For this problem, use the fact that the expected value of an event is a probabil

Question

For this problem, use the fact that the expected value of an event is a probability weighted average, the sum of each probable outcome multiplied by the probability of the event occurring You wish to hire Ron to manage the Dallas operations of your company. The profits from the operations depend partially on how hard Ron works, as follows. Probabilities Lazy Hard worker Profit = $10,000 60% 30% Profit = $60,000 40% 70% lf Ron is lazy, he will surf he nternet all day, and he views this as a zero cost opportunit, o ever, Ron would via worka n ? hard as a personal cost $1,000. What fixed percentage of the profits should you offer Ron? Assume Ron only cares about his expected payment less any "personalos." a e at You should offer Ron at least % of the profits. (Round your response to two decimal places.)

Explanation / Answer

Let p be the percent of Profits you pay Ron:

If Ron is lazy his expected payment is 0.60*15000P+0.40*55000P = 9000P+22000P = 31000P

If Ron works hard his expected payment is

0.30*15000P + 0.70*55000P-1500 = 4500P+ 38500P - 1500= 43000P-1500

To induce Ron to hard work you need : 43000P-1500 = 31000P

12000P = 1500

P = 0.125

So offer Ron 12.5% of the profits, and thid should induce him to hard work.

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