Paul owns a firm that produces output (Y) with capital (K) and labour (N) accord-ing Y = z (K^a) (N^1a) in which z is total factor productivity. Say that z = 100, that K = 1, and that a = 0.5. Each worker supplies one unit of labour. Each unit of labour is paid the wage rate w. The price at which output is sold is P = 1, Suppose that w = 6.25 in the labour market.

a) When Paul hires 16 workers, each worker produces 25 goods on average (that is, Y/N = 25). If he hires 9 more workers, then Y/N falls to 20. Has Paul hired lazy workers? Explain. Explain how Paul can make each worker more productive.

b) Paul observes the wage rate and then decides to hire 100 workers (i.e. to set N = 100). Is Paul a good businessman? Explain. How many workers should Paul hire?

c) The government decides to prevent any firm from polluting. Paul discovers that polluting can be avoided at the cost of 0.25 units of output per unit of output produced. How many workers will Paul hire if in = 6.25?

d) To alleviate the cost of reducing pollution, the government decides to pay Paul's firm 1.25 per worker hired. How many workers will Paul hire if in = 6,25?

e) How will the policies introduced in c) and in d) affect the firms inverse labour demand curve? How will the equilibrium wage be affected if all firms in the economy are identical to Paul's firm? Illustrate with a graph.