Tom is considering whether to set up a small company that would provide IT services to help students live and study at Lancaster University. He is evaluating three possible strategies: an expensive microcomputer system, a moderate microcomputer system, and a cheap microcomputer system. He also allows an option of doing nothing.
Tom calculated the expected profits of each option when the market is good as follows: for the expensive system, £200,000; for the moderate system, £150,000; for the cheap system, £100,000. He also calculated the expected losses when the market is bad as follows: for the expensive system, £120,000; for the moderate system, £80,000; for the cheap system, £60,000.
He believes the chances of a good market to be 80%, 65% and 40% for the expensive, moderate and cheap systems, respectively.
Draw a decision tree for Tom’s decision problem and assign the probabilities to lines and payoffs to leaves.
(6 marks)
Calculate the expected monetary payoffs (rounded to whole numbers) at the outcome nodes and at the decision nodes and identify his best decision option.
(6 marks)
Tom has been approached by a marketing research company that offers to study the
area to determine whether the market will be good or bad. Tom believes there is an 80% chance that the survey results will be positive (i.e. an 80% chance that the survey will predict a good market, irrespective of the computer system chosen).
In order to evaluate the reliability of the survey, Tom asks the company to provide him with information regarding its performance on past surveys. The company has data on 50 past surveys that it has conducted. In these 50 surveys, the company had predicted a good market in 34 cases, and a bad market in 16 cases. These data are summarised in the table below.
Draw a new, expanded decision tree which includes another decision point about whether Tom should conduct the survey, and calculate the revised probabilities of the market being good and of being bad under each strategy, depending on the survey results. (Probabilities should be rounded to two decimal places).
marks)
The cost of the study in (c) is £30,000. Calculate the revised payoffs and expected values of payoffs (rounded to whole numbers) at all nodes of the expanded decision tree and identify the best decision option at each decision point.
marks)
How much is the study in (c) worth to Tom using the Expected Value of Sample Information (rounded to whole numbers)? Advise Tom on whether he should purchase this survey or not.
(12 marks)
