9781118041581

hand, the manager can analyze the problem by means of the usual decision

tree after supplying utility values for possible final monetary wealth positions.

Finally, the manager averages back the tree and selects the course of action

that has the highest expected utility.

530 Chapter 12 Decision Making under Uncertainty

To solve the yacht dealer’s problem posed at the beginning of the chapter, we supply the

following information. The dealer incurs fixed costs amounting to $150,000 per year and

obtains yachts from the manufacturer at an average cost of $10,000 each. In a growing

economy, the demand for yachts is described by P  20  .05Q; in a slumping economy,

demand is P  20  .1Q, where P is measured in thousands of dollars.

Let’s start by finding the dealer’s profit-maximizing yacht order for each type of

economy. Setting MR MC, we find the dealer’s optimal quantity and price to be

QG100 and PG$15,000 for a growing economy; the resulting profit is G

$350,000. For the recession economy, we find QR50, PR$15,000, and R

$100,000. Of course, the dealer must place the order now, before knowing the true

direction of the economy. Let’s suppose the dealer must choose to order a round lot

of either 50 or 100 yachts. (Other possibilities are considered in Problem 15 at the

end of the chapter.) In light of a 60 percent chance of growth, which order, 50 or 100,

has the higher expected profit?

The decision tree in Figure 12.11 answers this question. If 100 yachts are ordered,

the dealer’s profit is either $350,000 or $150,000. Under slumping demand, the best

the dealer can do is sell all 100 yachts at a price of $10,000 each. (At this quantity, rev-

enue is maximized; that is, MR 0.) If 50 yachts are ordered, the possible outcomes

are $225,000 and $100,000. The first outcome occurs when the dealer plans for a reces-

sion but is pleasantly surprised by growing demand and sells the 50 yachts at a price

of $17,500 each. (Note that this price is obtained from the demand curve for a grow-

ing economy.)

Direct calculation shows that ordering 50 yachts generates an expected profit of

$175,000, whereas ordering 100 yachts produces only $150,000. Thus, a risk-neutral

dealer prefers the smaller (50-yacht) order. (A risk-averse dealer shares this preference,

because ordering 50 yachts is less risky than ordering 100.) This result might conflict

with one’s intuition. After all, a growing economy is more likely than not, and ordering

100 yachts is optimal in this case; therefore, one would judge 100 yachts to be the bet-

ter choice. What’s wrong with this reasoning? The key point is that the cost of making

a wrong decision differs across the two actions. Taking a large yacht order is very costly

(generates a large loss) if a slumping economy causes inventory to be sold at bargain

prices. The “cost” of placing a limited order and having too little inventory to accom-

modate a growing economy is relatively small. (At least the dealer can raise prices.) As

a result, the expected profit associated with the small order is significantly greater than

that of the large order.

Gearing Down

for a Recession

Revisited

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