An economy consists of two individuals, A and B and two goods, a private good, which is called good 1, and a public good, which is called good 2. Each individual i = A, B is endowed with 24 units of time, which can be used to produce an amount of a private good at a labour cost of a units of time, and an amount of a public good at a labour cost of 2x2 units of time. Individual i's utility function is given by u(x₁, x2) = (xi)¹/2(g)¹/2, for both i = A, B and where g denotes the aggregate provision of the public good, i.e. g = x2 + x. (a) Derive the allocation that maximises utilitarian welfare (i.e. the sum of both individ- ual's utility functions). 3

An economy consists of two individuals, A and B and two goods, a private good, which is called good 1, and a public good, which is called good 2. Each individual i = A, B is endowed with 24 units of time, which can be used to produce an amount of a private good at a labour cost of a units of time, and an amount of a public good at a labour cost of 2x2 units of time. Individual i's utility function is given by u(x₁, x2) = (xi)¹/2(g)¹/2, for both i = A, B and where g denotes the aggregate provision of the public good, i.e. g = x2 + x. (a) Derive the allocation that maximises utilitarian welfare (i.e. the sum of both individ- ual's utility functions). 3

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.1P

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