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RAINS and Chapter 14
ECON 4910
The Rains Model
• An example of applied environmental
economics.
• Illustrates how economic theory is
translated into a real world model.
• The lack of data makes compromises
necessary.
• This implies a few warts.
What is captured by the RAINS
model?
• Several versions of the model, some with
sulphur, NOx, ammonia etc.
• Here we focus on the sulphur model.
Components of the Rains model
• 38 regions (For the most part countries). These
are the sources of pollution, ei.
• 700 grid squares covering Europe, each 150 km
×150 km. These are receptors of pollution, dj.
• A meteorolocial model, a matrix where the
coefficent aij is the fraction of pollution from i that
ends up in j.
dj = Σiaij ei + bj
bj is exogenous depositions from sources not
covered in the model. Mainly United States
More components of the Rains
model
• Ecological consequences – A function that
maps depositions into ecological
consequences – fraction of ecosystems in
a grid square that is severly damaged.
• These functions are called critical loads.
The 5% critical load implies that 5% of
ecosystems will be destroyed or damaged.
• Stepwise function (Draw figure on Board)
The cost module
• For each source there is a purification cost
curve ci(ei).
• Purification is the cost of reducing
emissions keeping output constant
• Marginal cost curves in steps.
• Represented by ci = iei + Bi
The model
• Minimise ∑ci j=1,2 … , 38
• subject to ci ≥iei + Bi
dj = Σiaij ei + bj ≤ Di i = 1,2,…,700
Di are usually n% critical loads. That is we
allow 5% of the ecosystems in each grid to
be destroyed or severly damaged
Feasibility
• Turns out 5% critical loads are not
feasible. (Can’t be done)
• Question is: How to modify the model? Let
us try Gap Closure for the non-feasible
constraints.
• dj ≤ σ(dj(historical) – Dj) + Dj.
• Here σ is the ”percentage of closure”
• Alternative: Area exceedance closure
Now Questions
• What compromises have been made?
– Exogenous output
– No valuation of damages. Arbitrary protection
at 5% of ecosystems.
– Gap Closure not even related to ecosystem
protection
• So, is this a good model?
Economy-Wide effects
• Into macro-economics and the effect of
environemental regulation on total
productivity.
• Issue # 1. How does environmental
protection affect productivity.
• Issue # 2. How does environmental
protection affect our measures of
productivity
Productivity growth
• Production grows for three reasons:
– Increased use of inputs (such as labor and capital)
– Increased efficiency
– Technological progress
• Problem right here. Production must be
measured properly, i.e. include environmental
services. However, all three may lead to less
production of environmental services.
Total Factor Productivity Growth
• Consider the macro production function
Y=Af(L,K).
• Here A is a technology variable assumed
to capture the effect of progress.
(Einsteins theory of relativity, The Slutsky
Equation and the invention of Tofu.)
Some manipulations to decompose
productivity growth
• Differentiate to get
ΔY = ΔAf(L,K) + AF’LΔL + AF’KΔK
Divide by Y to get:
ΔY/Y =
ΔA/A + (LAF’L/AY)(ΔL/L) + (KAF’K/AY)(ΔK/L)
Use that pL = pYAF’Land pK = pYAF’K. and zero
profits in macro equilibrium to get:
Finally…
• Á/A = Ý/Y – sLĹ/L – sKK/K ´
Here sL = pLL/(pLL + PKK) and
sK = pKK/(pLL + PKK)
sK and sL are cost shares.
Technological growth Á/A is the increase in
production not attributed to increased input use.
The effect on prouctivity when we
look at a bad measure
• Productivity growth is often reported only as Labour
productivity growth.
• What is the effect of environmental regulations that
raises the price of capital?
Green National Accounting
• Why national accounting?
• Indispensable tool for planning purposes.
Macroeconomic policy without national
accounting does not make much sense.
• Important metric for people with a size
fetish. My GDP is bigger than your GDP.
• For both purposes it is important to get
things right.
Example - China
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Example - China
• GDP per capita in 2004: US$ 5600
• US GDP per capita in 2004: US$40100
• So USA is more than 7 times as rich as
China
• China GDP per capita grew at 9.1% in 2004
• USA grew at 4.4%
• If this continues…
But something is a amiss
• Each year 400000 Chinese die from
airpollution
• 70% of China’s freshwater is polluted to
the point of being undrinkable
• These things are not measured
What can go wrong with national
accounting
•
Some things are not measured correctly or at
all
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Goods not produced for sale in a market e.g. raising
kids, house cleaning, pollution induced health
problems.
Goods that are produced by government e.g. the
value of education
Prices do not reflect social cost
Some things are categorized wrong.
–
Extraction of natural resources such as fish and oil
represents (possibly) depletion of wealth rather than
production of income.
National Accounting
• Y = C + G + I + A – B.
• GDP equals Consumption + Real
Investment + Financial Investment through
trade surplus. All measured at market
prices.
• Here we only consider a closed economy
without a government.
Deriving GDP measure from a
Optimally Managed Economy
• Consider the following economy:
• Utility W=∑tU(ct)βt with Kt+1 – Kt = F(Kt,Rt)
– δKt – ct and Et+1 – Et = f(Et) – Rt
• Lagrangian for this problem is
• Λ= ∑t(U(ct)βt – λ(Kt+1 – Kt – (F(Kt,Rt) – δKt)
– ct) – μ (Et+1 – Et – (f(Et) – Rt))
• R is a natural resource
Deriving GDP measure from a
Optimally Managed Economy
• Let us look at the first term in the
Lagrangian:
(U(c0)β0 – λ(K0+1 – K0 – (F(K0,R0) – δK0) – ct)
– μ (E0 +1 – E0 – (f(E0 ) – R0 ))
Does it look familiar?
• How about now?
(U’()c0β0 – λ(K0+1 – K0 – (F(K0,R0) – δK0) –
ct) – μ (E0 +1 – E0 – (f(E0 ) – R0 ))
The point:
• If the market prices are equal to the shadow
prices and to marginal utility, GDP for period t is
equal to the corresponing term in the
Lagrangian! This can be shown formally but is a
bit tricky.
• (U’()c0β0 – λ(K0+1 – K0 – (F(K0,R0) – δK0) – ct) –
μ (E0 +1 – E0 – (f(E0 ) – R0 ))
=
• (pc0 – pK(Capital investment) – pE(Change in
resource stock))
A wrongly calculated GDP
• (pc0 – pK(Capital investment) +
pE(Resource extraction))
• Two errors are made. Resource extraction
counts as positive when it should be
negative (and vice versa)
• Note: In a steady state economy this does
not matter.
The relationship between wealth
and GDP
• It can be proven that if NNP is measured
correctly then:
– Wealth = NNP/Discount rate
– An increase in NNP implies higher utility
Issues not touched upon:
• Adjusting GDP for risk?
Catastrophic risk. The easy way is NNP +
Pr(catastrophe in a year)×Cost of catastrophe
• – Risk distributed across population. Very
contested topic
• – Income distribution?
Income distribution
• Although China is growing rapidly, a
largepart of the population is left behind.
– Imposes political risk on future NNP
development.
– Is a dollar to Farmer Poor Joe the same as a
dollar toBill Gates?
• Is distributionally skewed NNP growth
sustainable?
Income distribution - USA
• From 1985 to 2003, the richest 1% saw an
increase in income equal to 60% (adjusted
for inflation)
• From 1985 to 2003, the richest 1% saw an
increase in income equal to 2% (adjusted
for inflation)
• Based on tax returns. The truth is even
worse.
• Recipe for revolution