Question:
Suppose that the utility function \(π’: R^π_+βR_+\) represents a complete, transitive and continuous preference relation over all bundles of π goods. Then select the choices below in which the function also represents the same preference relation.
Suppose that the utility function \(π’: R^π_+βR_+\) represents a complete, transitive and continuous preference relation over all bundles of π goods. Then select the choices below in which the function also represents the same preference relation.
Updated On: Oct 1, 2024
- π(π₯1, π₯2, β¦ , π₯π ) = π’(π₯1, π₯2, β¦ , π₯π ) + (π’(π₯1, π₯2, β¦ , π₯π ))3
- \(π(π₯_1, π₯_2, β¦ , π₯_π ) = π’(π₯_1, π₯_2, β¦ , π₯_π ) + β^n_{i=1}π₯_i\)
- \(β(π₯_1, π₯_2, β¦ , π₯_π ) = (π’(π₯_1, π₯_2, β¦ , π₯_π )) ^{\frac{1}{n}}\)
- \(π(π₯_1, π₯_2, β¦ , π₯_π ) = π’(π₯_1, π₯_2, β¦ , π₯_π ) + (π₯^2_1 + π₯^2_2 + β― + π₯^2_n ) ^{0.5}\)
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The Correct Option is A, C
Solution and Explanation
The correct options is (A): π(π₯1, π₯2, β¦ , π₯π ) = π’(π₯1, π₯2, β¦ , π₯π ) + (π’(π₯1, π₯2, β¦ , π₯π ))3 and (C): \(β(π₯_1, π₯_2, β¦ , π₯_π ) = (π’(π₯_1, π₯_2, β¦ , π₯_π )) ^{\frac{1}{n}}\)
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