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{"ops":[{"insert":"(a) consider three consumers who care about the consumption of a private good and their consumption of a public good. their utility function are given by\nU"},{"attributes":{"script":"sub"},"insert":"i"},{"insert":"=X"},{"attributes":{"script":"sub"},"insert":"i"},{"insert":"G \t\t\t\t\t i = 1, 2, 3\nwhere X"},{"attributes":{"script":"sub"},"insert":"i"},{"insert":" is consumer i's consumption of the private good and G is the amount of the public good consumed by all. the unit cost of the private good is $1 and the unit cost of the public good is $10. individual wealth levels are w"},{"attributes":{"script":"sub"},"insert":"1"},{"insert":"=30, w"},{"attributes":{"script":"sub"},"insert":"2"},{"insert":"= 50 and w"},{"attributes":{"script":"sub"},"insert":"3"},{"insert":" = 20.\n\n(i) compute the marginal rate of substitution between G  and X for each of the three consumers.\n\n(ii) derive the samuelson condition for this model\n\n(iii) derive the aggregate resource constraint and compute the optimal level of public good consumption.\n\n(b) brief discuss the relevance of the samuelson condition in consideration to provide public goods in your country\n"}]}

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