Utility Tree

EXERCISE 39 Japanese Goods

Your U.S. corporation is considering importing certain goods from Japan for sale in the corporation’s nationwide chain of general merchandise stores. The corporation has narrowed its interest to three items—a decorative vase, a battery-powered electric hand drill, and a combination stereo radio and disc player—each of which is manufactured by a different Japanese firm. Because these firms historically have refused to deal with non-Japanese-owned companies, persuading them to sell their product to the corporation will be expensive and time-consuming. But they are feeling the pinch of increased competition and have begun making noises about relaxing their self-imposed prohibition against dealing with foreign merchandisers.

The U.S. corporation's management has decided that, rather than pursue all three Japanese firms simultaneously, it will concentrate its lobbying effort on one firm. Your job is to analyze the problem and identify which of the three products will give the biggest return to the corporation during the coming sales year. The corporation will then lobby that firm.

According to a research report, the vase will earn the corporation a profit of $100,000, the hand drill $200,000, and the stereo $500,000. The probability of persuading the firms that produce these products to sell to the corporation is estimated to be .9 for the vase, .5 for the drill, and .1 for the stereo. On which item should the corporation concentrate its lobbying effort? Using a utility tree, work out the problem on a sheet of paper.

BEFORE CONTINUING, WORK THE PROBLEM USING A UTILITY TREE.

The solution to Exercise 39 (page 337) shows the completed tree, whose perspective is the U.S. corporation’s profits. Here again we could usefully dispense with the “No” outcomes.

The calculation assumes no profit if a firm declines and leaves out lobbying costs. We multiply the utilities ($100,000, $200,000, $500,000) by their respective probabilities (.9, .5, .1) to produce the expected values ($90,000, $100,000, $50,000). The drill option is the preferred choice because it offers the greatest expected value: $100,000. Does the drill’s being the preferred choice pass the sanity check? Does it make sense? I think so. While the probability of the U.S. corporation’s marketing the drill is 55 percent of the probability of its marketing the vase, the profit from the drill is 100 percent more than that from the vase. And although the profit from the stereo is 150 percent more than that from the drill, the probability of marketing the stereo is only 20 percent of the probability of marketing the drill.

Concept Summary

The utility tree (or expected value decision tree) helps decision-makers choose among alternatives by calculating the expected value of each option. The expected value is the sum of each possible outcome's utility multiplied by its probability. The option with the highest expected value is typically the best under uncertainty, assuming risk neutrality.