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Four partners (Adams, Benson, Cagle, and Duncan) jointly own a piece of land with a
Chapter 3, Problem 9(choose chapter or problem)
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 \(s_{1}, s_{2}, s_{3}\), 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 $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 \(s_{1}, s_{2}, s_{3}\), and \(s_{4}\) as fair shares.
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QUESTION:
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 \(s_{1}, s_{2}, s_{3}\), 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 $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 \(s_{1}, s_{2}, s_{3}\), and \(s_{4}\) as fair shares.
ANSWER:Step 1 of 14
Total value of land \(v=\$ 400,000\)
Since land is divided into 4 parcels the mean value of one parcel will be:
\(v_{\text {mean }}=\frac{v_{n}}{4}\)
\(v_{\text {mean }}=\frac{400,000}{4}\)
\(v_{\text {mean }}=\$ 100,000\)
Let us assume that:
\(\begin{array}{l}\text{Value of parcel } s_{1}=\$ v_{1}\\ \text{Value of parcel } s_{2}=\$ v_{2}\\ \text{Value of parcel } s_{3}=\$ v_{3}\\ \text{Value of parcel } s_{4}=\$ v_{4}\end{array}\)
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