Vacuuming an apartment can be viewed as a public good. (Another possible interpr

Question

Vacuuming an apartment can be viewed as a public good. (Another possible interpretation would be that clean carpet is a common resource, but that's for another day.) When my brother Fo and I lived together after college, this was a frequent point of contention. He valued clean carpet at P = 80 - 4Q, where P is dollars and Q is quarter-hours of vacuuming. (The biggest gain is the first 15 minutes of sweeping and the gains become progressively smaller.) I, on the other hand, spent little time rolling around on the floor and valued clean carpet at only P = 40 - 2Q. We both valued our time quite highly, feeling we needed $12 every fifteen minutes to compensate us for vacuuming. (Where applicable, QC is my quantity and QF is my brother's) If we live together (and my brother behaves short-sightedly), what happens? QC = 8.5, QF = 8.5 QC = 12, QF = 17 QC = 0, QF = 17 QC = 18, QF = 18

Explanation / Answer

At P=12

for my brother

Q = 20-P/4 = 17

For me

Q=20-P/2 = 14

Now as i know that gains are progressively becoming smaller with every quarter hour of work so i will work less than desired quantity so option B is correct

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