University of University of Greenwich Business Greenwich Business school school

MSc in Financial Management and Investment MSc in Financial Management and Investment AnalysisAnalysis

Economics 1112Economics 1112

Economics for Finance and Economics for Finance and Investment Analysis Investment Analysis

October 2008 October 2008

Doc. 11 - Doc. 11 - Demand for energy ; Demand for energy ; some guidelines for some guidelines for coursework question one coursework question one Dr M. PourhosseiniDr M. Pourhosseini

Consumer and Consumer and producer demandproducer demand We can study demand for energy by We can study demand for energy by

considering the requirements of considering the requirements of consumers and producers consumers and producers

We define a two stage budgeting process We define a two stage budgeting process In stage one the consumers divide their In stage one the consumers divide their

budget between the demand for energy budget between the demand for energy and other goods . In stage two they divide and other goods . In stage two they divide they energy budget between different they energy budget between different fuels fuels

CONSUMER CONSUMER

Stage 1: The Stage 1: The consumer must consumer must decide how to decide how to allocate total allocate total expenditure) expenditure) between broad between broad categories of categories of consumption Energy consumption Energy (E) and other Goods (E) and other Goods (X) subject to the (X) subject to the budget constraints: budget constraints:

),,(* MPPfE XAE

E

Consumer split Consumer split expenditure between expenditure between Gas and Electricity Gas and Electricity

),,(* EPPfGa ElGaGa

),,(* EPPfEl GalElEl

PRODUCER PRODUCER

Stage 1:A cost Stage 1:A cost minimising firm will minimising firm will try to minimise the try to minimise the cost (C) of achieving cost (C) of achieving its output target Q . its output target Q . It uses inputs capital It uses inputs capital (K ) and Energy (E) (K ) and Energy (E) in combinations in combinations determined by their determined by their relative prices and relative prices and target output : target output :

),,( QPPfE kAE

E

Producer split Producer split expenditure between expenditure between Gas and Electricity Gas and Electricity

),,(* EPPfGa ElGaGa

),,(* EPPfEl GalElEl

Derivation of Derivation of elasticities elasticities We need a functional form to We need a functional form to

estimate price and income estimate price and income elasticities. elasticities.

A common model is a log-log (or A common model is a log-log (or linear in logs model linear in logs model

We write a functional form and We write a functional form and then estimate the elasticities then estimate the elasticities

Log-Log( or Linear in Log-Log( or Linear in logs model logs model

The first item The first item

is the nominal is the nominal price of price of aggregate energy aggregate energy

is the is the nominal price of nominal price of other goodsother goods

is nominal is nominal income income

XP

AEP

M

XAE LnPaLnMaLnPaaLnE 3210

Functional form and Functional form and derivation of Elasticities : derivation of Elasticities :

Log-Log ModelLog-Log Model We use this functional form We use this functional form

Then we estimateThen we estimate1.1. The own –price elasticity of energy demandThe own –price elasticity of energy demand2.2. Income elasticity of energy demand Income elasticity of energy demand 3.3. The cross-price elasticity of energy demand The cross-price elasticity of energy demand

XAE LnPaLnMaLnPaaLnE 3210

The own –price The own –price elasticity of energy elasticity of energy demanddemand

1aLnP

LnE

E

P

P

EA

E

AE

AE

p

1aLnP

LnE

E

P

P

EA

E

AE

AE

p

Income elasticity of Income elasticity of energy demandenergy demand

2aLnM

LnE

E

M

M

EM

The cross-price elasticity The cross-price elasticity of energy demand of energy demand

3aLnP

LnE

E

P

P

E

X

X

XM

Imposing restrictionsImposing restrictions

The present form The present form allows for allows for money money illusion :illusion :

It is possible for It is possible for

In other words : In other words :

0 XEM

0321 aaa

Substitution Substitution restriction into the restriction into the equation equation In other words In other words

0321 aaa

)( 213 aaa

XAE LnPaLnMaLnPaaLnE 3210

XXAE LnPaLnPaLnMaLnPaaLnE 21210

Rearranging log log Rearranging log log form form

XXAE LnPaLnPaLnMaLnPaaLnE 21210

)()( 210XX

AX

P

MLna

P

PLnaaLnE

Partial Adjustment Partial Adjustment ModelModel These elasticities These elasticities

can be used to can be used to estimate a Partial estimate a Partial Adjustment Adjustment Model (PAM) Model (PAM)

THE LOG-LOG THE LOG-LOG MODEL MAY BE MODEL MAY BE REDEFINED IN A REDEFINED IN A TIME-SERIES TIME-SERIES CONTEXT CONTEXT

ttt ype 210*

Short term vs Long Short term vs Long term elasticities term elasticities PAM PAM

Where Where

)( 1*

21 tt eeee

10