Background Space-Man parking is a garage located in the downtown area of a metro

Question

Background

Space-Man parking is a garage located in the downtown area of a metropolitan community. Located next to several shopping centers and restaurants. Space-Man slogan is “We always have a space, man!” Utilizing the moto Space-Man is focused on hourly parking, rather than monthly parking passes. Over the last few years Space-Man parking has chosen to increase the size of their parking structure. This decision was due in-part to a large concert venue being built close by. The owners are retiring and would like to use the profits from the newly renovated parking lot to fund their retirement.

Three future states of nature present themselves for Space-Man parking.

SoN1 - The arena is built in another location potentially drawing business away from Space-Man.

SoN2 - Status Quo the area is not built for the time being either locally or in another location.

SoN3 - The area is built in the local location increasing business.

Calculate and explain the equal likelihood decision and the expected value decision for the states of nature. Use this information to inform your decision.

That is the same question I am having. To me it seems as if they didn't write the question right.

Distant Arena Status Quo Area Built Probability 30% 30% 40% Year 1 $16,000 $93,000 $156,000 Year 2 -$42,000 $150,000 $427,000 Year 3 -$171,000 $319,000 $642,000 Year 4 -$337,000 $473,000 $933,000 Year 5 -$551,000 $516,000 $1,228,000

Explanation / Answer

Decision alternatives are not given, instead year is mentioned in place of decision alternatives. So, question is solved considering that these are decision alternatives and not years.

Equally likelihood (EL) decision:

In this criterion, each state of nature is given equal weightage. and expected payoff is calculated as average of payoffs for all states of nature.

Expected payoff of alternative 1 = (16000+93000+156000)/3 = 88,333

Expected payoff of alternative 2 = (-42000+150000+427000)/3 = 178,333

Expected payoff of alternative 3 = (-171000+319000+642000)/3 = 263,333

Expected payoff of alternative 4 = (-337000+473000+933000)/3 = 356,333

Expected payoff of alternative 5 = (-551000+516000+1228000)/3 = 397,667

Expected payoff of alternative 5 is the highest. Therefore, it should be selected.

Expected Value (EV) decision:

In this criterion, expected payoff is calculated as probability weighted sum of payoffs for all states of nature.

Expected Value of alternative 1 = (16000*0.3+93000*0.3+156000*0.4) = 95,100

Expected Value of alternative 2 = (-42000*0.3+150000*0.3+427000*0.4) = 203,200

Expected Value of alternative 3 = (-171000*0.3+319000*0.3+642000*0.4) = 301,200

Expected Value of alternative 4 = (-337000*0.3+473000*0.3+933000*0.4) = 414,000

Expected Value of alternative 5 = (-551000*0.3+516000*0.3+1228000*0.4) = 480,700

Expected Value of alternative 5 is the highest. Therefore, it should be selected.

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