Question

"Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $930,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.
The probability of a small box office earning $201,000 is 0.35. The probability of a medium box office of $1,590,000 is 0.45, and the probability of a large box office of $3,030,000 is 0.2.
Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $21,000 to get the novel evaluated by the movie critic.
The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.
If the movie will have a large box office, there is a 0.79 probability the critic will have a favorable opinion.
If the movie will have a medium box office, there is a 0.57 probability the critic will have a favorable opinion.
If the movie will have a small box office, there is a 0.15 probability the critic will have a favorable opinion.
Assume that Jay wants to maximize his expected monetary outcome. Enter the expected value of the preferred alternative. This includes whether or not to hire the movie critic and whether or not to go with the movie or network option."

Answer 1

Probability of Small Box-Office Earning =0.35 Earnings=$201,000          Critic Favorable =0.15

Probability of Medium Box-Office Earning =0.45   Earnings=$1,590,000       Critic Favorable =0.57

Probability of Large Box-Office Earning =0.2    Earnings=$3,030,000        Critic Favorable =0.79

Cost of getting Movie Reviewed from Critic =$21,000

Case-A : Movie Critic is Hired and Signed with Movie Company

Earnings in this Case = 0.35*201,000*0.15 + 0.45*1,590,000*0.57 + 0.2*3,030,000*0.79 - 21,000

                                = 10,552.5 + 407,835 + 478,740 - 21,000

                                = 876,127.5

Case-B : Movie Critic is Not Hired and Signed with Movie Company

Earnings in this Case = 0.35*201,000 + 0.45*1,590,000 + 0.2*3,030,000

                                = 70,350 + 715,500 + 606,000

                                =$1,391,850

Case-C: Signing with the Network

Single Lump Sum Payment =$930,000

From, all the above cases, we can compare that the maximum payoff will occur in the alternative-B,

Thus, maximum earnings =$1,391,850