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Suppose that a preference relation over R2 is represented by a utility function x(Ux.qu=)1x(u+)2(2), where u: R++ R and u: R++ R are strictly

Suppose that a preference relation over R+ is represented by a utility function 2(U14,2u=)14(14+)22(2), where u: R++ R and U2 

Suppose that a preference relation over R2 is represented by a utility function x(Ux.qu=)1x(u+)2(2), where u: R++ R and u: R++ R are strictly increasing, continuous and twice differentiable functions: u, are strictly concave. Prove that there exists numbers a > 0 and b R such that u(x) = au(x) + b.

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