(f) The poverty gap index (PGI) captures the average percentage shortfall in income om the poverty line. It is dened as follows: 1 _ l q" '3 y}' PCJ vii __f ) .l 3] J}.- where N is total population, q is the number of poor, 2 is the poverty line, and y,- is the income for person j living below the poverty line. Explain one benet of this measure relative to the poverty headcount. Explain one shortcoming of this measure. Hint: Use the transfer principle for both examples