Rowan has an exogenous income of $10000 and a utility over money given byu(w)=ln(w). If she plays with fireworks indoors, she derives a benefit equivalent to $100, but risks setting the house on fire with a 50% probability, which would cost him $8000 in repairs. If she doesn't play with fireworks, the probability of a fire is 20%.

A risk-neutral insurance company offers a contract that would pay all repairs in case of a fire. The price of the contract isp=8000 gwheregis a number between 0.2 and 0.5 chosen by the insurance company.

The insurance company chooses the price of the contract. Then Rowan decides whether to buy it or not, and then decides whether to play with fireworks or not.

You may round all numbers to the second decimal if necessary.

1. [5pts] If Rowan doesn't buy the insurance, would he play with fireworks or not?
2. [8pts] Suppose Rowan buys the insurance when g = 0.2, would he play with fireworks or not? If she buys andg= 0.5, would he play with fireworks or not?
3. [5pts] If the insurance company sets g = 0.2, does Rowan buys the insurance? Does the insurance company make positive profit?
4. [5pts] If the insurance company sets g = 0.5, does Rowan buys the insurance? Does the insurance company make positive profit?
5. [5pts] Is this an efficient outcome? Explain.