Question 3:Productivity,Output and Employment [30 marks]Suppose that the production function of the country Cashland isY=AKaN1-aThe labour supply curve isNS=c[(1-t)(1-)w]2where w is the real wage rate,t is the tax rate on labour income,I is the fraction of the real wagerate that disappears,and hence(1-t)(1-l)wis the after-tax real wage rate.(a)Derive the expression for the marginal product of capital (MPK)and the marginalproduct of labour (MPN).Then verify that the MPK and MPN exhibit diminishingreturns.Now assume that K 50,c=121,a =0.3,t 0.4 and=0.1.(b)Assume that the productivity level,A,is 8.Find the equation of the labour demand curve.Calculate the equilibrium levels of the real wage and employment,the level of full-employment output,and the total after tax-rate wage income of workers.(c)Assume that the productivity level,A,is 10.Find the equation of the labour demandcurve.Calculate the equilibrium levels of the real wage and employment,the level offull-employment output,and the total after tax-rate wage income of workers.(d)Compare the results you get between b)and c).Do they respect the results predicted bythe model used in Chapter 3?(e)Use the results in part c).Suppose there is a minimum wage that is lower than theequilibrium level of the real wage.Are the equilibrium levels of employment and full-employment output affected?If so,would they be lower or higher than without theminimum wage?