lorenzcurve {ClaimsProblems}

The Lorenz curve

Description

This function returns the Lorenz curve of any rule for a claims problem.

Usage

lorenzcurve(E, d, Rules, col = NULL, legend = TRUE)

Arguments

E

The endowment.

d

The vector of claims.

Rules

The rules: AA, APRO, CE, CEA, CEL, DT, MO, PIN, PRO, RA, Talmud.

col

The colours. If col=NULL then the sequence of default colors is: c("red", "blue", "green", "yellow", "pink", "coral4", "darkgray", "burlywood3", "black", "darkorange", "darkviolet").

legend

A logical value. The colour legend is shown if legend=TRUE.

Details

Let E> 0 be the endowment to be divided and d\in \mathcal{R}^n the vector of claims with d\ge 0 and such that the sum of claims D=\sum_{i=1}^{n} d_i\ge E exceeds the endowment.

Rearrange the claims from small to large, 0 \le d_1 \le...\le d_n. The Lorenz curve represents the proportion of the awards given to each subset of claimants by a specific rule R as a function of the cumulative distribution of population.

The Lorenz curve of a rule R for the claims problem (E,d) is the polygonal path connecting the n+1 points

(0,0), (\frac{1}{n},\frac{R_1(E,d)}{E}),\dots,(\frac{n-1}{n},\frac{\sum_{i=1}^{n-1}R_i(E,d)}{E}),(1,1)

Basically, it represents the cumulative percentage of the endowment assigned by the rule to each cumulative percentage of claimants.

Value

The graphical representation of the Lorenz curve of a rule (or several rules) for a claims problem.

References

Lorenz, M. O. (1905). Methods of measuring the concentration of wealth. Publications of the American statistical association, 9(70), 209-219.

Mirás Calvo, M.Á., Núñez Lugilde, I., Quinteiro Sandomingo, C., and Sánchez Rodríguez, E. (2022). Deviation from proportionality and Lorenz-domination for claims problems. Rev Econ Design. doi: 10.1007/s10058-022-00300-y

See Also

giniindex, cumawardscurve, deviationindex, indexgpath, lorenzdominance.

Examples

E=10
d=c(2,4,7,8)
Rules=c(AA,RA,Talmud,CEA,CEL)
col=c("red","blue","green","yellow","pink")
lorenzcurve(E,d,Rules,col)