For problems 1 -- 5 we will use data from the 2008 Mexico National Rural Household Survey (EncuestaNacional a HogaresRurales de México, acronym: ENHRUM) to study inequality and poverty in rural Mexico.

For problems 1 -- 5 we will use data from the 2008 Mexico National Rural Household Survey (EncuestaNacional a HogaresRurales de México, acronym: ENHRUM) to study inequality and poverty in rural Mexico. This data set was collected by UC Davis and the Colegio de México. The household data file called “Mexico Household Data” is available on StartSmite. This data set contains the following variables for the 1,437 sampled households:

(A) ID : The household identifying code(you don’t have to worry about this)

(B) yi: The household’s income in 2007, excluding government transfers. You will notice that the first (poorest) households actually had negative income in 2007, mostly due to agricultural and livestock losses.

(C) Ri: The rank of each household based on their income (i.e., The poorest is 1, the richest is 1,437).

(D) F(yi):the fraction of all households with income at or below household i’sincome.

(E) Ti: The amount of income transferred from the government to household i.

1. What is the average household income for rural Mexico’s in 2007 excluding government transfers? Report your answer in $US using the exchange rate of 10.8 Pesos per $1US.

2. In the year of the survey, the per-capita food poverty line in rural Mexico was 7,596 pesos. Based on this food poverty line, calculate the headcount poverty index and poverty gap. Assume each household has a single member. Briefly explain what each one means:

a. The Poverty Headcount Index

b. TheTotal Poverty Gap

3. Calculate the Gini coefficient of inequality for rural Mexican households excluding government transfers.

Mexico has two main government programs that transfer income to rural households. The first is PROCAMPO, which pays a fixed amount per acre to farmers who grew basic grains prior to the North American Free Trade Agreement (NAFTA). The goal of PROCAMPO was to replace pre-NAFTA output price supports which were no longer allowed under NAFTA. The second is OPORTUNIDADES, a welfare program that gives payments to poor women provided that their children are enrolled in schools and in the local clinic.

4. Add government transfers to household income in your spreadsheet. To explore the impacts of the government’s transfer program on poverty and inequality, re-calculate the following values with transfers included in household income:

a. Average household income (in $US using the exchange rate of 10.8 Pesos per $1US)

b. The Poverty Headcount Index

c. The Total Poverty Gap

d. The Gini coefficient

5. Briefly discuss the effectiveness of the Mexican government’s transfer program on poverty and inequality.

Questions 6 asks you to explore more deeply various measures of income inequality in the context of two hypothetical countries.

6. Consider a society (Society A) in which incomes take values in $100 increments between $100 and $1000. An equal proportion of the society’s population (10%) occupies each of the ten income classes. In other words, the income distribution for this society is as follows:

Table 1. Income Distribution in Society A
Income Level	Percent of Population	Cumulative percent of Income	Cumulative Percent of Population
$100	10%	1.8%	10%
$200	10%	5.5%	20%
$300	10%	10.9%	30%
$400	10%	18.2%	40%
$500	10%	27.3%	50%
$600	10%	38.2%	60%
$700	10%	50.9%	70%
$800	10%	65.5%	80%
$900	10%	81.8%	90%
$1000	10%	100.0%	100%

a. Fill out the last two columns of Table 1 and show this income distribution as a bar chart or histogram. NOTE: This is NOT the same as a Lorenz curve. Put the income level categories on the horizontal axis and Percent of population in each category on the vertical axis.

b. Now consider another society (Society B) in which 50% of the population have incomes equal to $300 and the other 50% have incomes equal to $800:

Table 2. Income Distribution in Society B
Income Level	Percent of Population	Cumulative percent of Income	Cumulative Percent of Population
$300	50%	27%	50%
$800	50%	73%	100%

Fill out Table 2 and create the same kind of income distribution diagram that you made in part (a) for this second economy.

c. Intuitively rank the level of inequality in these two societies. Which seems most ‘unequal’ to you? In which society might there be a greater awareness of inequality? In which might there be greater scope for social unrest? (Note: there is no single right answer to these questions. The point is to get you to think critically about our measures of inequality in the context of socio-economic polarization. Please explain your thinking carefully.)

d. On a single graph, graph the Lorenz curves for each society (you may want to fill out the cumulative population and cumulative income columns in the charts above before doing this). Which society has the more equal distribution by the Lorenz criterion?

e. Compute the Gini coefficient and the coefficient of variation for both societies. According to these measures of inequality, in which society is income more equally distributed?

f. Does your answer to part (c) coincide with the answers to parts (d) and (e)? If not, what is wrong with either your intuition or with the inequality criteria used in part (d)?

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