Question 14.43
13.
Abe, Beth, Charles, and David have decided to invest in rare coins. A dealer has offered to sell them a parcel containing 100 identical coins for $10,000. Each person invests all that he or she can afford, but there is not quite enough money, so Charles asks his Aunt Esther to join the group. The coins will be apportioned by the Hamilton method. Here are the amounts invested:
| Investments | |
|---|---|
| Abe | $3,619 |
| Beth | 1,862 |
| Charles | 2,258 |
| David | 2,010 |
| Esther | 251 |
| Total | $10,000 |
- How should the coins be apportioned among the five contributors?
- After the coins are distributed, the dealer mentions that there will be $50 in excise tax. Everyone empties his or her wallet: Abe finds $16 more, Beth has $2, Charles has $1, and David finds $32. This adds up to $51, so $1 is returned to Aunt Esther. The apportionment is recalculated, and one of the coins changes hands. Who has to give a coin to whom?
Explain what happened.
To see how this situation works out with a different apportionment method, refer to Exercise 31 on page 616.
13.
(a) Abe, 36 coins; Beth, 19 coins; Charles, 23 coins; David, 20 coins; Esther, 2 coins
(b) Charles must give Esther a coin.
(c) Blame the population paradox.