2. Consider a Cobb-Douglas production function given by Y=AK"L1"'. Deter-:1 (a) Let Y? L denote labour productivity, i.e., the average amount of output per worker. Another name for this 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 = MPH wage rate to = MPL Does an increase in K increase or decrease labour's share of income? Explain. (d) Suppose the growth rate of productivity is 3,; = Chill, the growth rate of the capital stock is pp; = CID-i, the growth rate of the labour force is 9;, = 0.02 and or = lf. 1What is the growth rate of output? 1What about the growth rate of output per worker