Henceforth, we refer to this type of elasticity as Gini Engel Elasticity<sup>9.</sup> Assume<sup>now that</sup> individuals are ranked according to income. If, iij(<sup>2</sup> ) >1, commodity j<sup>isconsidereda</sup> _luxury._ If the elasticity is between 0 and 1, the corresponding commodity<sup>is considereda</sup> _necessity._ When this elasticity is negative, the commodity is an _inferior good_ (Gamer 1993: 135).

Table 2.4. Gini Elasticities for Selected Expenditure Components in Guinea (1994)

|Aversion|Total Expenditure|Cereals|Beverages|Food|Electricity<br>|Energy<br>|Non-Food<br>|
|---|---|---|---|---|---|---|---|
|1.50|1.00|0.43|1.51|1.02<br>|1.83<br>|0.85<br>|1.29<br>|
|2.00|1.00|0.50|1.43|1.05|1.76|0.92<br>|1.24<br>|
|2.50|1.00|0.55<br>|1.39<br>|1.07<br>|1.70<br>|0.95<br>|1.21<br>|
|3.00|1.00|0.58|1.36<br>|1.07<br>|1.65<br>|0.97<br>|1.18<br>|
|3.50|1.00|0.61|1.34|1.08|1.61<br>|0.98<br>|1.17<br>|
|4.00|1.00|0.63|1.33|1.08|1.58<br>|0.99<br>|1.15<br>|
|4.50|1.00|0.65<br>|1.32<br>|1.08<br>|1.55<br>|0.99<br>|1.14<br>|
|5.00|1.00|0.66<br>|1.31<br>|1.08<br>|1.53<br>|1.00<br>|1.13<br>|
|5.50|1.00|0.68<br>|1.30<br>|1.08<br>|1.51<br>|1.00<br>|1.12<br>|
|6.00|1.00|0.69|1.30|1.08|1.49|1.00|1.12|

Source: Computed Table 2.4 presents Gini Engel elasticities for selected expenditure<sup>componentsin</sup> Guinea. This information reveals that food expenditure is distributed very<sup>much like total</sup> expenditure. The distribution of expenditure on energy is also very close<sup>tothat of total</sup> expenditure. Beverages and electricity are clearly luxury goods while cereals are<sup>a</sup> necessity. In general, it appears that inequality in the distribution of household expenditure in Guinea is due to non-food expenditure.

The area between a concentration curve and the 45 degree line is known<sup>asthe</sup> area of concentration. It is equal to - cov[xj, (1 - p)]/ _pj_ = cov(xj, p)I _,uj._<sup>Therefore,</sup> r%J(2) is equal to the area of concentration for **xj** divided by the area<sup>betweenthe45</sup> degree line and the Lorenz curve of x (Yitzhaki and Lewis 1996:549).<sup>Thisgeometric</sup> interpretation provides a necessary condition for characterizing<sup>the positionofa</sup> concentration curve relative to the 45 degree line and the Lorenz curve. Thus when<sup>the</sup> Gini Engel elasticity is negative, the concentration curve is concave and<sup>lies above the 45</sup> degree line. When the elasticity is equal to zero, the curve coincides with<sup>the 45degree</sup> line. When the elasticity is between zero and 1, the concentration curve lies<sup>between the</sup> 45 degree line and the Lorenz curve. Finally, when the elasticity is<sup>greaterthanonethe</sup> concentration curve lies below the Lorenz curve.

Finally, let qj stand for the cumulative distribution<sup>obtainedbyranking</sup> individuals by increasing order of component j. Let GJ(v) be the extended Gini coefficient of component j. Expression (2.19) also implies that the overall<sup>Giniis equal to</sup>

> **9** Yitzhaki (1994a) calls it Gini income elasticity. Furthermore, (2.19) shows<sup>that Engel-aggregationholds</sup> for these elasticities to the extent that their weighted sum is equal to one. The<sup>weightsare thesharesof the</sup> total budget spent on each commodity.

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