Question

Dillon DeMarco is considering opening a small Italian bakery in the nearby mall, close to the Italian section of the city. He has chosen a good location where he believes there will be interest in the bakery. However, Dillon is unsure how much interest there will be and is trying to decide whether to open a small, medium or large shop. It really depends on what the economy is like in the next year whether people are able to spend their money on his Italian delicacies. Based on the latest financial reports, there is a 25% probability for a strong economy, 35% probability for an average economy and 40% probability for a bad economy. The potential payoffs for a small, medium or large shop for a given year are shown in the decision table. Decision Table State of Nature Alternatives Strong Economy Average Economy Bad Economy Small Shop 25,000 17,000 30,000 Medium Shop 50,000 50,000 45,000 Large Shop 80,000 68,000 58,500 Probabilities 0.25 0.35 0.40 Calculate the Expected Monetary Values (EMV) for each alternative.

Answer 1

The Payoff Matrix is :

ALTERNATIVES	STRONG ECONOMY	AVERAGE ECONOMY	BAD ECONOMY
SMALL SHOP	25000	17000	30000
MEDIUM SHOP	50000	50000	45000
LARGE SHOP	80000	68000	58500
PROBABILITIES	0.25	0.35	0.40

Now to calculate the EMV for small/medium/large shop = (strong economy value against small/medium/large X probability of strong economy) + (average economy value against small/medium/large X probability of average economy) + (bad economy value against small/medium/large X probability of bad economy)

EMV(SMALL SHOP) = EMV_S = (25000*0.25)+(17000*0.35)+(30000*0.40) = 24200

EMV(MEDIUM SHOP) = EMVM = (50000*0.25)+(50000*0.35)+(45000*0.40) = 48000

EMV(LARGE SHOP) = EMVL = (80000*0.25)+(68000*0.35)+(58500*0.40) = 67200

The decision is to invest in LARGE SHOP as its EMV is the largest among three shops.