Lewis and Martin are successful comedians who get utility (U) from consumption (C). They each have the same utility function U(C)=ln(C), where ln is the natural logarithm. (This function, like the square root function used in the lecture, also demonstrates decreasing marginal utility of consumption. You can find the natural logarithm on any scientific calculator or google can calculate it too.) They each have income of $1000.

As is common with celebrities, occasionally they get sued for a variety of transgressions.

The costs of going to court are $500. There is a 10% chance that Lewis goes to court, and 25% that Martin goes to court. There is an insurance product called "liability insurance" that can protect individuals against lawsuits.

a. Calculate the risk premium and actuarially fair insurance premium for full insurance for each.

b. That is, an insurance policy that replaces 100% of the lost consumption.

c. Suppose the insurance company is unable to distinguish between the riskiness of Lewis and Martin. What would the actuarially fair premium be if the government required them to buy the insurance? (Liability insurance is often required for certain enterprises.)