Problem Solving

1. In this question, you will need to calculate the Head Count Ratio and Poverty Gap Index using the data provided below.

Poverty Gap Index (PGI) =

Where the variables are defined as follows:

N = Total population

z = Income at the poverty line

j = household number (if there are 4 households, j = 1, 2, 3, 4)

y_j = Income of individuals below the poverty line

q = Number of people below the poverty line

Consider the county Vernon with 8 households, hence j = 1 to 8. The income poverty line (z) = $45/month. The incomes (y_j) of the 8 households are:

y₁ = $40/month

y₂ = $35/month

y₃ = $30/month

y₄ = $25/month

y₅ = $20/month

y₆ = $15/month

y₇ = $10/month

y₈ = $5/month

Answer the following questions:

1. Calculate the Head Count Ratio (HCR). Show your calculations.

2. Calculate the PGI using the formula and the data in this question. Show your calculations.

3. Calculate the Squared PGI.