Suppose all workers have the same preferences represented by U$=$w$^3-(12$x$)^0\mathrm{.}5$ where w is the wage and x is the proportion of the firm$$s air that is composed of toxic pollutants. There are only three types of jobs in the economy, a clean job $($x $=0).$ a semi$-$clean job $($x $=0\mathrm{.}5).$ and a dirty job $($x $=1).$ Let w$0$ be the wage paid by the clean job and w$1$ be the wage paid for doing the semi$-$clean job. If the clean job pays $$15$ per hour ; a$.$ what is the wage in semi$-$clean jobs $?$ b$.$ what is the wage rate in dirty jobs $?$ c$.$ what is the compensating wage differential between these jobs $?$