The Value of Perfect Information
A complication that arises with decision trees is that they allow you to calculate the value of having further information, say about market conditions, which in turn allows you to decide whether or not it is worth paying for market research. This page looks at how to value perfect information
Information
Decision makers may be offered a forecast of a future outcome (for example a market research group may predict the forthcoming demand for a product). This forecast may turn out to be correct or incorrect. This page looks at how to calculate the value of the forecast.
- Perfect information - The forecast of the future outcome is always a correct prediction. If a firm can obtain a 100% accurate prediction they will always be able to undertake the most beneficial course of action for that prediction.
- Imperfect information - The forecast is usually correct, but can be incorrect. Imperfect information is not as valuable as perfect information.
The value of information (either perfect or imperfect) may be calculated as follows:
Expected Profit (Outcome) WITH the information LESS Expected Profit (Outcome) WITHOUT the information
Illustration : Geoffrey Ramsbottom
Geoffrey Ramsbottom runs a kitchen that provides food for various canteens throughout a large organisation. A particular salad is sold to the canteen for $10 and costs $8 to prepare. Therefore, the contribution per salad is $2. At present Geoffrey must decided in advance how many salads to prepare each day (40, 50, 60 or 70). Actual demand will also be 40, 50, 60 or 70 each day.
Geoffrey's payoff table looks as follows:
| Daily supply |
| Daily Demand | | Probability | 40 salads | 50 salads | 60 salads | 70 salads |
40 salads | 0.10 | $80 | $0 | $(80) | $(160) |
50 salads | 0.20 | $80 | $100 | $20 | $(60) |
60 salads | 0.40 | $80 | $100 | $120 | $40 |
70 salads | 0.30 | $80 | $100 | $120 | $140 |
The expected value associated with each choice are as follows:
- If choose to make 40 salads, EV = 1×80 = 80
- If choose to make 50 salads, EV = 0.10×0 + 0.90×100 = 90
- If choose to make 60 salads, EV = 0.10×(-80) + 0.20×20 + 0.70×120 = 80
- If choose to make 70 salads, EV = 0.10×(-160) + 0.20×(-60) + 0.40×40 + 0.30×140 = 30
Based on expected values without additional information, Geoffrey would choose to make 50 salads per day with an EV of $90 per day.
Suppose a new ordering system is being considered, whereby customers must order their salad online the day before. With this new system Mr Ramsbottom will know for certain the daily demand 24 hours in advance. He can adjust production levels on a daily basis.
How much is this system worth to Mr Ramsbottom?
With perfect information Geoffrey can vary the output each day in line with predicted demand. His EV is thus given as follows
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Created at 7/10/2012 1:58 PM by System Account
(GMT) Greenwich Mean Time : Dublin, Edinburgh, Lisbon, London
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Last modified at 7/1/2013 12:17 PM by System Account
(GMT) Greenwich Mean Time : Dublin, Edinburgh, Lisbon, London
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