DSE 2010 Question 23: Classical macroeconomics

Consider an economy with aggregate production $Y=\alpha K+\beta L$, $\alpha,\beta>0$, $K$ fixed in the short run. Competitive producers take the nominal wage $W$ and price $P$ as given and choose labour to maximize profit, generating labour demand. Labour supply is $L^{S}=-\gamma+\delta W/P$, with $\gamma,\delta>0$; there is perfect information about $P$ and $W$. The labour market will clear if and only if