英语经济类计算题， 求解，急 65
ConsideraneconomywithtwoindividualsAandB.Thereexistoneprivategoodandonepublicgoodinth...
Consider an economy with two individuals A and B.There exist one private good and one public good in the economy.The utility functions of individual A and individual B are given by
uA=z^2xA (xA 是一个函数)
uB=zxB^2 ( xB 是一个函数)
respectively,where ui is individual i’s utility,xi is individual i’s private good consumption (i=A,B),z is public good consumption.The production possibility frontier is given by
x+z=60
where x is the total production of the private good and z is the total production of the public good.The social welfare function is given by
w=uAuB
where w is the level of social welfare.Answer the following questions.
1,Calculate the marginal rate of substitution (MRS) of the public good for the private good for each individual(Note:MRSzx=(δui/δz)/ (δui/xi)for individual i)
2,Find the marginal rate of transformation(MRT)of the public good for the private good.
3,Derive the Pareto optimality condition for provision of public good (i.e.,apply the Samuelson’s condition)
4,From the production possibility frontier,the feasibility condition is given by xA+xB+z=60 .Using this feasibility condition and the optimality condition derived in question3 ,express xA and xB in terms of z.
5,Find the optimal production of the public good to maximize the social welfare function
6,What are the allocations of the private good for these individuals?
有些字母是拉丁文，百度打不出来 不过经济达人应该都知道吧，谢谢 展开
uA=z^2xA (xA 是一个函数)
uB=zxB^2 ( xB 是一个函数)
respectively,where ui is individual i’s utility,xi is individual i’s private good consumption (i=A,B),z is public good consumption.The production possibility frontier is given by
x+z=60
where x is the total production of the private good and z is the total production of the public good.The social welfare function is given by
w=uAuB
where w is the level of social welfare.Answer the following questions.
1,Calculate the marginal rate of substitution (MRS) of the public good for the private good for each individual(Note:MRSzx=(δui/δz)/ (δui/xi)for individual i)
2,Find the marginal rate of transformation(MRT)of the public good for the private good.
3,Derive the Pareto optimality condition for provision of public good (i.e.,apply the Samuelson’s condition)
4,From the production possibility frontier,the feasibility condition is given by xA+xB+z=60 .Using this feasibility condition and the optimality condition derived in question3 ,express xA and xB in terms of z.
5,Find the optimal production of the public good to maximize the social welfare function
6,What are the allocations of the private good for these individuals?
有些字母是拉丁文，百度打不出来 不过经济达人应该都知道吧，谢谢 展开
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