Dollar Department Stores has the opportunity of acquiring either 3, 5, or 10 lea

Question

Dollar Department Stores has the opportunity of acquiring either 3, 5, or 10 leases from the bankrupt Granite Variety Store chain. Dollar estimates the profit potential of the leases depends on the state of the economy over the next five years. There are four possible states of the economy as modeled by Dollar Department Stores, and its president estimates P(s1) = .4, P(s2) = .3, P(s3) = .1, and P(s4) = .2. The utility has also been estimated. Given the payoffs (in $1,000,000's) and utility values below, which decision should Dollar make using expected utility as its decision criterion?

Payoff Table

State Of The Economy

Over The Next 5 Years

The utility for a given payoff equals the number of millions of dollars (so a $5m payoff has a utility of 5, for example), with two exceptions:

     the utility for -$10m is -20;

the utility for -$20M is -50.

Explanation / Answer

Utility Table

Payoff (in millions)------ +10 +5 +2 +1 0 -1 -10 -20
Utility -------------- +10 +5 +2 +1 0 -1 -20 -50


MY ANSWER---
D1=10(.4)+5(.3)+(0(.1)+-20(.2)=1.5
D2=5(.4)+0(.3)+-1(.1)+-10(.2)=-.1
D3=2(.4)+1(.3)+0(.1)+-1(.2)=.9
D4=0

Dollar should pick d2

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