Economics

. Consider that a hockey playing professor with income , consumes hours of hockey at price and a composite good at price $1.

His utility is given by (, ) = ln() + . His probability of being injured as a function of hours of hockey played is () and the medical cost of a hockey injury is . Let () be strictly increasing in .

a. First, let us consider the case where our hockey playing prof is uninsured. Solve for the level of hockey he will play.

b. Now presume that once insured the insurer cannot observe the professor's hours of hockey playing. The insurer offers insurance at a price . This results in our professor having a certain utility but a lower level of income (due to paying for the insurance). Solve for the level of hockey the professor will play

c. Compare your results from parts a and b above. What can you say