Universitat Pompeu Fabra, 1996/1997
Due June 4, 1997.
1. Consider the list of incomes:
10,10,20,20,20,30,40,50.
- 1.1 What is the mean income? What is the Schutz
coefficient of inequality of this society?
- 1.2 Draw the Lorenz curve that corresponds to this
list, and draw the Schutz coefficient as well.
- 1.3 Find the discrete density function that
corresponds the above list of incomes.
2. Let p:R+→[0,1] be a discrete
density function that has positive values at points in S,
S={x1,...,xk}, and 0≤x1<...<xk.
- 2.1 Define the values of the Lorenz curve
L(p(x1)), L(p(x1)+p(x2)) and so on, i.e.,
L(∑i≤rp(xi)) for all 1≤r≤k.
- 2.2 Draw the Lorenz curve that corresponds to the
density function p(10)=0.4, p(20)=0.6, and p(x)=0 for all
x≠10, x≠20
3
- 3.1 Write a formula for the Gini coefficient of a
Lorenz curve generated from a discrete density function. (Note that the
triangulars do not sum up "nicely").
- 3.2 Compute the Gini coefficient of the Lorenz curve
that corresponds to the density function that is mentioned in 2.2.
- 3.3 Compute the Gini coefficient of the Lorenz curve
that corresponds to the density function that you found in 1.3.
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