As a result of an increase in demand for a town's parking facilities, the owners of a car park are reviewing their business operations. A decision has to be made to choose one of the following options:
Option 1. Make no change. Annual profit is $200,000. There is little likelihood that this will provoke new competition.
Option 2. Raise prices by 50%. If this occurs there is a 75% chance that an entrepreneur will set up in competition. The board's estimate of its annual profit in this situation would be as follows:
2A: With New Competitor 2B: Without New Competitior
Probability Profit $ Probability Profit $
0.3 300000 0.5 200000
0.4 240000 0.3 300000
0.3 160000 0.2 200000
Option 3. Expand the car park quickly at a cost of $10 000 keeping prices the same. The profits are then estimated to be like 2B in the attachment, except that the probabilities would be 0.6, 0.3 and 0.1 respectively.
1. Draw a labelled decision tree to depict the problem.
2. What decision should the owners take? Please show details of your calculations.
The solution provides step by step method for the calculation of expected profit and preparation of decision tree. Formula for the calculation and Interpretations of the results are also included.