$ \frac{Y}{L} = \left(\frac{K}{Y}\right)
^\left(\frac{\alpha}{1-\alpha}\right)E $
$ \frac{d\ln(L)}{dt} = n $
$ \frac{d\ln(E)}{dt} = g $
$ \frac{d\ln(K)}{dt} = s\frac{Y}{K} - \delta $
$ g = \frac{\gamma}{1+\gamma}h + \frac{1}{1+\gamma}(\rho - n) $
$ n = \beta(y - \bar{y}) $ if $ y ≤ y_{peak} $
$ n_{max} = \beta(y_{peak} - \bar{y}) $
$ n = \left(\frac{y}{y_{peak}}\right)^{-\eta} $ if $ y ≥ y_{peak} $
$ n^* = {\gamma}h $
$ {\gamma}h = \beta(y - \bar{y}) $
$ y^* = \bar{y} + \left(\frac{\gamma}{\beta}\right)h $
Equilibrium as long as:
$ y^* ≤ y_{peak} $
$ h ≤ \frac{\beta(y_{peak}-\bar{y})}{\gamma} $
Requires: $ h > \frac{\beta(y_{peak}-\bar{y})}{\gamma} $