Advanced Macroeconomics
Solow model: Defintion
Point of this model is to link capital accumulation to (long-term) economic growth, including a
(fix) savings rate which makes the model in itself less flexible.
Savings rate depends on (Solow model)
interest rate, life cycle, and income
1 multiple choice option
Constant returns at scale (assumption for F of production in Solow model)
Double the inputs, doubles the outputs
f(0) = 0 (Solow model)
no physical capital, no output in production
f'(k) > 0 (Solow model)
Increase in capital per human capital, increases production output
f''(k) < 0 (Solow model)
For every additional unit of capital, we get less and less output
Constant growth rate of A(t) (Solow model)
Å(t) = gA(t)
Exponential growth rate of A(t) (Solow model)
A(t) = A(0)e^gt
Depreciation rate (Solow model)
Pareto efficiency
the situation where one person cannot be better off without making someone else worse off.
Exogenous growth models
Solow, Ramsey, and Diamond (OLG); growth is driven by e.g., preferences or technologies
, Endogenous growth models
markets can display inefficiencies which may be corrected by the government
Consumption growth (endogenous growth models)
Varies between real gross return on capital (A) and discount rate
Romer 1990
Technological progress, resulting from investment in R&D by profit-seeking firms, leads to
increasing returns to scale and sustained growth. This model marked a significant shift from
traditional growth theories by showing how endogenous factors, particularly knowledge
creation and spillovers, can continually fuel economic expansion without diminishing returns.
Ramsey Model
Growth model, where savings rate is endogenously; Firms are owned by households (fixed)
Household budget constraint (Ramsey)
consumption + investment = Labor income + capital income+ profits
Dynamics of Consumption (Ramsey)
is at (c° = 0 | k*); on the left: higher return on capital, increase in consumption per unit of
effective labor; on the right: lower return on capital, thus a decrease in consumption per unit
of effective labor
Dynamics of Capital (Ramsey)
Fall in discount rate (Ramsey, saddle path)
c°-line moves to the right, moving the saddle path point, increasing consumption and
decreasing the savings rate.
Alpha (Cobb Dou
Alpha is the intensity of capital production
(1 - Alpha) in Cobb-Douglas
(1 - Alpha) is the intensity of effective labor in production
Solow model: Defintion
Point of this model is to link capital accumulation to (long-term) economic growth, including a
(fix) savings rate which makes the model in itself less flexible.
Savings rate depends on (Solow model)
interest rate, life cycle, and income
1 multiple choice option
Constant returns at scale (assumption for F of production in Solow model)
Double the inputs, doubles the outputs
f(0) = 0 (Solow model)
no physical capital, no output in production
f'(k) > 0 (Solow model)
Increase in capital per human capital, increases production output
f''(k) < 0 (Solow model)
For every additional unit of capital, we get less and less output
Constant growth rate of A(t) (Solow model)
Å(t) = gA(t)
Exponential growth rate of A(t) (Solow model)
A(t) = A(0)e^gt
Depreciation rate (Solow model)
Pareto efficiency
the situation where one person cannot be better off without making someone else worse off.
Exogenous growth models
Solow, Ramsey, and Diamond (OLG); growth is driven by e.g., preferences or technologies
, Endogenous growth models
markets can display inefficiencies which may be corrected by the government
Consumption growth (endogenous growth models)
Varies between real gross return on capital (A) and discount rate
Romer 1990
Technological progress, resulting from investment in R&D by profit-seeking firms, leads to
increasing returns to scale and sustained growth. This model marked a significant shift from
traditional growth theories by showing how endogenous factors, particularly knowledge
creation and spillovers, can continually fuel economic expansion without diminishing returns.
Ramsey Model
Growth model, where savings rate is endogenously; Firms are owned by households (fixed)
Household budget constraint (Ramsey)
consumption + investment = Labor income + capital income+ profits
Dynamics of Consumption (Ramsey)
is at (c° = 0 | k*); on the left: higher return on capital, increase in consumption per unit of
effective labor; on the right: lower return on capital, thus a decrease in consumption per unit
of effective labor
Dynamics of Capital (Ramsey)
Fall in discount rate (Ramsey, saddle path)
c°-line moves to the right, moving the saddle path point, increasing consumption and
decreasing the savings rate.
Alpha (Cobb Dou
Alpha is the intensity of capital production
(1 - Alpha) in Cobb-Douglas
(1 - Alpha) is the intensity of effective labor in production
