Exam 13: The Value of Information

Briefly describe the potential pitfalls associated with making intuitive predictions.

A company is trying to decide whether to build a large plant or a small plant to supply future sales of a new product. However, it is uncertain about the market response to the product; whether demand will be strong or weak. According to the firm's marketing department, the probability of strong demand is .3 and of weak demand is .7. The table below lists the firm's profits (in millions of dollars) depending on plant capacity and the market response: (a) The company must make its plant decision now, before it will know what the market response will be. Which plant size maximizes its expected profit? (b) Now suppose the company has a third option: building a modular plant. This is the same size as the small plant but is built so it can be expanded to the size of the large plant at a later date. The modular plant costs $4 million more to build than the small plant, but it allows the company the flexibility to observe the market response to the new product and immediately expand its capacity if demand warrants it (Note: If the modular plant is expanded, the firm’s total cost is also $4 million more than building a large plant in the first place). Should the company choose to build the modular plant? (c) Suppose that the firm can take a small-scale market survey that will help it forecast market demand. The test has two possible outcomes: positive or negative. In the past, products that went on to enjoy strong demand received positive test market scores in 4 of 6 cases: Pr(+|S) = 2/3. Products generating weak demand received negative test results in 5 of 7 cases: Pr(–|W) = 5/7. Compute the revised probabilities, Pr(S|+) and Pr(S|–).

The following table shows the probabilities of A, B, X, and Y. Compute the joint probability table. Then calculate Pr(BY) and Pr(XB). 455 416 104

Information is considered to be valueless if it:

A petrochemical company must decide whether to fill a specialty order for one of its customers. Its cost (and therefore profit) depends on the quality of the raw material it has on hand to make the chemical. The firm expects to earn $50,000 from the order if the material is high quality (H) but will lose $30,000 if it is low quality (L). The firm's engineers estimate these probabilities to be .32 and .68 respectively. Before making its decision, the firm can test the material with one of two outcomes, "favorable" or "unfavorable." A favorable test increases the chance of H to .5, while an unfavorable result reduces it to .2. The likelihood of a favorable test is .4. Determine the expected value of this test.

A firm hires an economist to conduct market research and determine demand for a new product. If the test is correct and the firm launches the product, it earns a profit of $600,000. If the firm launches the product when there is weak demand, it incurs a loss of $250,000. Strong Weak Total Accurate 0.2 0.2 0.4 Inaccurate 0.3 0.3 0.6 0.5 0.5 1.0 What is the firm's expected profit from an accurate and inaccurate test respectively? What can you conclude about the quality of the market research?

A firm is considering the development of a new technology with a declining probability of success in each research stage. The firm's researchers have estimated the probabilities at .35, .25, .15, .07, and .01 for the various stages. The profit the firm would receive for successful development is $100 million, while the cost of research in each period is $10 million. How many investment stages should the firm undertake before abandoning the project?