

industry

offers

an

example

that

illustrates

the

dynamics

of

innovation

and

copying

clearly.

When

a

new

fashion

style

is

created,

it

is

scarce

and

hence

valuable.

This

valuable

infor-

mation

will

be

copied

by

others.

As

more

people

copy

the

style,

P

increases,

-log

P

decreases

and

the

value

of

the

fashion

decreases.

To

satisfy

the

demands

for

high

value

fashions,

new

fashion

styles

“are

designed

to

create

artificial

scarcities

where

none

exists

natu-

rally”.

Protection

of

an

organism’s

source

of

low

entropy

to

prevent

access

by

others

is

also

a

universal

phenomenon

of

living

systems.

Animals

develop

immune

systems

to

protect

their

low

entropy

source

from

being

accessed

by

microbes.

Plants

make

themselves

poisonous

to

prevent

their

low

entropy

from

being

accessed

by

animals.

When

space

is

a

limiting

factor

in

survival

or

reproduc-

tion,

animals

defend

their

territory

vigorously

(

).

Whether

to

enforce

the

property

rights

depends

on

the

cost

of

enforcement

and

the

value

of

the

low

entropy