(4.21) $ \left( \frac{Y_{t, alt}/L_{t, alt}}{Y_{t, ini}/L_{t, ini}} \right)^* = \left( \frac{n+g_{in}+\delta}{(n+g_{in}+\Delta g + \delta) \right)^{\theta} (1+ \Delta g)^t $

(5.7) $ \ln(E) = \ln(H) - \frac{\ln(L)}{\gamma} $

Then since:

(5.8) $ y^{*mal} = \left( \frac{s}{\gamma h +\delta} \right)^\theta E $

(5.9) $ \ln(\phi) + \ln\left( y^{sub} \right) + \ln\left(1 + \frac{\gamma h}{\beta} \right) = \theta \ln(s) - \theta \ln(\gamma h +\delta) + \ln(E) $

The population and labor force in the full Malthusian equilibrium will be:

(5.10) $ \ln(L_t^{*mal}) = \gamma \left[ \ln(H_t) - \ln( y^{sub}) \right] + \gamma \theta \left( \ln(s) - \ln(\delta) \right) - \gamma \ln(\phi) + \left( - \gamma \theta \ln(1 + \gamma h/\delta) -\gamma ln\left(1 + \frac{\gamma h}{\beta} \right) \right) $

$ \frac{dK}{dt} = sY - \delta K = \left( \frac{s}{\kappa} - \delta \right) K $