Consider a labor market in which times may be either good or bad. If times are good (state 1), the market wage is 100. If times are bad (state 2), the market wage is 40. Workers in this market are expected utility maximizers, with utility function u = sqrt(w)

Assume that probability of bad times is 1/4

(a) An insurance company offers the workers income insurance, charging a premium P and paying compensation I in the bad state. If the insurance is actuarially fair, show that the workers will fully insure. What is their resulting consumption in each state, and what is their expected utility?

(b) Suppose instead that no income insurance is available, but the firm makes an agreement with its workers to pay them the same wage w, no matter how the market turns out. What is the lowest wage the firm could pay workers under such a scheme and still provide workers with the same level of expected utility?

(c) Draw the preferences of the workers, mark wealth levels, expected wealth, certainty equivalent, risk premium, constant expected consumption line, guaranteed consumption line, insrurance pre- mium. If you did not complete the previous parts, just use general notation. No need to be exact. Make sure you clearly label the entire graph.

(d) Now assume tha tinsurance company is charging for administrative costs and so the loading factor = 0.1. What is the workers' optimal coinsurance rate in this economy?