On the indeterminacy of equilibrium in an endogenous growth model with non-separable preferences (Q2019320)

Equilibrium indeterminacy is known to arise in a model of endogenous labor supply with non-separable preferences in which production activities use only human capital. The authors consider a more general setup of the two-sector endogenous growth model studied by \textit{K. Mino} [Econ. Lett. 62, No. 3, 311--317 (1999; Zbl 0917.90055)] by allowing alternative specifications for leisure. The final sector uses effective units of labor to produce a good that is only used for consumption: \(c = (nh)^{\beta_1}(nh)_e^{\phi_1},\: (0\le \beta_1<1, \phi_1>0)\), where \(c\) denotes consumption and \((nh)_e\) stands for sector--specific externalities derived from the portion of human capital employed in this sector. New human capital is produced using time and human capital as inputs according to: \[ \dot h =\gamma (vh)^{\beta_2}(vh)^{\phi_2}-\eta h, \] with \(\gamma >0, \beta_2 >0, \phi_2>0, \beta_2 +\phi_2=1\), where \((vh)_e\) refers to sector--specific externalities and \(\eta\) denotes the depreciation rate of human capital. The equilibrium for the pure leisure specification is characterized in Section 3.