The following payoff table provides profits based on various possible decision a

ID: 2900890 • Letter: T

Question

The following payoff table provides profits based on various possible decision alternatives and various levels of demand.

State of Nature

Demand

Alternatives Low Medium High

Altv 1 80 120 140

Altv 2 90 90 90

Altv 3 50 70 150

The probability of a low demand is 0.4, while the probability of a medium and high demand is each 0.3.

(a) What decision would an optimist make?

(b) What decision would a pessimist make?

(d) Calculate the expected value of perfect information for this situation.

a) For optimist, alpha=1

Decision will be based only on values in case of high demand

payoff is maximum for atlernative3 in case of high demand

An optimist should choose alternative 3

b) For pessimist, alpha=0

Decision will be based only on values in case of low demand

payoff is maximum for atlernative2 in case of low demand

A pessimist should choose alternative 2

c)Expected payoff:

Altv 1=0.4*80+0.3*120+0.3*140=110

Altv 2= 0.4*90+0.3*90+0.3*90=90

Altv 3= 0.4*50+0.3*70+0.3*150=86

Highest possible expected payoff=110

d) Given that we know market direction, expected maximum payoff=0.4*90+0.3*120+0.3*150=117

expected value of perfect information=117-110=7

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