W10P2 - Notebooklm Flashcards
Solow Growth Model
This model, invented by Robert Solow in 1956, is important for understanding long-term economic growth and serves as the backbone for many dynamic macroeconomic models, including those used for business cycle analysis. The main idea revolves around capital accumulation.
Capital Accumulation
The general idea is that a certain fraction of output is saved, and this saving becomes investment. Investment adds to the capital stock, and a higher capital stock allows for more production, leading to more saving and further increases in the capital stock.
Steady State
A state where investment is equal to depreciation, resulting in no change in the capital stock. In the Solow model, the economy grows only when converging towards this point.
Production Function
Similar to previous weeks, this function shows that output depends on capital and labour. In per capita terms, it is represented as y = f(k), where y is output per capita and k is capital per capita.
Diminishing Returns to Capital
When you increase capital, output increases, but the increase in output from adding more capital becomes less and less. Graphically, the production function flattens out.
Constant Returns to Scale
If both capital and labour are doubled, then output is also doubled. Mathematically, if you multiply both capital and labour by a constant (z), output is also multiplied by z. This property allows the production function to be expressed in per capita terms.
Per Capita Variables
Absolute GDP is less important than per capita GDP for comparisons between countries with different population sizes. Per capita values are denoted by lowercase variables (e.g., y for income per capita, k for capital per capita). They are calculated by dividing the original variable by the population size (L).
Closed Economy (in the Solow Model)
For simplicity, the initial Solow model assumes a closed economy with no government, focusing on long-run trends where government spending and net exports average out to zero. In this case, all savings are invested.
Saving Rate (s)
A certain fraction (s, lowercase) of income (y) is saved. Total saving (S, uppercase) equals s times total income (Y).
Investment (i) in Solow Model
In a closed economy with no government, investment (in per capita terms, i) is equal to saving per capita, which is the saving rate (s) times per capita income (y): i = sy = sf(k). Investment adds to the capital stock.
Depreciation (δ)
Over time, a certain fraction (δ, delta) of the capital stock disappears due to factors like obsolescence and wear and tear. The depreciation rate might be around 10-15%.
Capital Law of Motion
The change in the capital stock per capita (Δk) is equal to investment per capita minus depreciation per capita: Δk = i - δk = sf(k) - δk. This is the fundamental equation in the Solow model.
Convergence to Steady State
If investment (sf(k)) is greater than depreciation (δk), the capital stock increases. If depreciation is greater than investment, the capital stock decreases. The economy moves towards the point where investment equals depreciation – the steady state.
Economic Growth in Solow Model (Initial Stage)
The economy experiences growth (increasing per capita capital and output) only while it is converging towards its steady state. Once the steady state is reached, growth in per capita terms ceases.
Steady-State Capital Stock (kss) with Cobb-Douglas
With a Cobb-Douglas production function (y = k^α), the steady-state capital stock is derived by setting investment equal to depreciation (sk^α = δk) and solving for k, resulting in: kss = (s/δ)^(1/(1-α)).
Steady-State Income per Capita (yss) with Cobb-Douglas
Once the steady-state capital stock is known, steady-state income per capita is found using the production function: yss = (kss)^α = (s/δ)^(α/(1-α)).
Determinants of Steady-State Income per Capita
In the Solow model with a Cobb-Douglas production function, the steady-state income per capita positively depends on the saving rate (s) and negatively depends on the depreciation rate (δ).
