Download Y/L

Ecological Economics
Lectures 04 and 05
22nd and 26th April 2010
Tiago Domingos
Assistant Professor
Environment and Energy Section
Department of Mechanical Engineering
Collaboration: Rui Mota
Economic growth: Stylized facts
• Big differences in output per capita across countries.
• Growth rates vary substantially across countries.
• Convergence: In the long run, all countries will converge to
the same growth rate and level of income per worker.
– Income per worker converges to the same level across
countries conditional on the countries being structurally alike.
• Conditional on structural differences across countries, a
lower level of initial output tends to be associated with a
higher rate of growth.
• Growth rates of GDP per capita have been relatively
constant around 1.5-2 percent in Western Europe and North
America for at least 130 years.
Economic growth: Kaldor (1961) Stylized facts
• Per capita output Y/L grows over time.
• Physical capital per worker K/L grows over time
• Rate of return to capital r nearly constant (profit on capital).
• Ratio of capital to output K/Y nearly constant
• Shares of labor wL/Y and physical capital rK/Y in national
income nearly constant.
Solow Model
• Solow (1956) – Main theoretical tool for economic growth until the
1980’s.
• 1987 Nobel prize in Economics for his contribution to the theory of
economic growth.
•
(1924- )
• In spite of being very limited and largely inappropriate to account for the
growth dynamics of modern economies, in particular the disparities of
economic growth across time and space, the Solow model is the starting
point for almost all analysis of economic growth. – Benchmark Model
Solow Model – Rationale
• Is it possible for an economy to enjoy positive growth rates
forever by simply saving and investing in its capital stock?
• Starting point: Try to relate the growth rate with the
willingness to save and invest.
• Simple model where the only source of growth is
accumulation of physical capital (durable physical inputs –
machinery, buildings, pencils ...).
• General growth model:
– Households own assets and inputs to production, and choose
fractions of their income to consume and save.
– Firms hire inputs (e.g., L, K) and use them with technology to
produce goods that they sell to households or other firms
– Markets exist for goods and inputs in production.
Solow Model – Assumptions
• Closed economy with no government.
• Single composite good is produced and transacted (this
means that if we have more than one good the relative prices
are constant):
– the good can be used for consumption and investment;
– the good is produced, using capital and labor;
• Investment allows for capital accumulation, therefore
physical capital is a reproducible input.
• Population grows at an exogenous rate and all factors of
production are fully employed.
• All markets, i.e., factors, product and financial markets are
perfectly competitive.
Solow Model – Assumptions
• Can capital accumulation explain observed growth?
• How does capital accumulation behave along time and what are the
explanatory variables?
• Consumers:
– Receive income Y(t) from labour supply and ownership of firms
S (t )  sY (t ), 0  s  1
– consume a constant proportion of income
C (t )  (1  s )Y (t )
Solow Model – Assumptions
• Labour augmenting production function: Y (t )  F ( K (t ), A(t ) L(t ))
• Constant returns to scale
F (  K ,  AL)   F ( K , AL)  y ( t )  f ( k ); k 
K
AL
• Positive and decreasing returns to inputs:
f (0)  0, f '( k )  0, f ''( k )  0
• Inada (1964) conditions:
lim f ' (k )  , lim f ' ( k )  0
k 0
k 
– Ensure the existence of equilibrium.
• Example of a neoclassical production function:
1
– Cobb-Douglas:
F ( K , AL)  K a  AL 
– Intensive form:
f (k )  k a
Solow Model – Dynamics
• Labour and knowledge (exogenous):
L
n
L
• Dynamics of man-made Capital
dK
 K  sY   K
dt
• Dynamics per unit of effective labor
k  s f k   n  g    k
• s f k 
•
- actual investment per unit of effective labour
n  g    k
- break-even investment.
A
g
A
Solow Model – Balanced Growth Path
k
 lim k (t )  k *
k0  0 t 
How do the variables of the
model behave in the steady
state?
K*
AL

n

g

K*
AL
k0
k0
Y*
 n g
*
Y
K * L*
Y * L*
g * *
*
*
K L
Y L
t
Solow Model – Dynamics
• On the Balanced Growth Path (BGP)
– Each variable is growing at a constant rate.
– Growth of output per worker is determined
solely by the technological progress
• Stylized facts (Kaldor, 1961):
K*
AL

n

g

K*
AL
– Growth rates of labor, capital and output are
roughly constant;
Y*
 n g
*
Y
– Capital/output ratio roughly constant;
K * L*
Y * L*
g * *
*
*
K L
Y L
– Output per worker and capital per worker are
rising.
Solow Model – Central questions of growth theory
• Only changes in technological progress have growth effects on per capita
variables.
• Convergence occurs because savings allow for net capital accumulation,
but the presence of decreasing marginal returns imply that this effect
decreases with increases in the level of capital.
• Two possible sources of variation of Y/L:
– Changes in K/L;
– Changes in g.
• Variations in accumulation of capital do not explain a significant part of:
– Worldwide economic growth differences;
– Cross-country income differences.
• Identified source of growth is exogenous (assumed growth).
National Accounts
• The System of National Accounts is a comprehensive accounting
framework within which economic data can be compiled and presented
in a format that is designed for purposes of economic analysis, decisiontaking and policy-making.
• Integrates a set of macroeconomic accounts, balance sheets and tables
based on a set of internationally agreed concepts, definitions,
classifications and accounting rules.
• Accounts compiled for a succession of time periods, thus providing a
continuing flow of information, indispensable for the monitoring,
analysis and evaluation of the performance of an economy over time.
Aggregation
• 5 Sectors:
– Households
– Firms
– Financial Intermediaries (banks, …)
– Governments (national and local)
– Rest Of the World (ROW)
• 4 Markets (Supply and Demand):
– Goods and services
– Resources (labor, land and capital)
– Money (loanable funds)
– Foreign exchange
Circular flow of income
Households
€
Factor
payments: Y
Factors
€
Expenditures: C
Output
2
1
3
Firms
• Factors: Labor, Land, Capital
• Factor payments: Wage, Rents, Interests, Profits – become income.
• Expenditures: on goods and services (output)
• 1 – Income approach: Y = Wage + Rent + interest + operating surplus
• 2 – Output approach: Y = market value of all produced output (Σ VA)
• 3 – Expenditure approach: Y = C
Circular flow of income
ΔGov
S
FI
Households
C
G
Gov.
Lend
Borrow
Tr
X
T
M
Y
ROW
Firms
I
• Balance to:
– Households: Y - Tnet = C + S, Tnet = T- Tr
– Firms: Y = C + I + G + X - M
– Government: ΔGov = Tnet - G
– FI: S + ΔGov + B - L = I
– ROW: X - M = L - B
- Market for outputs
National Accounts Identity
C
I
X
M