3. Public Goods: A family of three bears are planning to spend a relaxing weeken
ID: 1120031 • Letter: 3
Question
3. Public Goods: A family of three bears are planning to spend a relaxing weekend in their den eating porridge, going out for long walks, and sleeping. However, given past experience, they are worried someone may break into their den while they are out walking and eat their porridge. To prevent this, they are thinking about hiring a security service to patrol the area around their den. The table gives each bear's marginal benefit for the number of times the security service patrols per hour: Mama Bear Papa Bear Baby Bear First patrol per hour Second patrol per hour Third patrol per hour Fourth patrol per hour Fifth patrol per hour $12 $10 $2 $1 $6 $4 $2 $1 $0 $5 Answer the following as briefly and concisely as possible Are the security service's patrols a public good for the bears? Why or why not? If it costs $20 for the first patrol per hour and then $12 for each additional patrol per hour, how many patrols per hour should the bears purchase to maximize their total surplus? If they choose the optimal number from part (b) and then split the cost of the patrols equally, how much surplus does each person obtain from the patrols? Is there any way to split the cost to ensure that everyone benefits? What practical problems does this solution raise? Suppose they agree in advance to choose the efficient number and split the cost of the patrols equally. When Papa Bear is asked his marginal benefit, will he have an incentive to lie? If so, what might he say. If not, why? a. b. c. d. e.Explanation / Answer
a. No, the security service's patrols are not public goods for the bears because they are paying the price for their services to them.
b.
b. from the above table we can say that given the cost and benifit of patroling, 2 hours of petroling would maximize their total surplus because that would cost them $32, which is equal to their total benifit of $32.
c. If the cost of $32 is split equally i.e. $32/3 = 10.67
the mamma bear will benefit $5.33; papa bear will benefit $1.33 and baby bear will lose $6.67.
d. the cost can be split according to the amount of benefit each one of them is reaping from the patroling services. the practical problem that will be faced is the dollar assertation of the benefit to ach one of them.
mamma bear papa bear baby bear cost per hour Total Utility Total Cost 1st patrol per hour $28 $17 $6 $20 $51 $20 2nd patrol per hour $16 $12 $4 $12 $32 $32 3rd patrol per hour $13 $10 $2 $12 $25 $44 4th patrol per hour $11 $2 $1 $12 $14 $56 5th patrol per hour $5 $1 $0 $12 $6 $68Related Questions
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