voluntary distribution consider an economy inhabited by four people, identified

Question

voluntary distribution

consider an economy inhabited by four people, identified by the numbers 1, 2, 3 and 4. The utility function of person i (where i is 1, 2, 3 or 4) is Ui = biZ Here, 6, is person i's consumption of bread and z is the quantity of a public good in the economy. Each person is endowed with 20 units of bread. Four units of bread are needed to produce each unit of public good. Which of the following allocations is Pareto optimal? "There is a Pareto optimal allocation in which person 4 consumes no bread." Imagine that the public good is provided through voluntary contributions. Let 1be the quantity of bread contributed by person i, and let be the quantity of bread contributed by the other three people. Person i's best response function is

Explanation / Answer

7. you calculate utility at various values of z and b and you will find that it reduces as we move away from z = 10 and b = 10 on either side. this values maximizes the utility function of all the 4 people. they can not increase their utility without reducing other people's utility.

8. if b4 = 0, then utility of person 4 is zero. so this solution can not be pareto optimal.

9. as seen in seventh, the pareto optimal allocation is: b1=b2=b3=b4=10, z=10. so, the contribution should be 10 from each. but in any case, it has to be less than 10.also it can not be (d) because it will become 0 at Vi bar = 20. so the correct option is (b) Vi = 10 - vi/2.

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