The background for this problem comes from Moby Dick; or, The Whale by Herman Melville. If you are interested, it is Chapter 16:

http://www.americanliterature.com/Melville/MobyDickorTheWhale/17.html

The ship owners never know beforehand how successful a voyage will be. Let%u2019s suppose that the barrels of oil from a voyage can range evenly from 1,200 barrels to 5,000 barrels, with revenue of $15 per barrel. The fixed cost of fitting out a ship and making the voyage is $5,000, and the variable cost is $5 per barrel. If I made my computations correctly, the expected profit is $26,000, though it ranges from $7,000 to $45,000.

Included in the fixed cost of $5,000 is the cost of feeding the crew for the voyage. The $5,000 does not include the crewmember pay above the cost of food that a crewmember gets for participating in the voyage.

Herman Melville writes as though the participants in the voyage all take a share of the profits. If they provide a lot of the capital, like providing funds to outfit the ship, they get a large share of the profits. If they sign on as crewmembers, they get smaller shares of the profit. Using my numbers from above, if Ishmael signs on for a 1/50th share of the profits, his expected share of the voyage is $520, though it ranges from $140 to $900. This substitutes for the voyage pay that Ishmael might get in addition to the cost of his food.

Required:

1. Consider the cost-volume-profit structure proposed above.

a. What is the profit remaining for other participants after Ishmael gets his 1/50th share, supposing that they retrieve 1,200 barrels?

b. What is the profit remaining for other participants after Ishmael gets his 1/50th share, supposing that they retrieve 5,000 barrels?

c. What is the expected profit remaining for other participants after Ishmael gets his 1/50th?

2. We can imagine that Ishmael might request a fixed wage rather than a share of profits. For example Ishmael might try to bargain for fixed wages of $520 and forego the share of profits. This would raise the fixed cost of the voyage to $5,520, and the variable cost per barrel would be unchanged.

a. What is the profit remaining for other participants with Ishmael getting a fixed $520 for the voyage supposing that they retrieve 1,200 barrels?

b. What is the profit remaining for other participants with Ishmael getting a fixed $520 for the voyage supposing that they retrieve 5,000 barrels?

c. What about at 3,000 barrels?

d. What would be the expected profits remaining to other participants if Ishmael were to make this bargain to take the fixed $520?

3. What seems to be the captain%u2019s and ship%u2019s outfitter%u2019s motivation for making all the participants, including the crewmembers, take a share of profits rather than giving a fixed wage? Is the motivation to build an incentive to work hard with a pay-for-outcome regime? Is the motivation risk-sharing?