Question

You and your friends want to buy a condo at the beach to time share. Each of you has single peaked preferences with a most preferred value that you are willing to spend. These values are: Mabel, $10,000; Gertrude, $20,000; Myron, $30,000; Wilber, $40,000; and you, $50,000. The condo costs $150,000. Explain how to implement a uniform rule mechanism to allocate costs and shares.

Answer 1

Answer:

Individual                   Cost                                Shares to be enjoyed

Mabel                      $10,000                            10000 / 150000 =  6.67%

Gertrude                 $20000                            20000 / 150000 = 13.3%

Myron                      $30000                            30000 / 150000 = 20%

Wilber                      $40000                            40000 / 150000 = 26.6%

You                          $50000                            50000 / 150000 = 33.3%

Explanation:

peaked preferences

Most preferred value to spend :

Mabel = $10,000

Gertrude = $20,000

Myron = $30,000

Wilber = $40,000

you = $50,000

cost of Condo = $150,000

Implementing a Uniform rule mechanism to allocate costs and shares

The uniform rule ; ∑ j∈I Uj (p) = Ω.

where Ω = fixed amount of resource

hence the summation of all allotment should = Ω ( $150,000 )

Number of friends = 5

cost of condo  = $150,000

If divide equally each person will have to pay ; $150,000 / 5 = $30,000

Total money to be spent by friends = 10,000 + 20,000 + 30,000 + 40,000 + 50,000  = $150,000

Individual                   Cost                                shares to be enjoyed

Mabel                      $10,000                            10000 / 150000 =  6.67∑%

Gertrude                 $20000                            20000 / 150000 = 13.3%

Myron                      $30000                            30000 / 150000 = 20%

Wilber                      $40000                            40000 / 150000 = 26.6%

You                          $50000                            50000 / 150000 = 33.3%

∑shares ≈ 100% ( 150,000 )