\(\dot K (t) = sY(t) - \delta K(t)\), growth rate of capital (savings) minus depreciation (endogenous-- asking, what drives K?)
Dynamic solution:
\(k_t^{1- \alpha} = [k_0^{1- \alpha} - \frac{s}{(n + g+ \delta)}]e^{-(1- \alpha)(n+g+ \alpha)t} + \frac{s}{(n+g+ \delta)}\)
RCK Model
New variables:
- \(\theta\) is willingness to change present consumption for future consumption (i.e. if lower, then one wants to reduce consumption now for future consumption).
- \(\rho\) is the discount rate (i.e. lower means that money is worth more now).
- \(\gamma\)
Diamond Model
First-Order Linear Differential Equations with Constant Coefficient and Constant Term