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POVERTY REDUCTION STRATEGY TN

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Annexure 1.1<br />

<strong>POVERTY</strong> MEASURES: AXIOMATIC FRAMEWORK: DEFINITIONS<br />

Focus Axiom<br />

Focus Axiom: P (x; z) – P (y; z) whenever x ε D is obtained from у ε D by an increment to a nonpoor<br />

person.<br />

Replication Invariance Axiom<br />

Replication Invariance Axiom: P (x; z) = P (y; z) whenever x is obtained from y by a (k-) replication.<br />

Continuity and Restricted Continuity Axioms<br />

Continuity Axiom: P (x; z) is continuous as a function of x on D for any given z.<br />

Restricted Continuity Axiom: P (x; z) is left continuous as a function of x i on D (z). This can also be<br />

phrased as requiring P (x; z) to be continuous in x,; in the neighborhood of x.<br />

Symmetry Axiom<br />

Symmetry Axiom: P (x; z) = P (y; z) whenever x ε D is obtained from y ε D by a permutation.<br />

Weak and Strong Monotonicity Axiom<br />

Weak Monotonicity Axiom: P (x; z) > P (y; z) whenever x ε D is obtained from y ε D by a simple<br />

decrement to a poor person.<br />

Strong Monotonicity Axiom: P (x; z) < P (y; z) whenever x ε D is obtained from y ε D by a simple<br />

increment to a poor person.<br />

Minimal and Weak Transfer Axioms<br />

Minimal Transfer Axiom: P (x; z) < P (y; z) [P (x; z) > P (y; z)] whenever x ε D is obtained from y ε<br />

D by a progressive (regressive) transfer between two poor persons with no one crossing the poverty<br />

line as a consequence of the transfer.<br />

Weak Transfer Axiom: P (x; z) < P (y; z) [P (x; z) > P (y; z)] whenever x ε D is obtained from y ε D<br />

by a progressive (regressive) transfer with at least the recipient (donor) being poor with no one<br />

crossing the poverty line as a consequence of the transfer.<br />

Regressive and Progressive Transfer Axioms<br />

Regressive Transfer Axiom: P (x; z) > P (y; z) whenever x ε D is obtained from y ε D by a regressive<br />

transfer with at least the donor being poor.<br />

Progressive Transfer Axiom: P (x; z) < P (y; z) whenever x ε D is obtained from y ε D by a<br />

progressive transfer with at least the recipient being poor.<br />

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