# Visualizing Inequalities in a 3-Person Economy

Yesterday, in the course on inequalities, I mentioned (too) briefly the 3-person Economy. I wanted to spend some time in a short post on visualisations of inequalities in such a context. As mentioned in the slides,  it is possible to use a ternary plot representation. In the case where we believe that the scale independence principle makes sense, i.e. . A distribution of incomes can be represented as a barycenter in an equilateral triangle (also called de Finetti diagram). The midpoint is the equal situation: the three agents share the same wealth. Because of the scale independence property, we can look at distribution of wealth on the simplex. A wealth distribution is a vector  where each component is one of the (red) distance below. A is on top of the triangle, and the vertical distance is proportional to the wealth of A. The closer to the bottom line, the poorer A is.

To visualize this distribution of wealth, we can use the trifield package. To add the point and the three segments, the code is

tripoint=function(s){
p=s/sum(s)
p1=c(0,s+s/2,s+s/2)/sum(s)
p2=c(s+s/2,0,s+s/2)/sum(s)
p3=c(s+s/2,s+s/2,0)/sum(s)
C <- abc2xy(matrix(p,1,3))
points(C,pch=19,col="red",cex=2)
C1 <- abc2xy(matrix(p1,1,3))
C2 <- abc2xy(matrix(p2,1,3))
C3 <- abc2xy(matrix(p3,1,3))
segments(C1,C1,C,C,lwd=2,col="red")
segments(C2,C2,C,C,lwd=2,col="red")
segments(C3,C3,C,C,lwd=2,col="red")
}

For instance, to visualize the equal case (inequality indices are defined as a distance to this situation)

tripoint(c(1,1,1)) For a case where there is inequality, use for instance tripoint(c(1,2,3)) 