Zoe is trying to decide how to divide her time between her job as a wedding phot
ID: 1213418 • Letter: Z
Question
Zoe is trying to decide how to divide her time between her job as a wedding photographer, which pays $27 per hour for as many hours as she chooses to work, and as a fossil collector, in which her pay depends on both the price of fossils and the number of fossils she finds. Earnings aside, Zoe is indifferent between the two tasks, and the number of fossils she can find depends on the number of hours a day she searches, as shown in the table below:
a. Using the information above, compute the lowest price that Zoe would accept per fossil in order to justify her spending more time collecting fossils and less time working as a wedding photographer. (Instruction: Round your answers to two decimal places.)
b. The relationship between the lowest price and the number of fossils collected is called the (Click to select)demand curvesupply curve.
per day Total fossils
per day Lowest price Zoe
would accept per fossil 1 6 $ 2 11 $ 3 15 $ 4 18 $ 5 20 $
Explanation / Answer
Answer:
If the price of a fossil is less than $6, Zoe should devote all her time to photography because when the price is say, $5 per fossil, an hour spent looking for fossils will give her 5($5) = $25, or less than she earn doing photography. If the price of fossils is $6, Zoe should spend one hour searching, will supply 5 fossils, and will get $30 in revenue, which is $3 more than she would earn from photography. However, an additional hour would yield only 4 additional fossils or $24 additional revenue. So she should not spend any further time looking for fossils. If the price of fossils rises to $7, the additional hour gathering fossils would yields an additional $28. So gathering fossils during that hour would then be the best choice, and Zoe would therefore supply 9 fossils per day. Using this rezoning, we can derive a price-quantity supplied relationship for fossils as follows table:
Hours per day
Total fossils per day
Additional no. of fossils found
Lowest price per fossil
1
5
5
$27/5 = $5.40
2
9
4
$27/4 = $6.75
3
12
3
$27/3 = $9.00
4
14
2
$27/2 = $13.50
5
15
1
$27/1 = $27.00
Hours per day
Total fossils per day
Additional no. of fossils found
Lowest price per fossil
1
5
5
$27/5 = $5.40
2
9
4
$27/4 = $6.75
3
12
3
$27/3 = $9.00
4
14
2
$27/2 = $13.50
5
15
1
$27/1 = $27.00
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