Question

Zoe is trying to decide how to divide her time between her job as a wedding photographer, which pays $30 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 this information, 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. Instructions: Complete the table below. Enter your responses rounded to two decimal places. Hours per day Total fossils per day Lowest price Zoe would accept per fossil 1 6 $ 2 11 $ 3 15 $ 4 18 $ 5 20 $

b. The relationship between the lowest price and the number of fossils collected is called the .

Answer 1

Zoe can either be a photographer or a fossil collector. She is geeting $30 per hour for being a photographer and her rate of fossil collector is not given. Also we know that she is indifferent between a fossil collector and a photographer.

The table given shows us the number of fossils she collects with the number of hours spent.

Hours per day	fossils per day	additional fossils each hour	lowest price for per fossil
1	6	6	30/6=$ 5
2	11	5	30/5=$ 6
3	15	4	30/4= $7.5
4	18	3	30/3=$ 10
5	20	2	30/2= $15

For finding the lowest price per fossil , we would need to divide the per hour pay as a photographer by the additional number of fossils.

Reason being that she should atleast be compensated for the time she is not spending on photography by the price of each fossil she gets , since she is indifferent between them.

So for the first hour, if she decides to spend her time collecting fossils, the minimum she should earn is her opportunity cost of $30 which she would have got by being the photographer.

In this hour she is finding 6 fossils , so the price per fossil to atleast compensate her photographer wage is $ 30/6= $5.

Similarly in the next hour she is finding 5 fossils, her wage foregone is same $30, so the price per fossil should be $30/5=$6.

In the third hour the price for 4 additional fossils would be $30/4= $7.5

In the fourth hour, price for additional 3 fossils be 30/3=$10

In the last hour , the price for additional 2 fossils would be $30/2=$15.

b) The relationship between the lowest price and the number of fossils collected is known as the supply curve. It is the supply of fossils Zoe is willing to have at the lowest price ie the minimum price at which she would be trading for a given hour.

(You can comment for doubts)