Chapter 3, Problem 7E

Four partners (Adams, Benson, Cagle, and Duncan) jointly own a piece of land with a market value of $400,000. Suppose that the land is subdivided into four parcels $s_1,s_2,s_3\text{, and }{s}_4$. The partners are planning to split up, with each partner getting one of the four parcels.

a. To Adams, $s_1$ is worth $40,000 more than $s_2$, $s_2$ and $s_3$ are equal in value, and $s_4$ is worth $20,000 more than $s_1$. Determine which of the four parcels are fair shares to Adams.

b. To Benson, $s_1$ is worth $40,000 more than $s_2$, $s_4$ is worth $8,000 more than $s_3$, and together $s_4$ and $s_3$ have a combined value equal to 40% of the value of the land. Determine which of the four parcels are fair shares to Benson.

c. To Cagle, $s_1$ is worth $40,000 more than $s_2$ and $20,000 more than $s_4$, and $s_3$ is worth twice as much as $s_4$. Determine which of the four parcels are fair shares to Cagle.

d. To Duncan, $s_1$ is worth $4,000 more than $s_2$; $s_2$ and $s_3$ have equal value; and $s_1,s_2$, and $s_3$ have a combined value equal to 70% of the value of the land. Determine which of the four parcels are fair shares to Duncan.

e. Find a fair division of the land using the parcels $s_1,s_2,s_3\text{, and }{s}_4$ as fair shares.