Key Equations:
Dynamics of consumption:
\(\frac{C_{2, t + 1}}{C_{1, t}} = (\frac{1 + r}{1 + \rho})^{\frac{1}{\theta}}\)
Dynamics of capital:
\(\dot k = 0 = k^* = s(f'(k^*)) \frac{f(k^*) - k^*f'(k^*)}{(1 + n)(1 + g)}\)
Solving the model with CD production function and log utility will yield:
\(k^*=( \frac{1 - \alpha}{(2 + \rho)(1 + n)(1 + g)} )^{\frac{1}{1 - \alpha}}\)