3. (25 points) Magna is a firm that employs capital K and labour N to produce automobile parts. Its production function is given by Y = (K,N) = zK-a in which z is total factor productivity. Assume that z = 100, K = 1, a = 0.5 and each worker supplies one unit of labour paid at the wage rate w. Further, output is sold for P = 1 and the wage rate is 6.25 in the labour market. a) When Magna hires 16 workers, each worker produces 25 goods on average (average product is 25). If they hire 9 more workers, then average product falls to 20. Has Magna hired lazy workers? How Magna can make each worker more productive. b) If Magna hires 100 workers (i.e. to set N = 100). Is this a good decision? How many workers should Magna hire (optimal labour selection)? c) The government decides to prevent any firm from polluting. Magna discovers that polluting can be avoided at the cost of 0.25 units of output per unit of output produced. How many workers will Magna hire if w = 6.25? d) If the government decides to subsidize Magna (to alleviate the cost of pollution reduction) by 1.25 per worker hired. How many workers will Magna hire if the wage rate is unchanged? 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 Magna's firm? Illustrate graphically.