A company is hiring a salesperson. If the salesperson works hard, there is a 90% chance that the sales revenue will be $1 million and 10% chance $500,000. However, if the person pays no effort, the chance of sales revenue being $1 million will be reduced to 40% and $500,000 increased to 60%. Penny has applied to the job. She is currently working at a restaurant, which pays her $30,000 a year and requires no effort. The company is risk-neutral and maximizes its (expected) profit. a. Penny's utility is U= w 0.7 -c(e), where w is her annual salary and e is the level of her effort. e can take two values, eh for working hard and el for no effort. c(eh)=650 and c(el)=0

Suppose that Penny's effort is not observable. Write down the PC and ICC of the offer package to induce Penny to work hard. Write out the profit maximization problem of the company. What is the optimal package the firm will offer to Penny?