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On shadow pricing

Authors:
SWP792
On
Shadow
Pricing
Edward
Tower
Garry
Pursell
WORLD
BANK
STAFF
WORKING
PAPERS
Number
792
i
..
-M
- -
. .,
,
i ." ld792
1
Public Disclosure AuthorizedPublic Disclosure AuthorizedPublic Disclosure AuthorizedPublic Disclosure Authorized
I
WORLD
BANK
STAFF
WORKING
PAPERS
Number
792
On
Shadow
Pricing
Edward
Tower
Garry
Pursell
The
World
Bank
Washington,
D.C.,
U.S.A.
Copyright
1986
The
International
Bank
for
Reconstruction
and
Development/THE
WORLD
BANK
1818
H
Street,
N.W.
Washington,
D.C.
20433,
U.S.A.
All
rights
reserved
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1986
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Edward
Tower
is
professor
of
economics
at
Duke
University
and
a
consultant
to
the
World
Bank;
Garry
Pursell
is
operational
policy
adviser
in
the
Industrial
Strategy
and
Policy
Division
of
the
Bank.
Library
of
Congress
Cataloging-in-Publication
Data
Tower,
Edward.
On
shadow
pricing.
(World
Bank
staff
working
papers
;
no.
792)
Bibliography:
p.
1.
Shadow
prices.
2.
Equilibrium
(Economics)
I.
Pursell,
Garry.
II.
Title.
III.
Series.
HB143.T68
1986
338.5'2
85-29595
ISBN
0-8213-0695-2
ABSTRACT
The
principal
purpose
of
the
monograph
is
to
use
general
equilibrium
methodology
to
explain
the
logical
foundations
of
shadow
prices
and
the
techniques
for
deriving
shadow
price
expressions.
We
first
discuss
the
nature
and
meaning
of
shadow
prices.
Then
we
build
a
simple
model
in
which
each
traded
good
is
produced
with
intermediate
inputs
and
a
value
added
aggregate
which
are
used
in
fixed
proportions
and
with
constant
returns
to
scale,
where
the
value
added
aggregate
is
a
variable
proportions
function
of
a
sector
specific
fixed
factor
and
an
intersectorally
mobile
factor
of
production
which
is
common
to
all
sectors.
Using
this
model
we
first
derive
shadow
prices
for
labor,
traded
goods,
non-traded
goods
and
foreign
exchange
assuming
full
employment
and
a
flexible
real
exchange
rate,
with
household
welfare
being
held
constant
by
adjustments
in
income
taxes.
The
same
basic
approach
is
then
extended
to
more
complex
models
including
models
with
alternative
adjustment
mechanisms.
We
also
discuss
how
to
shadow
price
factors,
goods,
policy
parameters
and
autonomous
parameters
in
terms
of
other
goods
whose
shadow
prices
are
known
without
having
to
solve
a
full-fledged
general
equilibrium
model.
This
work
explains
the
logical
foundations
of
formulae
in
Squire
and
van
der
Tak
(1975)
and
Ray
(1984)
and
generalizes
their
approaches.
The
first
three
appendices
comment
from
a
general
equilibrium
perspective
on
some
of
the
shadow
price
expressions
proposed
in
three
books
on
shadow
pricing,
while
appendices
D
and
E
illustrate
the
kind
of
analysis
that
is
needed
if
the
models
are
so
complex
that
they
require
matrix
inversion.
ACKNOWLEDGEMENTS
This
paper
was
written
while
Tower
(who
teaches
at
Duke
University)
was
consulting
with
Garry
Pursell
at
the
World
Bank's
Industrial
Development
and
Finance
Department
(which
subsequently
became
the
present
Industrial
Strategy
and
Policy
Division
of
the
Industry
Department)
in
connection
with
the
Incentives
and
Comparative
Advantage
(INCA)
Unit
research
project
(RP0672-
44).
The
INCA
Unit
was
established
to
support
the
many
studies
at
the
Bank
and
in
developing
countries,
which
involve
the
estimation
of
empirical
incentive
and
cost-benefit
(comparative
advantage)
indicators.
The
authors
are
grateful
to
the
following
people
(both
Bank
staff
members
and
others)
for
helpful
comments:
Clive
Bell,
Trent
Bertrand,
Phil
Brock,
Pat
Conway,
Shanta
Devarajan,
Kiyoun
Han,
Gordon
Hughes,
Glenn
Jenkins,
Kent
Kimbrough,
Elio
Londero,
Anandarup
Ray,
Neil
Roger,
Sudhir
Shetty,
and
Lyn
Squire.
Thanks
also
go
to
Vivian
Cherian
for
help
provided
at
various
stages
and
to
Wanda
Jedierowski,
Pat
Johnson,
Stacy
Miller
and
F.L.
Smith
for
typing
various
versions.
TABLE
OF
CONTENTS
Chapter
I.
INTRODUCTION
.............................
1
I.1
Overview
............................
I
I.2
A
Non-Technical
Introduction
to
the
Issues
Involved
in
Shadow
Pricing
and
the
Results
of
the
Monograph
......................................
4
a.
The
Model
................................
4
b.
The
Shadow
Price
of
Labor
.....................
11
c.
The
Shadow-Price
of
Labor
Continued:
A
Simple
Geometric
Illustration
..............
15
d.
Shadow
Pricing
Traded
Goods
...................
22
e.
Shadow
Pricing
Non-traded
Goods
and
Services
..................................
23
f.
Shadow
Pricing
Foreign
Exchange
in
Utility
Numeraire
......................
25
g.
Putting
It
All
Together
.......................
28
h.
Summary
of
the
Monograph's
Main
Results
.......
29
Chapter
II.
A
GEOMETRIC
APPROACH
TO
SHADOW
PRICING
LABOR
IN
TERMS
OF
FOREIGN
EXCHANGE
AND
DERIVING
THE
SHADOW
PRICE
OF
FOREIGN
EXCHANGE
IN
UTILITY
NUMERAIRE
......................
31
II.1
Introduction
.........................................................
31
I1.2
On
Targets,
Instruments
and
Tradeoffs:
The
Logical
Structure
of
The
Model
...............
32
II.3
Shadow
Pricing
Labor
.......................
.
34
II.4
Many
Commodities,
Some
of
Which
are
Imported
and
Some
of
Which
are
Exported
...................
40
II.5
Non-Standard
Adjustment
Mechanisms
................
41
11.6
Proving
That
the
Conversion
Factor
For
Converting
Domestic
Real
Income
Into
Foreign
Exchange
is
the
Sum
of
the
Shadow
Prices
of
Goods,
Each
Weighted
By
the
Marginal
Propensity
to
Consume
It
....................
.
42
II.7
Calculating
the
Shadow
Price
of
Foreign
Exchange
.................................
.
44
II.8
Integrating
Our
Results
With
Those
of
Bacha-Taylor
(1971)
...............................
47
Chapter
III.
HOW
TO
USE
SOME
SHADOW
PRICES
TO
FIND
OTHERS:
TRICKS
FOR
LAZY
PEOPLE
WHO
DON'T
LIKE
SOLVING
GENERAL
EQUILIBRIUM
SYSTEMS
........................................
50
III.1
Introduction
..........................
50
III.2
Shadow
Pricing
a
Factor
of
Production
as
the
Sum
of
Its
Marginal
Net
Products
with
Each
Valued
at
Its
Shadow
Price
......................
50
III.3
Shadow
Pricing
Goods
in
Terms
of
the
Shadow
Prices
of
Other
Goods
and
Shadow
Pricing
Policy
and
Non-Policy
Parameters
in
Terms
of
the
Shadow
Prices
of
Goods
............
54
III.4
Shadow
Pricing
a
Good
or
Factor
in
Terms
of
Other
Goods
and
Factors
........................
57
III.5
Using
Demand
Side
and
Supply
Side
Conversion
Factors
to
Shadow
Price
a
Non-Traded
Good
.........
58
III.6
Using
Demand
Side,
Supply
Side
and
Foreign
Market
Conversion
Factors
to
Shadow
Price
a
Good
With
a
Variable
World
Price
...................
62
III.7
Shadow
Pricing
Policy
Parameters
in
Terms
of
Other
Shadow
Prices
...........................
64
III.8
Shadow
Pricing
Autonomous
Non-Policy
Parameters
in
Terms
of
Other
Shadow
Prices
.................
66
III.9
Dealing
With
the
Heterogeneity
of
Individual
Consuming
Units:
An
Example
Involving
the
Shadow
Pricing
of
a
Good
in
Terms
of
the
Shadow
Prices
of
Other
Goods
.............................
67
III.10
Shadow
Pricing
Several
Interrelated
Items
at
Once
.....................................
71
III.11
The
Shadow
Price
of
Foreign
Exchange
when
the
Adjustment
Mechanism
Consists
of
Changes
in
Distorting
Taxes
..................................
72
III.12
A
Note
on
the
Choice
of
Numeraire
and
the
Possibility
of
a
Negative
Shadow
Price
of
Foreign
Exchange
..................................
73
Chapter
IV.
SHADOW
PRICING
IN
AN
ECONOMY
WITH
NO
INTERRELATIONS
BETWEEN
THE
DEMANDS
FOR
NON-TRADED
GOODS
AND
TRADED
GOODS
WITH
VARIABLE
WORLD
PRICES,
AND
A
FIXED
EQUILIBRIUM
WAGE
RATE
...................
.......
75
IV.1
Introduction
..............
........
75
IV.2
Deriving
the
Fundamental
Equation
of
Shadow
Pricing
.................
.
..................
.
77
IV.3
Deriving
Shadow
Prices
of
Goods
and
Labor
.........
85
IV.4
Calculating
Shadow
Prices
of
Goods
and
Labor
......
89
IV.5
Coping
with
Monopoly,
Monopsony
and
Intermediate
Inputs
with
Variable
World
Prices
....
93
IV.6
The
Shadow
Price
of
Foreign
Exchange
in
Utility
Numeraire
.................................
94
Chapter
V.
SHADOW
PRICING
WHEN
THE
EQUILIBRIUM
WAGE
RATE
IS
VARIABLE
................
...........................
96
V.1
Introduction
.......
. .........
..........
96
V.2
Deriving
Shadow
Prices
.......................
96
Chapter
VI.
SHADOW
PRICING
WHEN
THE
DEMAND
FOR
EACH
GOOD
DEPENDS
ON
ITS
PRICE
RELATIVE
TO
A
SINGLE
NON-TRADED
GOOD
.............
100
VI.1
Introduction
.....................................
100
VI.2
The
Model
.........................
101
Appendix
A.*
Some
Comments
on
chapter
4
of
Anandarup
Ray's
Issues
in
Cost
Benefit
Analysis
entitled
"Valuation
of
Traded
and
Non-Traded
Goods"
.......
109
Appendix
B.*
Notes
on
Squire
and
van
der
Tak's
(1975,
pp.
144-145)
Formulae
for
Shadow
Pricing
Exportables
with
Variable
World
Prices
and
Non-Tradeables
.........
114
Appendix
C.*
On
Terry
A.
Powers'
(ed.)
Estimating
Accounting
Prices
for
Project
Appraisal
............................
117
Appendix
D.
Shadow
Pricing
in
an
Economy
with
a
Universal
Minimum
Wage
and
Unemployment
............................
119
Appendix
E.
Shadow
Pricing
in
a
Fully
Employed
Economy
.................
124
REFERENCES
..............................................................
128
*Edward
Tower
is
sole
author
of
appendices
A,
B,
and
C.
Chapter
I
INTRODUCTION
1.
Overview
The
purpose
of
this
monograph
is
to
illustrate
by
example
what
general
equilibrium
methodology
has
to
tell
us
about
calculating
shadow
prices
for
goods,
factors
of
production,
and
foreign
exchange
and
to
provide
a
few
new
simple
formulae
which
deal
explicitly
with
the
interindustry
structure
of
production,
variable
world
prices
and
non
standard
macroeconomic
adjustment
mechanisms.
It
has
its
genesis
in
Garry
Pursell's
(1978)
paper
which
estimated
shadow
exchange
rates
for
the
Ivory
Coast
and
Tower
(1984).
In
essence,
the
monograph
uses
the
approaches
discussed
in
Tower's
paper
to
make
the
derivations
of
the
formulas
in
the
Pursell
paper
more
formal
and
to
generalize
them.1
Throughout
the
paper
we
keep
the
economic
structure
of
the
models
con-
sidered
fairly
simple,
assuming
for
the
most
part
that
each
good
is
produced
with
intermediate
inputs
and
a
value
added
aggregate
which
are
used
in
fixed
lWe
developed
most
of
these
ideas
before
realizing
that
E.
Sieper
covered
much
of
the
same
ground
as
we
cover
in
our
chapters
I
and
II
in
an
important
unpublished
paper
in
1981.
We
share
the
same
views
as
Sieper
regarding
the
logic
of
shadow
pricing.
However,
some
of
Sieper's
shadow
price
expressions
are
reduced
forms
and
others
which
are
expressed
in
structural
parameters
require
matrix
inversion.
Our
expressions
involve
structural
parameters
and
are
derived
under
the
assumption
of
specific
demand
and
supply
relationships
which
were
used
in
order
to
generate
simple
expressions
for
shadow
prices.
Also,
unlike
Sieper,
we
explicitly
incorporate
the
effective
protection
concept
in
our
models.
The
Jenkins-Kuo
(forthcoming)
paper
also
builds
a
model
which
is
very
close
in
spirit
to
ours,
except
that
it
employs
the
Armington
assumption
of
imperfect
substitution
between
domestically
and
foreign
produced
varieties
of
the
same
good.
2
proportions
and
with
constant
returns
to
scale.
Then
we
permit
the
value
added
aggregate
to
be
a
constant
returns
to
scale,
variable
proportions
function
of
a
fixed
factor
which
is
specific
to
the
sector
which
employs
it
and
a
factor
which
is
mobile
between
sectors.
Thus
we
can
think
of
the
model
as
describing
a
short-run
equilibrium
where
the
capital
stock
is
the
fixed
factor
and
labor
is
the
mobile
factor:
this
is
the
terminology
we
will
use
throughout
the
paper.
There
is,
however,
an
alternative
interpretation
of
the
model
which
makes
it
a
reasonable
description
of
an
economy
in
long
run
equilibrium.
We
can
think
of
capital
services
as
being
like
any
other
intermediate
input.
The
simplest
assumption
we
could
make
is
that
capital
is
available
on
the
world
capital
market
at
a
fixed
real
interest
rate
or
that
the
supply
of
domestic
savings
is
perfectly
elastic,
and
that
there
is
an
international
market
in
used
machinery
so
that
a
machine
can
be
easily
converted
into
foreign
exchange.
Then
we
could
assume
that
the
fixed
factor
in
each
sector
is
sector
specific
managerial
or
technical
skill
with
less
skilled
or
more-generally
skilled
labor
being
the
intersectorally
mobile
factor
of
production
in
limited
aggregate
supply.
Alternatively,
we
may
interpret
the
fixed
factor
as
being
a
limited
quantity
of
venture
capital
in
each
sector
created
either
by
a
desire
for
portfolio
diversification
or
else
a
moral
hazard
problem
which
means
that
managers
must
provide
their
own
risk
capital.
Thus,
we
believe
that
our
model
is
quite
a
useful
one
in
that
it
can
be
interpreted
to
fit
a
wide
range
of
circumstances.
While
we
do
work
entirely
with
one
mobile
primary
factor
the
only
reason
we
do
this
is
to
obtain
tractable
formulae,
but
if
one
is
willing
to
settle
for
more
complex
formulae
which
involve
matrix
inversion,
one
can
introduce
an
unlimited
number
of
mobile
factors.
3
The
result
which
emerges
from
all
but
one
of
our
formulae
is
that
deviations
of
our
shadow
prices
from
market
prices
turn
out
to
be
weighted
averages
of
distortions
in
production
and
consumption
with
the
weights
based
on
supply
and
compensated
demand
elasticities
and
other
parameters
describing
the
base
equilibrium.
The
exception
is
the
shadow
price
of
foreign
exchange
in
utility
numeraire
which
also
requires
knowledge
of
marginal
propensities
to
spend.
Moreover,
in
our
simplest
models,
with
no
domestic
distortions
and
fixed
world
prices,
these
distortions
are
simply
effective
tariffs
and
nominal
tariffs.
Also,
reassuringly,
the
shadow
prices
of
traded
goods
which
have
fixed
world
prices
attached
simply
turn
out
to
be
those
fixed
world
prices.
Much
of
the
paper
is
quite
mathematical.
This
is
inevitable
because
we
wish
to
emphasize
the
logical
foundations
of
the
shadow
prices
we
derive,
as
well
as
the
techniques
used
to
derive
them,
as
opposed
to
writing
a
cook
book
for
the
project
evaluator.
Still,
the
paper
should
have
use
as
a
cookbook,
for
certain
formulae
are
developed
which
are
unavailable
elsewhere
and
are
quite
simple
and
useful.
For
a
discussion
of
the
mathematical
tools
used,
which
would
also
serve
as
an
introduction
to
the
ideas
developed
here,
the
reader
is
referred
to
chapters
II
and
V
of
Tower
(1984).
A
reader's
guide
is
appropriate.
In
Chapters
I
and
II
we
use
a
simple
model,
which
lends
itself
to
the
use
of
geometric
reasoning,
to
lay
out
the
main
ideas
of
the
paper,
namely
how
to
think
about
shadow
prices
and
how
to
derive
them
in
some
simple
cases.
Chapter
III
discusses
the
how
to
shadow
price
goods,
factors,
policy
parameters
and
autonomous
non-policy
parameters
in
terms
of
the
shadow
prices
of
other
goods,
which
are
assumed
to
be
known.
It
also
discusses
the
logic
of
various
different
types
of
conversion
factors
and
shows
how
to
use
them
in
shadow
pricing
one
item
in
terms
of
other
items.
Chapter
IV
builds
a
set
of
tools
for
the
formal
derivation
of
shadow
4
prices
which
we
then
apply
in
chapters
IV
and
V
and
VI
to
derive
shadow
prices
under
various
assumptions.
The
first
three
appendices
consist
of
sets
of
comments
on
pieces
dealing
with
problems
of
shadow
pricing
which
cost
some
effort
to
understand.
Finally,
Appendices
D
and
E
illustrate
the
kind
of
analysis
that
can
be
done
if
one
is
willing
to
use
models
that
are
sufficiently
complex
to
require
matrix
inversion.
Many
readers
will
wish
to
read
through
chapter
IV
and
skip
lightly
over
the
rest
of
the
monograph,
since
chapters
V
and
VI
are
similar
in
construction
to
IV,
except
that
the
assumptions
used
and
formulae
derived
there
are
different.
The
first
three
of
the
appendices
will
interest
only
those
readers
who
are
concerned
with
the
literature
considered
there,
and
the
last
two
appendices
indicate
the
sort
of
methodology
that
one
can
use
with
more
complex
models
rather
than
coming
up
with
particular
formulae
that
one
would
be
likely
to
want
to
apply.
We
now
provide
a
non-technical
summary
of
the
issues
involved
in
shadow
pricing
and
the
results
of
the
monograph.
Those
readers
who
are
already
familiar
with
the
basic
ideas
of
shadow
pricing
may
wish
to
skim
the
rest
of
this
chapter,
and
pick
up
the
model
in
chapter
II
where
it
is
laid
out
more
tersely.
2.
A
Non-technical
Introduction
to
the
Issues
Involved
in
Shadow
Pricing
and
the
Results
of
The
Monograph
a.
The
Model
In
order
to
understand
the
meaning
of
the
shadow
prices
we
are
about
to
derive
it
is
convenient
to
work
initially
with
the
very
simple
model
economy
which
is
illustrated
schematically
in
figure
1.
It
consists
of
households
Figure
1
MASSAGES
THE
GOVERNMENT
PUBLIC
GOODS
LABOR
LIC
HOUSEHOLDS
WORKS
REA
R
II
D
G
FOREIGN
EXCHANGE
WIDGE
F
E
FACTORY
G
E
T
DG/
\
\
/
EPOR
/FOREIGN\
<
/
t
SECTORl
6
which
supply
a
fixed
quantity
of
labor
for
the
production
of
traded
goods
(widgets),
non-traded
labor
services
(massages),
and
public
goods
supplied
by
the
government.
As
we
have
noted
previously,
labor
is
the
sole
intersectorally
mobile
factor
of
production.
To
produce
widgets,
labor
and
an
imported
intermediate
input
(plastic)are
combined
with
a
fixed
quantity
of
sector
specific
capital.
This
means
that
there
are
diminishing
returns
to
the
application
of
labor
and
an
upward
sloping
supply
curve
in
this
industry.
In
this
initial
and
simplest
model
we
assume
that
widgets
are
the
country's
sole
export
and
that
our
model
country
is
so
small
relative
to
the
world
market
that
it
has
no
perceptible
influence
on
the
world
price
of
either
widgets
or
plastic.
The
export
of
widgets
is
subject
to
an
export
subsidy
at
the
rate
T
expressed
as
a
fraction
of
the
world
price,
p*.
More
precisely,
p*
is
the
border
(f.o.b.)
price
of
widgets
(expressed
in
the
domestic
currency
at
the
market
exchange
rate).
The
ex-factory
price
of
widgets
sold
domestically
is
given
by
p
=
p*
(1
+
T
).
While
in
this
case
the
domestic
price
of
widgets
will
exceed
the
border
price
by
the
amount
of
the
export
subsidy,
we
could
also
conceive
of
T
as
an
export
tax,
in
which
case
T
would
be
negative
and
the
domestic
price
would
be
less
than
the
export
price.
In
the
initial
model
there
are
no
domestic
sales
or
value
added
taxes,
so
that
p
is
also
the
price
paid
for
widgets
by
households.
In
chapter
II
we
introduce
a
value-added
tax
on
widgets,
but
as
we
shall
see
the
same
principles
continue
to
apply
to
the
derivation
of
the
shadow
prices.
The
assumption
that
the
ex-factory
price
of
widgets
is
also
the
consumer
price
means
that
there
are
no
wholesale
or
retail
margins
(which
is
also
implied
by
our
assumption
that
"massages"
is
the
only
non-traded
activity).
Furthermore,
the
production
of
widgets
is
assumed
to
require
no
non-traded
intermediate
inputs,
an
assumption
which
(as
7
demonstrated
in
appendices
D
and
E)
does
not
alter
any
essential
principles,
but
does
simplify
the
shadow
price
expressions.
Widget
production
requires
an
intermediate
input
("plastic")
which
is
used
in
fixed
technical
proportions
and
which
is
imported
at
a
given
world
(c.i.f.)
price.
The
assumption
of
fixed
technical
raw
material
input-output
coefficients
is
not
needed
when
relative
prices
of
all
primary
and
intermediate
factors
are
fixed,
but
dropping
it
would
complicate
things
in
models
where
these
relative
prices
vary.
Our
rationale
for
keeping
it
is
the
standard
one
that
substitution
between
individual
material
inputs
and
between
material
inputs
and
components
of
value
added
is
probably
low
or
in
any
event
sufficiently
low
and
sufficiently
difficult
to
estimate
as
to
be
a
minor
source
of
error
relative
to
others,
in
empirical
applications.
In
this
initial
model
plastic
is
the
economy's
sole
import,
so
that
the
balance
of
trade
in
any
given
period
is
simply
the
difference
between
the
border
value
of
widget
exports
and
plastic
imports.
In
later
versions
of
the
model
(e.g.,
chapter
II),
we
relax
this
assumption
by
allowing
for
domestic
production
of
both
intermediate
inputs
such
as
plastics
and
importable
consumer
goods
other
than
widgets,
as
well
as
for
the
import
of
consumer
goods
which
are
not
produced
domestically,
and
we
show
that
these
extensions
do
not
change
any
of
our
essential
conclusions
about
shadow
prices
and
leave
us
with
very
similar
expressions
for
them.
In
the
production
of
non-traded
services,
we
initially
assume
that
labor
is
the
sole
input
(hence
"massages").
This
means
that
the
price
of
these
services
is
simply
the
wage
rate,
given
our
assumption
of
a
competitive
labor
market.
Later,
in
chapter
III,
we
allow
for
intermediate
material
inputs
used
in
the
production
of
non-traded
goods
and
services,
and
finally
for
the
existence
of
sector
specific
capital,
which
implies
diminishing
returns
and
an
8
upward
sloping
supply
curve
in
the
production
of
non-tradeds.
Since
this
in
turn
means
that
changes
in
the
demand
for
non-tradeds
are
accompanied
by
changes
in
their
prices
we
show
that
the
shadow
price
formulas
become
correspondingly
more
complex.
In
our
simple
model,
the
government
collects
taxes
which
it
uses
to
pay
for
the
production
of
various
public
services,
and
it
holds
the
country's
foreign
exchange
reserves.
The
taxes
are
income
taxes
on
households
plus
net
receipts
from
trade
taxes
and
subsidies,
i.e.,
the
difference
between
receipts
from
the
import
duties
on
plastic
minus
the
export
subsidies
on
widgets.
Obviously,
depending
on
the
relative
importance
of
import
tariffs
and
export
subsidies,
trade
taxes
could
represent
a
net
outlay
rather
than
net
income
for
the
government.
The
government
itself
is
envisaged
as
an
abstract
entity
employing
labor
and
other
factors
to
produce
an
exogenously
fixed
supply
of
various
public
goods
such
as
defense,
health
and
education
services,
etc.
Since
there
is
no
saving
in
our
model,
these
services
are
financed
through
taxes
rather
than
borrowing.
However,
the
results
in
no
way
depend
on
the
existence
of
a
minimal
Adam
Smith
style
government.
There
is
no
reason
that
the
government
should
not
also
own
part
or
even
all
of
the
capital
in
the
sectors
producing
traded
goods,
(and
in
the
non-traded
sectors
once
sector-
specific
capital
is
introduced)
provided
only
that
the
market
structures
remain
competitive
and
production
and
pricing
decisions
continue
to
be
made
in
accordance
with
profit
maximising
principles.1
Compared
with
our
simple
model,
the
only
difference
would
be
that
government
income
would
include
a
profit
component
while
the
taxable
income
of
households
would
be
lower
to
the
'Actually
imperfect
competition
does
not
destroy
the
applicability
of
the
analysis
because
a
monopolist/monopolist
can
be
thought
of
as
a
perfect
competitor
who
attaches
implicit
taxes
to
his
output
and
use
of
inputs
with
upward
sloping
supplies.
For
more
on
this
see
Tower
(1984,
sec.
V.8.a).
9
same
extent.
Operating
losses
requiring
subsidies
or
operating
surpluses
by
government
enterprises
could
also
be
handled
by
treating
them
as
negative
or
positive
sales
taxes,
although
only
value
added
taxes,
not
those
particular
taxes,
are
dealt
with
in
our
paper.
As
regards
households,
as
noted
previously,
we
assume
that
the
total
quantity
of
labor
supplied
is
fixed
over
the
relevant
range
of
variation
of
prices,
real
wages
and
income
taxes.
This
assumption
simplifies
the
analysis
by
doing
away
with
the
need
to
treat
leisure
as
a
consumption
good,
the
demand
for
which
would
depend
on
these
variables.
1
In
particular,
changes
in
income
taxes
are
assumed
to
have
no
effect
on
the
labor
supply.
Real
income
or
welfare
is
assumed
not
to
depend
on
the
distribution
of
income
between
households.
Also,
households
are
assumed
to
be
utility
maximisers,
so
that
in
equilibrium
the
marginal
utilities
of
the
goods
they
consume
will
be
proportional
to
their
prices.
Thus,
a
change
in
the
standard
of
living
(or
national
welfare),
dy,
is
defined
as
the
change
in
the
consumption
of
goods
by
households
dCi
multiplied
by
their
consumer
prices
p.
.
That
is
c
dy
=
Ep
.dC..
In
effect
we
treat
all
households
together
as
though
they
are
1
1
one
single
household.
While
utility
maximisation
is
necessary
for
legitimate
use
of
our
welfare
criterion
and
hence
for
the
formulae
we
develop,
the
simple
aggregation
of
households
is
not
essential,
although
information
requirements
and
the
complexity
of
shadow
price
expressions
would
increase
if
welfare
weights
depending
on
the
distribution
of
real
incomes
between
households
were
lAlternatively
one
may
think
of
"massages"
as
leisure
and
pretend
that
widgets
are
the
only
marketed
goods
which
are
consumed.
10
introduced.1
The
dC
1
are
assumed
to
include
"private"
goods
only
(which
as
noted
above
could
be
produced
by
government
owned
corporations)
as
distinct
from
the
"public'
goods
and
services
such
as
defense,
law
and
order,
etc.
which
are
supplied
free
of
charge
by
the
government.
While
the
latter
affect
the
absolute
level
of
the
standard
of
living,
since
the
quantity
supplied
is
constant,
they
have
no
effect
on
changes
in
the
standard
of
living.
In
order
to
further
simplify
our
model,
we
assume
that
there
is
no
private
saving
-
all
disposable
household
income
after
the
payment
of
income
taxes
is
fully
spent
on
traded
goods
(widgets)
or
non-traded
labor
services
(massages).
Since
there
is
no
change
in
government
expenditure
on
public
goods,
any
change
in
net
government
income
must
be
accompanied
by
an
equal
increase
or
decrease
in
the
foreign
exchange
reserves
held
by
the
government
(valuing
the
change
in
foreign
exchange
holdings
in
"border
pesos").
2
We
now
imagine
that
the
possibility
of
undertaking
a
new
project
arises.
The
project
could
be
either
undertaken
directly
by
the
government,
or
could
be
undertaken
privately
provided
government
permission
(and
perhaps
a
subsidy)
is
given.
To
simplify,
we
can
assume
that
the
project
will
export
a
product
not
consumed
domestically
(say
a
mineral),
so
that
in
order
to
know
whether
it
is
economically
worthwhile
undertaking,
the
government
will
need
to
compare
the
foreign
exchange
shadow
value
of
the
inputs
which
will
be
needed
'Alternatively,
we
can
recognize
that
income
distribution
is
a
variable
of
concern
to
the
policymaker,
but
that
he
or
she
has
already
adjusted
the
income
tax,
so
that
at
the
margin
changes
in
the
income
distribution
do
not
matter.
In
other
words,
the
policymaker
uses
the
income
tax
to
optimize
the
income
distribution
and
project
evaluation
to
maximize
efficiency,
which
as
Harberger
(1978a;
1978b)
argues
is
a
sensible
solution
of
this
assignment
problem.
2
This
result
follows
from
the
fact
that
since
the
private
sector
spends
all
of
its
disposable
income
its
budget
is
always
in
balance.
Therefore,
the
government's
budget
deficit
must
be
equal
to
the
foreign
sector's
budget
surplus,
i.e.,
the
rate
at
which
the
government
loses
reserves.
to
produce
it,
with
the
foreign
exchange
which
would
be
earned
by
the
exports.
This
means
that
the
government
will
need
to
know
the
shadow
prices
of
labor,
traded
products
(widgets
and
plastics),
and
non-traded
services
and
products
(massages)
which
the
project
may
require.
In
the
following
sections
we
first
discuss
the
shadow
price
of
labor
in
some
detail,
as
a
way
of
illustrating
how
our
model
works.
We
then
discuss
in
turn
the
shadow
pricing
of
traded
products
and
non-traded
services
and
products.
Next,
we
discuss
the
shadow
price
of
foreign
exchange
itself
in
terms
of
the
standard
of
living
or
"utility
numeraire."
Finally
we
summarize
how
the
shadow
prices
would
be
used
to
evaluate
the
project,
and
provide
a
succinct
summary
of
some
principal
conclusions
of
later
chapters.
b.
The
Shadow
Price
of
Labor
A
simple
story
that
illustrates
the
meaning
of
the
shadow
price
of
labor
is
the
following.
Consider
an
economy
with
a
fixed
set
of
tariffs,
export
taxes
and
subsidies.
The
government
is
contemplating
a
project
which
requires
one
man-day
of
labor
to
produce
one
dollar's
worth
of
foreign
exchange,
and
wants
to
know
if
it
should
undertake
the
project.
To
answer
this
question
we
need
to
know
how
many
dollars
a
man-day
of
labor
is
worth.
To
figure
that
out
we
need
to
know
the
rate
at
which
the
government
is
able
to
convert
man-days
into
dollars
by
alternative
means.
The
standard
story
implicit
in
most
analyses
but
explicit
in
few
is
the
following.
The
government
stands
ready
to
hire
labor
at
the
going
market
wage.
It
can
induce
the
private
sector
to
release
labor
by
revaluing
the
currency,
and
holding
the
money
wage
constant,
which
will
create
some
unemployed
labor
(which
now
seeks
employment
in
the
public
sector)
while
using
up
foreign
exchange
and
raising
or
lowering
the
standard
of
living.
Then
by
12
adjusting
the
income
tax,
the
government
can
put
the
standard
of
living
back
to
where
it
was
before.
Once
this
has
worked
itself
out,
the
ratio
of
the
change
in
foreign
exchange
used
to
the
labor
released
by
the
private
sector
is
noted
and
defined
as
the
shadow
price
of
labor,
for
it
is
the
amount
of
foreign
exchange
that
the
government
must
pay
to
the
private
sector
to
compensate
it
for
each
unit
of
labor
released.
If
and
only
if
our
project
converts
labor
into
foreign
exchange
on
better
terms
than
this
is
it
a
good
thing.
Moreover,
by
definition
this
will
be
the
case
if
and
only
if
the
foreign
exchange
earned
exceeds
the
cost
of
the
labor
used
when
valued
at
its
shadow
price.
This
can
be
spelled
out
in
more
detail
using
our
simple
widget-massage
model.
As
the
exchange
rate
is
revalued,
the
widget
processing
margin
is
squeezed
and
production
is
cut
back,
releasing
labor.
At
the
same
time,
since
the
domestic
consumer
price
of
widgets
falls,
household
demand
is
diverted
from
massages
to
widgets,
thus
releasing
additional
labor
from
the
massage
sector.
What
is
the
impact
of
this
on
household
real
income
(welfare)?
On
the
one
hand,
since
the
price
of
widgets
has
declined
while
the
price
of
massages
has
not
changed,
real
income
will
have
increased.
On
the
other
hand,
the
reduced
return
to
the
specific
factor
(measured
in
units
of
domestic
currency)
will
have
lowered
household
nominal
income
even
if
the
government
hires
the
surplus
labor
in
the
project
at
the
same
wage.1
In
this
simple
model,
since
there
is
only
one
traded
product
which
is
being
exported,
there
'Since
we
are
testing
whether
or
not
the
project
ought
to
be
undertaken,
the
labor
is
obviously
not
yet
employed
in
the
project.
Indeed,
unless
the
project
is
actually
undertaken,
none
of
the
above
actually
happens.
We
are
rather
estimating
what
would
happen
if
the
project
were
to
go
ahead.
13
must
be
a
decrease
in
real
income.
1
The
government
now
cuts
income
taxes
so
as
to
restore
household
real
income
to
its
previous
level,
which
will
increase
spending
on
widgets
and
massages.
This
will
result
in
some
increase
in
massage
production
and
some
re-employment
of
labor
there,
while
in
the
widget
sector
there
will
be
a
further
reduction
in
exports
but
no
change
in
production
or
employment.
In
the
final
equilibrium
the
amount
of
labor
released
from
widget
production
will
depend
on
the
elasticity
of
supply
of
widgets,
and
the
amount
of
labor
released
from
massage
production
will
depend
on
how
closely
widgets
substitute
for
massages
in
household
consumption,
i.e.,
on
the
income-compensated
cross
elasticity
of
demand
between
widgets
and
massages.
What
is
the
effect
of
all
this
on
foreign
exchange
reserves?
First,
the
reduction
in
widget
production
will
lead
to
a
decline
in
net
foreign
exchange
earnings
equal
to
the
difference
between
the
export
value
of
the
reduced
production
of
widgets,
minus
the
c.i.f.
value
of
the
reduction
in
plastic
imports
which
are
used
to
produce
the
widgets.
Secondly,
the
switch
of
household
consumption
demand
from
massages
to
widgets
will
lead
to
a
decline
in
foreign
exchange
reserves
equal
to
the
export
value
of
the
extra
widgets
which
are
now
consumed
domestically.
Again,
the
importance
of
these
two
effects
will
depend
respectively
on
the
supply
elasticity
of
widgets
and
the
compensated
cross
elasticity
of
demand
between
widgets
and
massages.
As
pointed
out
previously,
the
ratio
of
the
net
decline
in
foreign
exchange
reserves
to
the
amount
of
labor
released
is
defined
as
the
shadow
price
of
labor,
since
it
shows
how
much
extra
foreign
exchange
is
required
to
maintain
the
standard
of
living
while
withdrawing
a
unit
of
labor
from
producing
traded
and
non-traded
goods
for
use
in
the
project.
lIf
there
is
more
than
one
traded
product,
some
of
which
are
being
imported
and
some
exported,
real
income
may
increase
or
decrease.
14
In
the
adjustment
process
we
have
just
described,
the
government
operates
on
the
exchange
rate
and
the
income
tax,
while
the
nominal
wage
remains
unchanged.
We
get
the
same
results
if
the
exchange
rate
is
fixed
and
the
nominal
wage
is
allowed
to
vary
with
constancy
of
the
living
standard
again
maintained
by
varying
the
income
tax.
In
this
scenario,
the
government
hires
the
labor
it
requires
for
the
project,
which
has
the
effect
of
forcing
up
the
nominal
wage,
thus
leading
to
a
reduction
in
widget
production
(which
faces
unchanged
widget
and
plastic
prices)
and
a
switch
of
consumption
from
massages
(whose
price
has
increased)
to
widgets.
The
inital
net
effect
is
again
to
decrease
real
household
income,
so
the
government
decreases
income
taxes
in
order
to
restore
the
initial
level
of
household
real
income.
In
the
final
equilibrium
the
amount
of
labor
released
and
the
compensating
rundown
of
foreign
exchange
reserves
will
depend
as
before
on
the
elasticity
of
the
supply
of
widgets
and
the
compensated
cross
elasticity
of
demand
between
massages
and
widgets.
We
again
get
the
same
result
if
we
assume
that,
following
the
withdrawal
of
labor,
wage
flexibility
and
the
effect
of
price
changes
on
the
real
value
of
money
balances
held
by
households
(the
real
balance
effect)
are
such
that
full
employment
of
the
remaining
labor
and
balance
of
payments
equilibrium
are
automatically
maintained
at
a
given
exchange
rate.
In
this
case,
in
order
to
keep
real
household
income
unchanged,
the
government
again
releases
foreign
exchange,
which
we
can
conceive
as
being
done
indirectly
by
reducing
income
taxes,
thereby
inducing
increased
household
expenditure
and
decreased
exports
of
widgets.
15
c.
The
Shadow
Price
of
Labor
Continued:
A
Simple
Geometric
Illustration
The
verbal
description
for
deriving
the
shadow
price
of
labor
is
illustrated
for
the
simplest
widget
massage
model
in
Figure
2.
The
two
related
diagrams
show
the
demand
and
supply
conditions
for
widgets,
using
the
following
definitions: