(Solved): Consider the Solow-Swan model with Cobb-Douglas technology: (1) Y = AK@HL, where K is the physi ...

Consider the Solow-Swan model with Cobb-Douglas technology: (1) Y? = AK@HL, where K is the physical capital, He is the human capital, L, is the population. Assume that the rate of technological progress is zero so A is a constant and we normalize A = 1. Suppose that the rate of population growth is constant at rate n. The law of motion of physical capital is: (2) Kt = SKYt - 8Kt, The law of motion of human capital is: 2 (3) H? = SHY - SHt, where sk and share the constant savings rates and > 0 is the constant rate of depreciation. Define capital per worker as k = K/L, human capital per worker by h = H/L. • (a) Write down output per worker, y, as a function of k, and h. Write down the growth rates of k and h as functions of k and h. . (b) Define the steady state of the economy and solve it. . (c) Now imagine a pandemic hits the economy and the lockdown pol- icy keeps the population quarantined and the saving rate for human capital decreases. How would that affect the steady state? • (d) Does there exit the golden rule steady state? If yes, specify the golden rule.