Question

Zoe is trying to decide how to divide her time between her job as a wedding photographer, which pays $40 per hour for as many hours as she chooses to work, and as a rock collector, in which case her pay depends both on the price of the rocks and the number of them she finds. These are special rocks so they have value! Earnings aside, Zoe is indifferent between the two jobs.   The number of rocks she can expect to find depends on the number of hours she searches:

Hours per day	Total rocks per day
0	0
1	7
2	13
3	17
4	20
5	21

The marginal cost of spending one hour hunting for rocks is equal to $________ .

If the price per rock is $10 then the marginal benefit of spending one hour hunting for rocks is equal to $______ .

If the price per rock is $20, then her best choice is to spend ______ hours hunting for rocks.

If the price per rock falls to $10 then her best choice is to spend ________ hours hunting for rocks.

Answer 1

The cost of hunting rocks per hour is equal to what Zoe must be giving up that she would have done in this hour . This is known as the opportunity cost. Zoe's opportunity cost is the cost of not working as a photographer which is $40 ie the pay she gets as a photographer per hour.

If the price of each rock is $10, the marginal benefit would be the product of rocks collected in first hour and the price of each rock which is $ 7*10=$70

If the price per rock is$20, below is the trade off given as per her pay as a photographer and benefit as rock hunter.

Hours per day	Marginal benefit from rocks when price is $10	Opportunity cost per hour(marginal cost per hour)	Marginal benefit from rocks when price is $20
0	0	40
1	7*10=$70	40	7*20=$140
2	6*10=$60	40	6*20=$120
3	4*10°$40	40	4*20=80
4	3*10=$30	40	3*20=$60
5	1*10=$10	40	1*20=$20

If price is rock is$20, it is better that she spends 4 hours collecting rocks because till then her marginal benefit is more than the marginal cost.

It is better if she spends 3 hours in collecting rocks and rest in photography when the price per rock is$10 because after 3 hours her marginal benefit from collecting rocks is less the the marginal cost.

(You can comment for doubts)