The operations manager for a well-drilling company must recommend whether to build a new facility,expand his existing one,or do nothing.He estimates that long-run profits (in $000)will vary with the amount of precipitation (rainfall)as follows: If he feels the chances of low,normal,and high precipitation are 30%,20%,and 50%,respectively,what is his expected value of perfect information?

Question

The operations manager for a well-drilling company must recommend whether to build a new facility,expand his existing one,or do nothing.He estimates that long-run profits (in $000)will vary with the amount of precipitation (rainfall)as follows:  If he feels the chances of low,normal,and high precipitation are 30%,20%,and 50%,respectively,what is his expected value of perfect information?

Quizplus · Accepted Answer

To find the expected value of perfect information, we need to calculate the expected value (EV) for each decision under each possible state of nature, and then multiply each EV by the probability that state of nature occurs. Then we add up all these values.

For example, the EV of building a new facility under low precipitation is $90, the EV under normal precipitation is $150, and the EV under high precipitation is $200. To find the overall EV of building a new facility, we multiply each EV by its probability and add them up:

(0.3 x $90,000) + (0.2 x $150,000) + (0.5 x $200,000) = $147,000

We repeat this process for expanding the existing facility and doing nothing, and we get the following table:

|     | Low Precipitation | Normal Precipitation | High Precipitation | Probability | EV     |
|-----|------------------|----------------------|--------------------|-------------|--------|
| Build new facility     | $90,000           | $150,000              | $200,000          | 0.3         | $147,000|
| Expand existing facility   | $70,000           | $100,000              | $120,000          | 0.3         | $95,000 |
| Do nothing        | $80,000           | $80,000               | $80,000           | 0.4         | $80,000 |

To find the expected value of perfect information, we need to find the difference between the maximum and minimum EVs in each row, and then multiply that by the probability of that row. For example, the difference between the maximum and minimum EVs in the "build new facility" row is $110,000 ($200,000 - $90,000).

We then multiply this by the probability of high precipitation, since that is the state of nature where the EV difference is the largest:

$110,000 x 0.5 = $55,000

We repeat this process for all rows, and then add up the results:

$55,000 + $20,000 + $0 = $75,000

Therefore, the expected value of perfect information is $75,000.

The best decision depends on what level of risk the operations manager is willing to accept. If they are risk-averse, they may choose the option with the highest EV (building a new facility), even though it has a lower EV than the expected value of perfect information. If they are risk-neutral, they may choose the option with the highest EV, regardless of the expected value of perfect information. If they are risk-seeking, they may choose a riskier option with the potential for higher profits.

The Operations Manager for a Well-Drilling Company Must Recommend Whether