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

 

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Suppose that a preference relation over R2 is represented by a utility function x(U₁x.qu=)1x(₁u+)2(2), where u₁: R++→ R and u₂: R++→ R are strictly increasing, continuous and twice differentiable functions: u₁, ₂ are strictly concave. Prove that there exists numbers a > 0 and b R such that u₁(x) = au₂(x) + b. Suppose that a preference relation over R2 is represented by a utility function x(U₁x.qu=)1x(₁u+)2(2), where u₁: R++→ R and u₂: R++→ R are strictly increasing, continuous and twice differentiable functions: u₁, ₂ are strictly concave. Prove that there exists numbers a > 0 and b R such that u₁(x) = au₂(x) + b.

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Periodic review system also called fixed interval reorder system has four original econom... View the full answer