Question 1. The demand and supply of labour with changes in unemployment and total factor productivity (35 points) Output is produced by the following Cobb-Douglas production function: Y - AK"[(-) (1) The variables are as defined in the text and in class except for L, which is actual employment. This variable is in turn related to the total labour force (N, which includes both employed and unemployed workers) as follows: L - (1-M)N (2) The term / is the natural unemployment rate, itself the result of structural features of the economy. You can think of N as the total supply of labour, call it NS . As well, N' can change as labour-market conditions change. Notice that the equilibrium the condition is now L - (1-4)N' a) Start by using equation (1) to find an expression for the demand for labour (L) and how it is related to the real wage rate (w) and the natural rate of unemployment (u). Next, use your equation to find an expression for N in terms of the real wage. Suppose that the supply of labour is given by: N - W (3) Find an expression for the real wage. Here just set the expression you found for N equal to (3) and solve for w. b) You are given the following values for the variables in the model. A = 204.8; a = 0.5; and K = 25 Refer to the Table 1 at the end of this question, which you will have to complete. Now calculate the values for: the real wage rate (w); employment (L); output (1); labour productivity (Y/L); and labour supply (N* ) that are consistent with these initial values under four different assumptions: 1) The natural rate is zero ( u = 0). 2) The natural rate is 5% ( / = 0.05). 3) The natural rate is 5% (/ = 0.05) and total factor productivity increases by 3% ( A - 204.8 x (1.03) ). 4) Total factor productivity increases by 3% ( A- 204.8x(1.03) ) and the natural rate falls to 3% ( / = 0.03). Be sure to show your calculations for each of the four cases. You need only show your numerical results to one decimal point. c) You will notice that a pattern emerges among the 5 variables as first the natural rate of unemployment rises, then total factor productivity increases, followed by a decline in the natural rate of unemployment. Based on your knowledge of labour markets, explain briefly what is driving these patterns for w, L, Y, Y/L and N' . Table 1 A increases by 3% (1) (2) (3) (4) 4= 0 " = 0.05 4 = 0.05 # = 0.03 W L y Y/L NS