Lecture 12_Modeling Energy Demand

8/2/2019 Lecture 12_Modeling Energy Demand

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HE310: Energy Economics

Lecture XII

Modeling Energy Demand

03 November 2011


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Modeling Energy Demand

Energy Balances Modeling Energy

Household or Consumer Demand

Budget Constraints Indifference Curve

Income Expansion Path

Engel Curve and Consumption Changes

Industrial, Commercial and Electricity Sectors Marginal Revenue Product for a Producer

Econometric Issues

2


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Energy Balances An accounting procedure

The primary sources of energy, the transformation of energy andthe final consumption of energy

An overall snapshot of the energy situation at a given time

for a given region

Sources of primary energy (E-prim) minus stock or changes

(Stk) and losses (Loss) must balance with end useconsumption (E-end) of energy products

E-prim Stk Loss = E-end

The Total Primary Energy Supply (TPES)

What the region produces plus what they buy from others(imports) minus what they sell to others (export) minus

international marine bunkers (bunkers: fuel oil sold to ships

engaged in international transport) minus any stock or inventory

changes (stock)

TPES =production + imports exports bunkers stock 3


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World Energy Balances, 2006

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Disaggregated U.S. Energy Consumption, 2002

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World Oil Balances, 2006

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World Coal Balance, 2006

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Modeling Energy

End-use demand Consumers use energy for the end-use products they

consume

Factor demand

All other sectors use energy as an intermediate goodor as a factor of production

Modeling energy

Through simple optimization models, this illustrates

how optimal decisions should be made for both end-use and factor demands for energy

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Household or Consumer Demand

Consumers have n goods to choose

A simple model

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goodththeofconsumedamounttheis

andgoodththeofpricetheis

income,theisYwhere

...

good.ththeofnconsumptiorepresents

andfunctionutilitytheiswhere

),,...,,(

i

12211

21

i-Q

i-P

QPQPQPQPY

i-X

U

XXXU

i

n

i iinn

i

n

==+++=


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Budget Constraints

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N= Y/PN (PE/PN)E

Nare all non-energy goods, Eare all energy goods

PN is the price of non-energy goods, PE is the price of energy goods

Y= 160, PE= 4, PN= 2

N= 80 2E

Y = 320 PE:4 -> 8N = 80 2E


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Indifference Curve and Marginal Rate of

Substitution

11

5.05.0

),(

),(

ENU

ENUU

ENUU

=

=

=

)/()(

0

N

U

E

U

dE

dN

dEE

UdN

N

UdU

dEE

UdN

N

UU

=

=

+

=

+

=

The consumer would trade off Nfor Eat point a.


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Map of Indifference Curves and Highest

Utility on the Budget Constraint

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The isoquant I1represent a lower level of utility than I2The slope of the indifference curve:

The slope of the budget constraint:


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Tracing Out a Consumers Income

Expansion Path

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B1 = 160

B2 = 240

B3 = 320


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Engel Curve and Consumption Changes

with Changing Energy price

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Engel Curve

Income on the horizontal axes

Consumption of a good on a

vertical axes

When the price lowers

from 4 to 2 to 1, the

optimal consumption ofthe two goods moves

from a to b to c.


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Consumption as a Function of Price

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Derived from the Engels Curve, putting

energy consumption on the horizontal

axes and the price on the axes gives the

traditional demand curve


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Comparing a Subsidy with Equal Cost Cash

Payment

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A per unit energy subsidyThe initial budget: PEE+ PNN= B

The subsidized budget constraint

(PE - sb)E+ PNN= B

B = budget, sb= the subsidy per unit

This subsidy is equivalent to a price

decreases and moves the consumers

from point a to b

Suppose giving the consumer the same amount of income as the subsidy costs

the government at the original prices.

The new budget line is represented by the dotted line that goes through point b.

The consumer would choose point cunder the increase income.


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Derivation of Demand Curve

Max U(E, N) subject to PEE+ PNN= Y

Y- PEE+ PNN= 0

= U(E, N) + (Y- PEE+ PNN)

General solutions forEand N

E= f(PE, PN, Y)

N= g(PE,PN, Y)

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N

N

E

E

P

U

P

U=


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Factor Demand for the Industrial,

Commercial and Electricity Sectors

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Suppose a firm sell goodX

To produceX, it needs energy (E) and non-energy (NE)

Max = PXX(N, E) PNN PEE

AssumeX

E>0,X

N> 0,X

EE< 0,X

NN< 0

N

N

E

E

N

E

N

E

N

E

NX

EX

NNXN

EEXE

P

X

P

X

P

P

X

X

P

P

XP

XP

PXP

PXP

=

=

=

==

==

0

0

Factors should be hired up to the

point where the ratio of their

marginal products is equal to the

ratio of the prices

Factors should be hired up to the

point where the marginal product

per dollar is equal across factors


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Marginal Revenue Product for a Producer

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EEXE XP

E

X=

EP

The slope of marginal revenue product


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Econometric Issues

Energy demand equations can be estimated on actual

energy data using statistical techniques

Many energy demand models have been estimated

ignoring the supply side of the market

Shifting demand and supply over time trace out prices

If both the demand and supply curves shift, we will not get the

demand or the supply curve

Simultaneous system bias

This problem occurs when an equation is estimated from asimultaneous system

Unaccounted for random events are called errors

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Changes in Demand and Supply over Time

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a) The demand equation can be estimatedb) The supply equation can be estimated

c) The resulting nine data points make neither the demand nor the

supply curve be estimated


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Price and Error are Related in Demand

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A positive error raises the price

A negative error lowers the price

This relationship between the errors and the price

affects the estimates


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The Price and Errors are not Independent

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Small circles: observations when the errors and price are not related

When the estimation is based on the observations represented by the

xs, the estimated line would be steeper than the true line


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When to Use OLS to Estimate Demand

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When supply is perfectly elastic, errors in the demand equation do not

influence supply. OLS is appropriate

If governments regulate price as they have often done in the electricitysector, random shifts in demand are the prevented from changing the price.

OLS is appropriate

If marginal costs are flat (i.e., the supply curve is the marginal cost curve in

a competitive market), supply will be perfectly elastic. OLS is appropriate


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Primary Results of New Survey Work

The average elasticities in most categories are well

behaved.

The short run price and income elasticities are usually

between about 20% and 60% of the long run price and

income elasticities

The exceptions on price: vehicles miles traveled, kerosene and

fuel oil

The exceptions on income: coal, residential energy, residential

gas and industrial gas In most cases, there is a quite lot of variation across

studies

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Variations in Price and Income Elasticities

Coal price elasticities are reasonably consistent acrossstudies but income elasticities are negative for the U.K.

and positive for Japan and Colombia

Diesel fuel estimates are income elastic and are all from

developing countries All elasticity estimates for the highway fuel demand

(gasoline and diesel fuel) are from Europe and income

elastic

The average price elasticity of gasoline is -0.6 and theincome elasticity is 0.7

Non-petroleum energy sources are more income elastic

than oil and the heavier end of the barrel

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Key Points

Energy balances An accounting procedure and TPES

Modeling energy

Household budget constraints, indifference curve and Engel

curve Comparison of a per unit energy subsidy and equal cost

cash payment

Derivation of energy demand curve

Factor demand and marginal revenue product of a producer Econometric issues

Identification problem and simultaneous system bias

Uses of ordinary least squares (OLS)

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Supplements

Determinants of Demand in Energy Markets

Various Elasticities

A Theoretical Framework for Deriving Energy Demand

Empirical Results and Interpretation of Elasticity of Energy

Demand

Demand for Crude Oil

Estimated Equation, Derivation of Long-run Elasticity and

Empirical Results

Survey of Empirical Studies (Dahl, 1993 and 1994)

Oil Price and Income Elasticities; Gasoline Price and IncomeElasticities; Transport Fuel Demand Elasticities

Price Elasticities of U.S. Consumer Expenditures

Price Elasticities of U.S. Investment Expenditures

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Determinants of Demand in Energy Markets

Non-price determinants Income or GDP: Per capita or aggregate Prices of related goods Cause a change in demand: The demand schedule

shifts An increase in population shifts the demand curve to the

right At every price, more energy is demanded

Price/quantity relationship

Does not provide a whole picture But fundamental and a starting point

Price changes lead to changes in the quantitydemanded

Price does not change demand


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Elasticity of Demand (Recap)

Elasticity

A measure of the percentage change in one variable in

respect of a percentage change in another variable

Elasticity of demand Usually taken to refer to the (own) price elasticity of

demand.

However, care should be taken to specify which

elasticity of demand is being discussed Cross elasticity of demand

Income elasticity of demand


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Price Elasticity of Demand (Recap)

The responsiveness of the quantity demanded for a good to its ownprice

Price elasticity of demand (p)

p = 1

Unit elasticity

p < 1

Inelastic demand

Unresponsive to price change p > 1

Elastic

Responsive to price change

p = 0

]/[

]/[

(P)priceinchange%

(Q)quantityinchange%

PdP

QdQ

p

=

=


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Cross and Income Elasticity (Recap)

Cross elasticity The sensitivity of quantity demand for goodx to price changes in

good y(xy)

The greater the number of switchable, the closer will xybe to unity

xy> 0, Two goods are called substitute

xy< 0, Two goods are called complementary

Income elasticity The responsiveness of demand for a good to changes in income

I(I)

]/[

]/[

ofpriceinchange%

ofquantityinchange%

yy

x

xy

PdP

QdQ

y

x

=

=

]/[

]/[

inchange%

inchange%

IdI

QdQ

I

QI

=

=


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Demand for Energy: Theoretical Framework

(Nordhaus, 1979)

Preference relationship between two broadly defined goods Energy services (E)

Non-energy goods (X)

Utility function U = U(E, X)

With budget constraint

Y = pEE + X

Y= Income in terms of non-energy good

pE= The relative price of energy to non-energy goods

This preference relationship yields consumption choices (orsegments) representing a chosen point when faced by a particularconstraint This utility function yields consumption bundles such as

c1, c2, .., cn


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Preference Function (E, X)

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Energy Demand Function: Derivation

Every time a consumer is faced with

Price-income pair (pE, Y)

A choice of quantity (E, X)

Energy demand function, maximizing index of consumption ct, can

be written subject to budget constraint

Eit = E(pit, Yt)

Wherepit is price ofi-th energy resource at time t and income yt is the

level of income at time t Function form

i

it

n

t

it

i

it

n

i

itt EXEAXc )(

11

=

=

++=

11)1/(1 )1(,)1(,)(

,......,1,

===

==

iiiiiiii

iitiit

i

ii

Akwhere

NiYpkE


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Demand Equations for Estimation

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Elasticity of Demand: Empirical Results

Price Income

Aggregate -0.85(0.10)

0.79

(0.08)

Transportation -0.36

(0.12)

1.34

(0.08)

Residential -0.79(0.08)

1.08

(0.12)

Industry other than energy -0.52(0.17)

0.76

(0.16)

Energy -0.58(0.11)

-0.05

(0.12)

Dependant Variable: per capita energy ineach sector


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Empirical Results: Interpretation

The long-run response of energy consumption to price is verysubstantial

Most inelastic is transportation sector Relative inelasticity is quite plausible

The least possibility for technological substitution in this sector

Followed by intermediate values for industry other than energy andenergy sector

Residential sector is the most elastic Relatively high elasticity is also plausible

High degree of substitutability between fuels and capital in this sector

Income elasticity Private automobiles are both highly income elastic and relatively

energy-intensive

High income elasticity of transportation


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Demand for Crude Oil (Cooper, 2003)

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The Estimated Equation

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The estimated equation for the USA


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Derivation of Long-run Elasticity

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Derivation of Long-run Elasticity

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Empirical Studies (Dahl, 1993 and 1994):

Demand for Oil and Oil Products

The demand for oil in developing countries

Income elastic and income elasticity is greater than

1.32

A small but negative price elasticity (-0.30) The demand for oil products in developing

countries

Long-run gasoline price elasticity is as high as -1.25

Short-run gasoline price elasticity is as low as -0.07

Income elasticity of gasoline is greater than 1

Kerosene appears to be less income elastic


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Oil Price and Income Elasticities

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Source: Dahl (1993)


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Gasoline Price Elasticities

45Source: Dahl (1994)


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Gasoline Income Elasticities

46Source: Dahl (1994)


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Transport Fuel Demand

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Price Elasticities of U.S. Consumer

Expenditures: 1970-2006 (Kilian 2008)

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Price Elasticities of U.S. Investment

Expenditures: 1970-2006 (Kilian, 2008)

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Lecture 12_Modeling Energy Demand