Question

Problem 8: Consider the standard Solow model. The expression for output per worker and the dynamics of capital per worker are given by the following expression: y = Ak" where δ > 0 is the depreciation rate of capital (a) Using a Solow diagram, what is the effect of an increase in productivity A on steady state capital? (label the axes and mark the initial and the final steady state level of capital) (b) Find an algebraic expression for the steady state capital per worker. (c) What happens to steady state output and consumption after a positive productivity shock? Justify your response. (d) If the real wage equals the marginal product of labor, what is the growth rate of the real wage in steady state?

Answer 1

Initially the steady stake capital per worker & output per worker are k* & y*. Inverse in productivity A shifts production function upwards to 'y' which also shifts the investment curve upwards to sy'. New equilibrium is reached where steady state level of capital & output per worker are higher at k & y* respectively. b) At steady state, delta k = 0 sy - sk = 0 sy = delta k k = sy/delta = s A k^alpha/delta k k/k^alpha = sA/delta k^1 - alpha = sA/delta k^x = (sA/delta)^1/1 - alpha \r\n c) Steady state output increases after increase in productivity because output depends positivity on A & consumption also increase because consumption depends positively on output. d) we know, w = mP_L Increase in productivity increases mP_L equal to delta_y, i.e. y' - y. growth rate of mP_L = y' - y/y times 100 therefore Growth rate of real wage = y' - y/y times 100