Consider the basic Solow model with no population growth and no technological progress and a production function of the form F (K, H ), where H denotes the efficiency units of labor (human capital) given by

where N is the set of all individuals in the population, and hi is the human capital of individual i. Assume that H is fixed. Suppose there are no human capital externalities and factor markets are competitive.

(a) Calculate the steady-state equilibrium of this economy.

(b) Prove that if 10% higher h at the individual level is associated with a% higher earnings, then a 10% increase in the country's stock of human capital H will lead to a% increase in steadystate output. Compare this result to the immediate impact of an unanticipated 10% increase in H (i.e., consider the impact of a 10% increase in H with the stock of capital unchanged).