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개념 기사 기사 작성법
내가 아는 수학개념을 쉽게 설명해주세요!
[개념 기사] 공평하게 돈을 내는 방법은?
베네딕트0724 2020.03.16 19:31

친구들과 노래방에 갔다고 생각해보세요. 노래방에서는 돈을 어떻게 나눠 내야 할까요?

노래방의 사용료를 인원 수로 나누어 각자 같은 비용을 내면 됩니다.

그런데, 엘리베이터를 설치할 때는 다릅니다. 엘리베이터를 높이 설치할수록 비용이 많이 드는데, 2층에 사는 사람은 2층까지, 3층에 사는 사람은 3층까지만 엘리베이터가 필요합니다.

2층에 사는 가민이는 4층짜리 엘리베이터를 설치하는데 같은 비용을 내는 것에 불만을 가지고 있네요.

가민이는 3층, 4층에 사는 나민이, 다민이를 어떻게 설득할까요?

사진 출처 : pxhere.com

 

공평한 분배 이론, 섀플리 값

이 문제를 해결하기 위해서는 섀플리 값을 알아야 합니다. 섀플리 값은 2012년 노벨 경제학상의 수상자, 로이드 섀플리가 창시한 분배이론입니다. 각자에게 필요한 금액만 분담하고, 필요없는 부분에 대한 금액은 지불하지 않는 방법입니다. 무슨 말인지 잘 모르겠죠? 가민이의 예시로 돌아가봅시다.

섀플리 값을 창시한 로이드 섀플리(출처 : ru.m.wikipedia.org)

 

엘리베이터를 2층까지 설치하는 데는 150만원이 필요합니다. 3층, 4층까지 엘리베이터를 설치하는 데는 각각 140만원, 100만원이 추가로 필요합니다. 4층에 사는 다민이는 엘리베이터 설치 비용을 똑같이 나눌 것을 제안했습니다.

가민 나민 다민
130만원 130만원 130만원

 

2층짜리 엘리베이터만 필요했던 가민이는 섀플리 값을 이용해서 이렇게 제안했어요.

층별 설치 비용 2층 3층 4층 총 분담 금액
가민 50만원 0 0 50만원
나민 50만원 70만원 0 120만원
다민 50만원 70만원 100만원 220만원

가민이는 3층, 4층을 설치하는데 필요한 돈은 지불하지 않았고, 나민이는 4층을 설치하는데 필요한 돈은 지불하지 않았어요. 여러분은 어떤 방법이 더 공평한 것 같나요? 여러분만의 분배 방법이 있다면 알려주세요!

 

<오늘의 QUIZ~>

엘리베이터를 2층까지 설치하는데 100만원, 3층까지 설치하는데 80만원이 필요하다고 합니다.

2층에 사는 수동이와 3층에 사는 과동이가 내야 할 금액을 섀플리 값을 이용해 구해보세요!

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