M & S Corp has a fertilizer plant. The probability of an explosion at the plant depends on how much the firm spends on safety as given by the table. If an explosion occurs, the loss to society (damaged equipment, death of employee, etc) is expected to be $250 million.

Safety Expenditure ($ in m) Probability of Loss

0.0 0.03

0.5 0.02

1.0 0.016

1.5 0.013

2.0 0.011

2.5 0.010

1Find the optimal level of safety expenditure.

2Suppose the corporation has to pay only one-half of the losses that occur, how much would M & S spend on safety? Why?