Consider a Cobb-Douglas production function given by

Y=AK^aL^1-a, 0< <1

(a) Let Y/L denote labour productivity, i.e., the average amount of output per worker. Another name for this is the average product of labour. Is the average product of labour larger or smaller than the marginal product of labour? Explain.

(b) Does an increase in K increase or decrease the marginal product of labour? Explain.

(c) Suppose that capital is paid the marginal product of capital and labour is paid the marginal product of labour, that is

rental rate r= MPK

wage rate w= MPL

Does an increase in K increase or decrease labour's share of income? Explain.

(d) Suppose the growth rate of productivity is g_A = 0.01, the growth rate of the capital stock is g_K= 0.04, the growth rate of the labour force is g_L= 0.02 and = 1/2. What is the growth rate of output? What about the growth rate of output per worker?