Growth Models
Solow Growth Model
- One sector, closed economy with no government
- \(g, n, \delta\) are exogenous and constant
- Ex ante saving equals ex ante investment
- The production function must have constant returns to scale (homogeneous of degree one) and diminishing marginal returns
- Recall, the growth rate of a variable can be found taking the time derivative of its natural log
Key Equations:
The production function in intensive (per effective worker) form:
\(y_t = k_t ^\alpha\)
In equilibrium,
\(sf(k_t) = (n + g + \delta) k_t\)
And the golden-rule level (optimal value of the saving rate to maximize consumption):
\(f'(k_t) = (n + g + \delta)\)
Corresponding Graphs:
Effects of...
Ramsey-Cass-Koopmans
- Two-sector, one-commodity economy: households supply labor and capital to firms
- These inputs are paid their marginal products (i.e. w and r). Mathematically per effective worker, \(w_t = k_t - k_t(f'(k_t))\)