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={x_{1},...,x_{k}}, and 0≤x_{1}<...<x_{k}.

**2.1**Define the values of the Lorenz curve L(p(x_{1})), L(p(x_{1})+p(x_{2})) and so on, i.e., L(∑_{i≤r}p(x_{i})) 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.