Ecological EconomicsLecture 09

20th May 2010

Tiago DomingosAssistant Professor

Environment and Energy SectionDepartment of Mechanical Engineering

Collaboration: Rui Pedro Mota

rmota@ist.utl.pt

• What part of the change in national accounts aggregates at current prices stems from a change in the quantities produced and what part stems from a change in prices?

Temporal Comparison - Real vs Nominal

Item Quantity

Price

2007

Bread 100 €1.00

Butter 20 €5.00

2008

Bread 160 € 0.50

Butter 22 € 22.50

Nominal GDP in:

- 2007, €200

- 2008, €575

Real GDP in 2007 prices:

- 2007, €200

- 2008, €270

Price Level

GDP Deflator

• Nominal and real GDP are calculated as shown above.

• GDP Deflatoryear x = (Nominal GDPyear x ÷ Real GDPyear x ) * 100.

• Nominal GDP increases because production increases and because prices increase (Inflation).

• Use the GDP deflator to take out the effect of inflation and reveal real GDP.

• The Base year for current SNA is 2000.

• Inflation rate = rate of change of price level, 130% = (230-100)/100*100

Price Level and GDP deflator

Year Nominal GDP

Real GDP GDP deflator

2007 €200 €200 100

2008 €575 €250 230

Real vs. Nominal (Portugal)

0

20

40

60

80

100

120

140

160

180

200

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Mill

iard

s eu

ros

Gross domestic product at 2000market prices

Gross domestic product atcurrent market prices

Source: AMECO database

• Consumer Price Index (CPI)

– It is based on a fixed (changes every 5 years) basket of goods that are normally an important part of households’ consumption.

• 1 – Fix the Basket - which prices are most important to the typical consumer? Put weights by surveying consumers and finding the basket of goods and services that the typical consumer buys.

• 2 – Find the prices for each good and service in the basket.

• 3 – Compute the basket’s cost (price * quantity)

• 4 – Choose a base year and compute the CPI Formula

• 5 – Compute inflation as the rate of change in CPI

Price Level and CPI

CPI and Inflation

GDP deflator vs CPI

• Both reflect the current level of prices relative to the level of prices in the base year.

-Prices of all goods and services produced domestically.

- Compares the price of currently produced goods.

-Prices of all goods and services bought by consumers.

- Compares a fixed basket of goods and services.

GDP Deflator CPI

GDP deflator vs CPI (Portugal)

Inflation

0

5

10

15

20

25

30

35

1964 1969 1974 1979 1984 1989 1994 1999 2004

% CPI

GDP Deflator

Source: AMECO database and UN data

Oil Price shock, 1973

Calvin and Hobbes on time preference

• What is more valuable: enjoyment now or later? – Time preference or discount rate is the rate at which the agent is willing to postpone

consumption.

• Is Calvin’s discount rate high or low, with regard to smacking Susie? – The role of uncertainty and sunk costs.

Calvin and Hobbes on time preference

• Very high discount rate is not prudent.

• In the presence of uncertainty, discount the future at its lowest possible rate. (Weitzman, 1998 JEEM)

Discounted Utilitarianism

• Representative household’s welfare at time t

– Utility depends on present consumption bundle.

– Welfare depends on the present and future utilities.

• Discount factor: €1 in T periods from now, is worth exp(−rT ) today. Same applies to utility.

• In discrete time,

• is the utility discount rate, i.e., the rate at which the value of a small increment of utility changes as its date is delayed.

( ) ( ( )) s t

tW t u c s e ds 0''( ) '( )u c u c

1

( )( ) s

s ts t

u cW t

• Ouput is produced using capital and labor (Assume a constant population normalized to 1). Capital does not depreciate. There is no technological progress.

• The output is either consumed or invested, i.e., added to the capital stock (as in Solow’s model)

• The social planner (benevolent dictator) chooses how much the representative household should consume/invest (add to capital to provide consumption in future)

( )f k c k

Discounted Utilitarianism Ramsey Model

0max ( ) t

cu c e dt

00 0( ) , ( )k f k c k k k

s.t.

• Any solution must obey:

• If the interest rate is the marginal productivity of capital, then the Ramsey rules rewrites as

0

1 1

0 0

0t

t

dc du c cf k

c dt dc u c

dkf k c k k

dtu c t k t e

* '' *

* '

** *

' * *

( )( ) ,

( )

( ) , ( )

lim ( ( )) ( )

0

* *( ( ), ( ))k t c t

Discounted Utilitarianism Ramsey Model

r g

- Instantaneous elasticity of substitution between consumption in two dates

Discounted Utilitarianism

• Elasticity of substitution between consumption at two points in time t and s, is given by

• Taking the limit as s converges to t, it is obtained the inverse of the negative elasticity of marginal utility

• The larger the elasticity the easier it is to forgo current consumption.

' '

' '

( ) ( )( )

( ) ( )s ts t

s t s t

d c cu c u cc

c c d u c u c

11'

'

( )( )

( )

du c cc

dc u c

Ramsey Rule

• Ro – Discount rate. Used to compare the welfare of generations living in different times.

• h – Curvature of utility function. Aversion to inequality across/within generations.

– How peoples’ wellbeing changes as income increases.

– Large h means larger aversion to intertemporal inequality.

• Ro and h depend on peoples’ preferences.

• G is related to economic growth and technological progress.

r g

Ramsey Rule with technology (Barro and Sala-i-Martin, p. 97)

• Consumption per unit of effective labor

• Consumption per capita

• Absolute consumption

r g x

( , ) ( ) ( )dK dk

F K AL C K f k c n x kdt dt

'ˆˆ, , , , ,

K C C c dA dLk c c xA nL r f

AL L AL A dt dt

r G n

r g

ˆ

ˆc

gc

cg

c

CG

C