All workers face tradeoffs. Self-selection allows workers to exploit these tradeoffs when choosing jobs, thus maximizing utility. One trade off is between pay and safety. Some workers are willing to take a hazardous job if it is accompanied by higher pay. Others, safety conscious individuals, prefer safety and a lower salary. Assume M is the amount of resources available to fund a particular job. The employer can pay it in salary, but then the job is dangerous, or uses some of the resources to remove the danger and pay a lower salary. Let P be the price per unit of safety, and the price per unit of salary is 1. Thus, for each job, the budget constraint is M = PS + W, where S is "units" of safety, and W is salary. Workers have utility functions given by U=f(W,S). Finally, let there be two types of jobs; risky, denoted by subscript R, and harmless, denoted by subscript H. Thus risky jobs have budget constraints MR=PRS+W, and harmless jobs have a budget constraint MH=PHS+W.
a. Show that if MR=MH and PR>PH, all workers will take harmless jobs.
b. Show that if MR=MH and PR=PH, some workers will take hazardous jobs, and some will take safe jobs.
c. Show that under 2, if OSHA (the Occupational Safety and Health Administration) forces all jobs to have at most a maximum level of danger, many (risk loving) workers will suffer a utility loss