I’ve to work late every Saturday night.

So, I need to have a good sleep every Sunday morning.

Peter

Sunday is our family day!

We used to playing on the playground on every Sunday morning.

Lee’s family

Suppose there’re only 5 hours in the morning , the transaction cost is 0….

Since the property right of a silent environment in the playground is not well-defined, so they don’t care about each other and the LEEs play all the 5 hours in the Sunday morning.

Peter can’t stand with the noise of the LEEs… So, he writes a letter to the Lee’s family.

Dear Lee's family,

I really can’t sleep on Sunday morning with the

noise made by your children.

I’m willing to pay you money for giving me silent

morning on Sunday.

Your neighbour, Peter

The Lee’s family also write a letter to Peter.

Dear Peter,

We’re sorry. But we’re also willing to pay

you money for letting us play on the playground on every

Sunday morning.

Your neighbour, Lee’s family

If the property right of a silent environment in the playground is given to Peter, he can sleep 5 hours in the Sunday morning. But his neighbour will try to negotiate with him by paying money to him as compensation, then … …

$ 20$ 05th

$ 30$ 204th

$ 40$ 303rd

$ 50$ 502nd

$ 400$ 5001st

Maximum amount willing to pay for

playing on the playground (Lee’s

family)

Marginal Private Benefit of sleeping

(Peter)Hours

MPB (min. amt. need to receive) of Peter to sleep in the 5th hour : $0

Lee’s family’s max. amt. willing to pay for playing the 1st hour on the playground : $400

Min. < Max.

$ 20$ 05th

$ 30$ 204th

$ 40$ 303rd

$ 50$ 502nd

$ 400$ 5001st

Maximum amount willing to pay for

playing on the playground (Lee’s

family)

Marginal Private Benefit of sleeping

(Peter)Hours

MPB (min. amt. need to receive) of Peter to sleep in the 4th hour : $20

Lee’s family’s max. amt. willing to pay for playing the 2nd hour on the playground : $50

Min.<Max.

$ 20$ 05th

$ 30$ 204th

$ 40$ 303rd

$ 50$ 502nd

$ 400$ 5001st

Maximum amount willing to pay for

playing on the playground (Lee’s

family)

Marginal Private Benefit of sleeping

(Peter)Hours

MPB (min. amt. need to receive) of Peter to sleep in the 3rd hour : $30

Lee’s family’s max. amt. willing to pay for playing the 3rd hour on the playground : $40

Min. < Max.

$ 20$ 05th

$ 30$ 204th

$ 40$ 303rd

$ 50$ 502nd

$ 400$ 5001st

Maximum amount willing to pay for

playing on the playground (Lee’s

family)

Marginal Private Benefit of sleeping

(Peter)Hours

MPB (min. amt. need to receive) of Peter to sleep in the 2nd hour : $50

Lee’s family’s max. amt. willing to pay for playing the 4th hour on the playground : $30

Max. < Min.

$ 20$ 05th

$ 30$ 204th

$ 40$ 303rd

$ 50$ 502nd

$ 400$ 5001st

Maximum amount willing to pay for

playing on the playground (Lee’s

family)

Marginal Private Benefit of sleeping

(Peter)Hours

MPB (min. amt. need to receive) of Peter to sleep in the 1st hour : $500

Lee’s family’s max. amt. willing to pay for playing the 5th hour on the playground : $20

Max. < Min.

When the property right of a silent environment in the playground is given to Peter, after negotiation,

Peter will sleep 2 hours while the Lee’s family will play 3 hours on Sunday morning.

If the property right of a silent environment in the playground is given to the Lee’s family, they will play 5 hours in the Sunday morning. But Peter must negotiate with them by paying money to

them as compensation. Then … …

$ 20$ 05th

$ 30$ 204th

$ 40$ 303rd

$ 50$ 502nd

$ 400$ 5001st

Marginal Private Benefit

of playing on the playground (Lee’s

family)

Maximum amount willing to pay for sleeping (Peter)

Hours

MPB (min. amt. need to receive) of the Lee’s family for not playing in the playground in the 5th hour : $20

Peter’s max. amt. willing to pay for sleeping in the 1st hour : $500Max.> Min.

$ 20$ 05th

$ 30$ 204th

$ 40$ 303rd

$ 50$ 502nd

$ 400$ 5001st

Marginal Private Benefit

of playing on the playground (Lee’s

family)

Maximum amount willing to pay for sleeping (Peter)

Hours

MPB (min. amt. need to receive) of the Lee’s family for not playing in the playground in the 4th hour : $30

Peter’s max. amt. willing to pay for sleeping in the 2nd hour : $50Max. > Min.

$ 20$ 05th

$ 30$ 204th

$ 40$ 303rd

$ 50$ 502nd

$ 400$ 5001st

Marginal Private Benefit

of playing on the playground (Lee’s

family)

Maximum amount willing to pay for sleeping (Peter)

Hours

MPB (min. amt. need to receive) of the Lee’s family for not playing in the playground in the 3rd hour : $40

Peter’s max. amt. willing to pay for sleeping in the 3rd hour : $30Min. > Max.

$ 20$ 05th

$ 30$ 204th

$ 40$ 303rd

$ 50$ 502nd

$ 400$ 5001st

Marginal Private Benefit

of playing on the playground (Lee’s

family)

Maximum amount willing to pay for sleeping (Peter)

Hours

MPB (min. amt. need to receive) of the Lee’s family for not playing in the playground in the 2nd hour : $50

Peter’s max. amt. willing to pay for sleeping in the 4th hour : $20Min. > Max.

$ 20$ 05th

$ 30$ 204th

$ 40$ 303rd

$ 50$ 502nd

$ 400$ 5001st

Marginal Private Benefit

of playing on the playground (Lee’s

family)

Maximum amount willing to pay for sleeping (Peter)

Hours

MPB (min. amt. need to receive) of the Lee’s family for not playing in the playground in the 1st hour : $400

Peter’s max. amt. willing to pay for sleeping in the 5th hour : $0 Min. > Max.

When the property rights of the playground is given to the Lee’s family,

The Lee’s family will play 3 hours while Peter will sleep 2 hours on Sunday morning.

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