**1. Poverty Measures:** The national poverty line in South Africa in terms of monthly per-capita income is Z=325 Rand. Calculate and report in Table 2 the various poverty indices for 1993 and 2004. Report these results in Table 1 below using 2 decimals.

Table 1: Poverty Measures [3.5 points each]

2004

Poverty Headcount

Index

Poverty Gap Index

FGT-2

**2. Income Inequality: Lorenz Curve**

Plot the Lorenz curves for per-capita income for 1993 and 2004 in Excel. Put the two Lorenz curves on a single graph. While there are multiples ways to generate the Lorenz curves, we would like you to divide your sample into ten deciles of per-capita income (so that you have 10 points on the horizontal axis). Replicating and filling out Table 2 in Excel may help you plot the Lorenz curve for each year. Please paste your final graph into the box bellowed “ Figure 1: Lorenz Curves for 1993 & 2004.” (Report all numbers as a

percentage and use two decimal points. E.g., 12.25% )

Table 2: Template for Lorenz curve [0.3 for each entry in the table]

Income

Decile

Percent of

Population

Cumulative

percent of

Population

Cumulative

Percent of

Income 1993

Cumulative

Percent of

Income 2004

0 0 0 0 0

1 10%

2 10%

3 10%

4 10%

5 10%

6 10%

7 10%

1

In the year 2000, the market exchange rate was approximately 7 Rand/$US, while the PPP exchange rate was a bit under 3 Rand/$PPP.

1993

8 10%

9 10%

10 10%

3

Figure 1: Lorenz Curves for 1993 & 2004 [9 points]

Remember: the excel file that shows that you did this exact same graph may be requested (10% of the groups may be randomly

selected to submit them) your points will be lost if there is any discrepancy or the excel file not submitted.

**3. Income Inequality: Gini Coefficient**

Use the covariance formula to calculate the Gini coefficient and report the Gini coefficients for 1993 and 2004 in the table below.2

Your Gini coefficients should be between 0 and 1. (Use two decimal spaces for display)

Table 3: Gini coefficients for 1993 & 2004 [4 points each]

1993 2004

Gini coefficient

2 See Chapter 5 of Taylor and Lybbert (page 101) for instructions on calculating the Gini coefficient in Excel.

4

Based on your Lorenz curves and Gini coefficients, briefly explain what you conclude about the evolution of inequality. [2 points]

**4. Poverty Dynamics**

Because it is a panel data set, the KIDS data set permits us to see poverty transitions. Using the KIDS data, calculate the fraction (i.e., your number will be between 0 and 1) of households in each of the four cells in Table 3. Report results as a percentage using 2 decimal points. E.g., 12.25%

Table 3: Transition Matrix for Poverty in South Africa [6 points each]

Poor in

2004

Not Poor in

2004

Poor in

1993

Not Poor in

1993

**5. POLICY 1: A policy to reduce the Headcount Index**

Assume we are in the year 2004, and you are hired by the president of South Africa to design a policy to reduce the poverty headcount Index as much as possible. In order to simplify your calculations, assume that if the income of a household is exactly equal to the poverty line Z=325, the household is not poor. In order to implement the policy, the president imposes a tax of 10% on the income of all households earning 1,705 Rand per capita or more.

5

a. How much money does the South African government collect in tax revenues in 2004? [4 points]

Total amount

collected in

tax revenues

b. Describe – in words- your policy (how would you allocate the tax revenues to poor households to achieve the goal of minimizing the poverty headcount index?) Hint: Under this policy, you should not give a transfer to any household unless that transfer changes their poverty status. You may end up with a few dollars left (total amount transferred can be less than the total amount collected in taxes) [8 points]

c. Recompute the Poverty Head Count Index, the Poverty Gap Index, and the FGT-2 index after your tax and transfer policy is implemented. Report these results in Table 4 below using 2 decimals. Table 4: Poverty Measures After Policy 1 [1 point each]

2004-after implementing your

policy

Headcount Index

Poverty Gap Index

FGT-2

6

**6. POLICY 2: A policy to reduce extreme poverty**

The president is also considering an alternative policy whose objective is to reduce extreme poverty. This policy consists of (1) imposing a tax of 10% on the incomes of households earning 1,705 Rand per capita or more (as in Policy 1 above) and (2) transferring to each household earning less than 200 Rand per capita an amount of money enough to bring their income per capita up to exactly 200 Rand per capita.

a. How much money would the government need to spend in order to implement this policy [5 points]

Total amount

spent by the

government

b. Recompute the Poverty Head Count Index, Poverty Gap Index, and FGT-2 after this new policy. Report your results in Table 5 using 2 decimal points.

Table 5: Poverty Measures [1 point each]

2004-after

implementing the

alternative policy

Headcount Index

Poverty Gap Index

FGT-2

7

To compare the previous two policies, answer the following questions [1 point each]

Question Answer

Which policy is more expensive for the government? (Hint: if the difference in government expenditure is

less than 70 RND, consider them as being equal) Compare the Poverty Gap Index across the two

policies. Are they similar? If yes, explain. If they are very different, explain.

Under which policy do we achieve the lowest FGT2?

Why?