If we introduce leisure into a standard human capital accumulation framework without physical capital and consider a mass 1 of infinitely-lived workers are endowed with 1 unit of time at each point of time where workers can allocate the 1 unit of time between production function, leisure and human capital accumulation. Utility function becomes:

u(c(t), l(t)) =log(c(t)) +log(l(t))

wherel(t) denotes leisure time. Production of output requires human capital as the only

input:

Y(t) =Au(t)H(t)

whereu(t) is the time worker allocates to production in periodt. The remaining 1u(t)l(t) unit of time is used in human capital accumulation according to the following technology:

H(t) =(1u(t)l(t))H(t),GivenH0.

Is the time allocated to human capital accumulation on Balanced Growth Path: 0, 1/(1+) or / ?