Mr. Warren operated a real estate agency that specialized in finding buyers for commercial properties. Warren was approached one day by a prospective client, who had three properties that he wished to have sold. The client wished to receive the following prices:
Property Price
Allston $25,000
Belmont $50,000
Cambridge $100,000
Warren would receive a commission of 4% on any of the properties he was able to sell. The client laid down the following conditions for an exclusive listing:
(i) Allston had to be sold first.
(ii) If Warren failed to sell Allston within a month, then the deal was off. Warren would not receive any commission or the chance to sell other properties.
(iii) If Warren could sell Allston within a month, he would get the commission for the sale and an option to sell the second property. At this stage, if Warren decided not to sell any more properties, then the contract would terminate. However, if Warren decided to sell a second property, then he had to choose between Belmont and Cambridge at this stage (but not both). Once he made the choice, he had one month to sell the property.
(iv) If Warren failed to sell the second property within a month, then the deal was off.
Warren would not receive any further commission or the chance to sell the third property.
(v) If successful, Warren had the option to terminate the contract or sell the third property. If Warren decided to sell the third property, the terms were same as in the previous cases. After the client left, Warren proceeded to analyze the proposal to determine whether or not to accept it. He figured his selling costs and his chances of selling each property at the price set by the client to be:
Selling Cost Probability of Sale
Allston $800 0.7
Belmont $200 0.6
Cambridge $400 0.5
He believed that the sale of a particular property would not make it more or less likely that