4. The total product of labour function is w given by Y = A . (200 N 0.05 N ? ), where N is aggregate employment and A is total factor productivity, and the marginal A=2 initially. The aggregate quantity of S labour supplied is N = 500 +5w , where w is the real wage. (a) Determine the demand for labour and find the equilibrium employment and the real wage. (b) Suppose there is a negative supply shock that reduces A to 1. Suppose that the wage is sticky downwards so that it takes some time for it to decline in response to the negative supply shock. Determine the resulting levels of employment and unemployment. Is unemployment voluntary or involuntary? (c) Illustrate and explain the qualitative effect of this shock on equilibrium employment and the real wage. Is the decline in employment voluntary or involuntary?