The CEO of McBurger considers opening a new restaurant with two size options: la
ID: 3247169 • Letter: T
Question
The CEO of McBurger considers opening a new restaurant with two size options: large model (Large) and small model (Small). She anticipates two possible states of peak-hour demand at the new location: high demand (H) with a probability of 0.75 and low demand (L) with a probability of 0.25. The CEO uses the expected value criterion for decision making and she developed the original decision tree below.
A market research firm called BurgerMarket can give McBurger a survey about whether demand will be high or low. The survey result on the demand will be either favorable (f) or unfavorable (u). The CEO would like to determine the expected value of the survey and calculated: P(f) = 0.6, P(u) = 0.4 P(H|f) = 0.9, P(L|f) = 0.1, P(H|u) = 0.7, P(L|u) = 0.3
If the survey costs 0.5 (or $500), would the CEO buy it?
Explanation / Answer
For large model, the payouts for High and low demand are $12,000 and -$6,000
For small model, the payouts for High and low demand are $10,000 and -$2,000
Before taking the survey,
Expected payoff for large model = 0.75 * $12,000 - 0.25 * $6,000 = $7,500
Expected payoff for small model = 0.75 * $10,000 + 0.25 * $2,000 = $8,000
So McBurger would choose the option with maximum expected payoff which is $8,000 for small model.
After taking the survey,
When the BurgerMarket predict favorable demand, then expected payoff for high model
= P(H|f)* $12,000 - P(L|f) * $6,000
= 0.9* $12,000 - 0.1 * $6,000 = $10,200
When the BurgerMarket predict favorable demand, then expected payoff for low model
= P(H|f)* $10,000 + P(L|f) * $2,000
= 0.9* $10,000 + 0.1 * $2,000 = $9,200
So, when BurgerMarket predict favorable demand, McBurger would choose large model and the expected payoff is $10,200
When the BurgerMarket predict unfavorable demand, then expected payoff for high model
= P(H|u)* $12,000 - P(L|u) * $6,000
= 0.7* $12,000 - 0.3 * $6,000 = $6,600
When the BurgerMarket predict unfavorable demand, then expected payoff for low model
= P(H|u)* $10,000 + P(L|u) * $2,000
= 0.7* $10,000 + 0.3 * $2,000 = $7,600
So, when BurgerMarket predict unfavorable demand, McBurger would choose small model and the expected payoff is $7,600
Total Expected Payoff = P(f)*$10,200 + P(u)*$7,600
= 0.6*$10,200 + 0.4*$7,600 = $9,160
Expected gain from the survey = $9,160 - $8,000 = $1,160
As expected gain ($1,160) is greater than the survey costs of $500, CEO would buy it.
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