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Ecological Economics Lecture 09 20th May 2010 Tiago Domingos Assistant Professor Environment and Energy Section Department of Mechanical Engineering Collaboration: Rui Pedro Mota [email protected] Temporal Comparison - Real vs Nominal • 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? Nominal GDP in: Item - 2007, €200 2007 - 2008, €575 Quantity Price Bread 100 €1.00 Real GDP in 2007 prices: Butter 20 €5.00 - 2007, €200 2008 Bread 160 € 0.50 Butter 22 € 22.50 - 2008, €270 Price Level GDP Deflator Price Level and GDP deflator • Nominal and real GDP are calculated as shown above. • GDP Deflatoryear x = (Nominal GDPyear x ÷ Real GDPyear x ) * 100. Year Nominal GDP Real GDP GDP deflator 2007 €200 €200 100 2008 €575 €250 230 • 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 Real vs. Nominal (Portugal) 200 Milliards euros 180 160 Gross domestic product at 2000 market prices 140 Gross domestic product at current market prices 120 100 80 60 40 20 0 1960 1965 Source: AMECO database 1970 1975 1980 1985 1990 1995 2000 2005 Price Level and CPI • 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 CPI and Inflation GDP deflator vs CPI • Both reflect the current level of prices relative to the level of prices in the base year. GDP Deflator CPI -Prices of all goods and services produced domestically. -Prices of all goods and services bought by consumers. - Compares the price of currently produced goods. - Compares a fixed basket of goods and services. GDP deflator vs CPI (Portugal) Inflation 35 Oil Price shock, 1973 30 25 20 % CPI GDP Deflator 15 10 5 0 1964 1969 1974 Source: AMECO database and UN data 1979 1984 1989 1994 1999 2004 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 W (t ) u(c( s ))e t s t u ''(c ) 0 u '(c ) ds – 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, W (t ) s t u(cs ) 1 s t • 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. Discounted Utilitarianism Ramsey Model • 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) f (k ) c k • The social planner (benevolent dictator) chooses how much the representative household should consume/invest (add to capital to provide consumption in future) max u(c )e t dt c s.t. 0 k f ( k ) c k , k ( 0) k 0 0 Discounted Utilitarianism Ramsey Model • Any solution (k (t ), c (t )) * * 0 must obey: 1 dc* 1 ' * du ' ( c ) c - Instantaneous elasticity f (k ) , * ' c dt dc u ( c ) of substitution between consumption in two dates dk * * * f (k ) c , k ( 0) k 0 0 dt lim u ' ( c* ( t ))k * ( t )e t 0 t • If the interest rate is the marginal productivity of capital, then the Ramsey rules rewrites as r g Discounted Utilitarianism • Elasticity of substitution between consumption at two points in time t and s, is given by d cs ct u ' (cs ) u ' (ct ) (c ) cs ct d u ' (cs ) u ' (ct ) • Taking the limit as s converges to t, it is obtained the inverse of the negative elasticity of marginal utility 1 du ' (c ) c 1 (c ) ' dc u ( c ) • The larger the elasticity the easier it is to forgo current consumption. Ramsey Rule r g • 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. Ramsey Rule with technology (Barro and Sala-i-Martin, p. 97) dK dk F ( K , AL) C K f (k ) c (n x )k dt dt K C C cˆ dA dL ˆ k , c , c , xA, nL, r f ' AL L AL A dt dt • Consumption per unit of effective labor r g x cˆ g cˆ • Consumption per capita r g g c c • Absolute consumption r G n C G C