JNU SSS 2011 Question 19: Keynesian cross and the multiplier

Let $Y$ : aggregate real output per year, $P$ : the price level, $C$ : money value of aggregate consumption expenditure per year, $I$ : money value of aggregate investment expenditure per year, $L$ : aggregate employment (in labour hours per year), $L^*$ : total labour supply (in labour hours per year) and $w$ : hourly money wage rate. Let $W$ denote the money value of aggregate wage income per year and $R$ the money value of aggregate non-wage income per year. Consider an economy in which labour is homogeneous, the aggregate productivity of labour ($Y/L$) is a constant $a$ and the price level (when output is below its full employment level) is a factor $m$ times the wage cost per unit of aggregate output. The price at full employment is always greater than or equal to that at below full employment. In equilibrium, $PY = C + I$.

If $I = 4000$, $C = 1000 + 0\cdot 8W + 0\cdot 6R$, $w = 10$, $m = \frac{4}{3}$, $a = 16$, $L^* = 2000$, what is the fraction of total labour supply which remains unemployed in the economy?