Problem $2($Worker$\text{'}$s choice of safe$/$risky job$)$

Consider a competitive economy that has four different jobs that vary by their

wage and risk level. The table below describes each of the four jobs.

All workers are equally productive, but workers vary in their preferences.

Consider a worker who values his wage and the risk level according to the

following utility function:

U$($w$,$r$)=4$w$+($y$)/($r$^(3))$

$1.$ For what positive values of y does the worker choose to work in job A$?$ Repeat this for job D$.$

$2.$ Suppose the government regulated the workplace and required all jobs to have a risk factor of $1/8.$ What wage would the worker need to earn now to be just as well off as when y $=10?$