End of Chapter Exercises: Solutions
Chapter 11
1. From the data in the table on the distribution of income (by quintile) between
two states, A and B, you are required to compare the degree of income
inequality between the two states using Lorenz curves and Gini Coefficients.
Percentage of Total
Disposable Income
State A
State B
50%
35%
20%
30%
15%
25%
10%
6%
5%
4%
100%
100%
Quintile
1st
2nd
3rd
4th
5th
Total
Answer:
100%
80%
60%
B
40%
A
20%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
Area under Lorenz curve: A = 0.3; B= 0.328
Gini Coefficient: A = (0.5-0.3)/0.5 = 0.4; B= (0.5-0.328)/0.5 = 0.344
Therefore state B is less unequal than state A
100%
2. The data in the table below shows the breakdown of the referent group (RG)
benefits for two projects (A and B), information about each sub-group’s
income level and marginal propensity to save (mps). In addition you have
ascertained that the mean income level is $30,000 per annum, that an
appropriate value for ‘n’ (the elasticity of marginal utility with respect to an
increase in income) is 2, and that the premium on savings relative to
consumption is 10%.
Income p.a.
mps
Net Benefits - A
Net Benefits - B
RG1
$20,000
0.05
$10
$20
RG2
$40,000
0.20
$20
$30
RG3
$90,000
0.60
$90
$40
With this information you are required to calculate and compare the projects’ net
benefits in terms of:
(i) unweighted aggregate referent group net benefits;
(ii) aggregate net benefits weighted for atemporal distributional objectives
(assuming consumption and savings have the same value at the margin);
and,
(iii) aggregate net benefits weighted for both atemporal and intertemporal
distributional objectives.
Answer:
(i)
(ii)
(iii)
A=$120; B=$90
weights: RG1 = 2.25; RG2 = 0.56; RG3 = 0.11.
Weighted Net Benefits: A = $44; B=$66
A=$99; B=$92
3. You have been provided with the following information about three public
sector projects with a breakdown of the referent group net benefits
(unweighted) among the three referent group (RG) categories:
Project A
Project B
Project C
RG 1
$30
$40
$40
RG 2
$30
$20
$30
RG 3
$60
$40
$10
With the knowledge that all three projects are considered to have equivalent
weighted net benefits, and that the three distribution weights are to have an
(unweighted) average of 1, you are required to find the implicit values of the
three distribution weights for RG1, RG2 and RG3 respectively. (Hint: follow
Weisbrod’s method and note that the solution value for the weighted net
benefit of each project is $100).
Answer:
RG1=1.67; RG2=1.00; RG1=0.33