ISonsider a model of human capital accumulation. Consumption goods are produced using only human capital according to the production function "r' = zuH, where H denotes the economy's supply of human capital, u is the fraction of human capital allocated to producing oonsumption 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 v. A fraction 1 u of current human capital is allocated to producing future human capital. which is determined by the equation H'r = M + b ulH. with M 3 D being the minimum amount of human capital if all workers were unskilled, and b 7:: 1 giving the productivitv 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 human capital H with no longrun growth in '1'". Explain why there is always some value of u :r t} such that this model generates positive longrun growth in H and 'r'. In the case where the model generates longrun growth in '1'. if each worker receives a wage equal to z multiplied by their human capital. explain what must happen over time to the 'skill premiun'f. the ratio of the wages of high-skilled to unskilled workers