Homework SourseMiles is considering buying a new pickup truck for his lawn
Miles is considering buying a new pickup truck for his lawn service firm. The economy in town seems to be growing, and he is wondering whether he should opt for a subcompact, compact, or full-size pickup truck. The smaller truck would have better fuel economy, but would sacrifice capacity and some durability. A friend at the Bureau of Economic Research told him that there is a 30% chance of lower gas prices in his area this year, a 20% chance of higher gas prices, and a 50% chance that gas prices will stay roughly unchanged. Based on this information, Miles has developed a decision table that indicates the profit amount he would end up with after a year for each combination of truck and gas prices.
States of Nature
Alternatives
Lower gas prices
Gas prices unchanged
Higher gas prices
Probability
.3
.5
.2
Subcompact
$16,000
$21,000
$23,000
Compact
$15,000
$20,000
$22,000
Full size
$18,000
$19,000
$6,000
Calculate the expected monetary value for full size
20 points
QUESTION 9
Miles is considering buying a new pickup truck for his lawn service firm. The economy in town seems to be growing, and he is wondering whether he should opt for a subcompact, compact, or full-size pickup truck. The smaller truck would have better fuel economy, but would sacrifice capacity and some durability. A friend at the Bureau of Economic Research told him that there is a 30% chance of lower gas prices in his area this year, a 20% chance of higher gas prices, and a 50% chance that gas prices will stay roughly unchanged. Based on this information, Miles has developed a decision table that indicates the profit amount he would end up with after a year for each combination of truck and gas prices.
States of Nature
Alternatives
Lower gas prices
Gas prices unchanged
Higher gas prices
Probability
.3
.5
.2
Subcompact
$16,000
$21,000
$23,000
Compact
$15,000
$20,000
$22,000
Full size
$18,000
$19,000
$6,000
Which option would you recommend for Miles?
Subcompact
Compact
Full size
There is no difference among the options
| States of Nature | |||
| Alternatives | Lower gas prices | Gas prices unchanged | Higher gas prices |
| Probability | .3 | .5 | .2 |
| Subcompact | $16,000 | $21,000 | $23,000 |
| Compact | $15,000 | $20,000 | $22,000 |
| Full size | $18,000 | $19,000 | $6,000 |
Solution
Miles should go for subcompact as it has a higher EMV.
| EMV for Subcompact | 0.3*16000+0.5*21000+0.2*23000 | = | $19,900 |
| EMV for Compact | 0.3*15000+0.5*20000+0.2*22000 | = | $18,900 |
| EMV for Full size | 0.3*18000+0.5*19000+0.2*6000 | = | $16,100 |
