UDI'ISIUEI a model or human capital accumulation. consumption goods are produced using only human capital according to the production function V = zuH, where H denotes the economy's supply of human capital, u is the fraction of human capital allocated to pmducing consumption goods, and z is the exogenous and xed level of total factor productivity. Assume the population is constant over time, so H is proportional to average human capital per person, and output and consumption per person are proportional to 'r'. A fraction 1 u of current human capital is allocated to producing future human capital, which is determined by the equation H" = M + till ujH, with M :r- D being the minimum amount of human capital if all workers were unskilled, and b 2: 1 giving the productivity of the production process for human capital. By plotting H" against H in a diagram, derive a condition for u such that there exists a steady state for hum an capital H with no longrun growth in lr'. Explain why there is always some value of u :s- t} such that this model generates positive longrun growth in H and Y