Key Equations:
From solving the constrained lifetime utility maximization problem of the households, we can find the dynamics of consumption:
\(\frac{\dot C_t}{C_t} = \frac{(r - \rho)}{\theta}\)
which says that the consumption changes over time by the interest rate minus the discount rate, over the coefficient of risk averseion (which is assumed constant here). Dynamics of capital:
\(\dot k_t = f(k_t) - c_t - (n + g)k_t\)
just like the Solow model, where the change in capital investment will be the income minus consumption and the break-even amount to mitigate for population growth and "effectiveness" growth.