what is a lorenz curve 
a lorenz curve developed by american economist max lorenz in 1905 is a graphical representation of income inequality or wealth inequality the graph plots percentiles of the population on the horizontal axis according to income or wealth and plots cumulative income or wealth on the vertical axis understanding the lorenz curvein practice a lorenz curve is usually a mathematical function estimated from an incomplete set of observations of income or wealth the lorenz curve is often accompanied by a straight diagonal line with a slope of 1 which represents perfect equality in income or wealth distribution the lorenz curve lies beneath it showing the observed or estimated distribution while the lorenz curve is most often used to represent economic inequality it can also demonstrate unequal distribution in any system the farther the curve is from the baseline represented by the straight diagonal line the higher the level of inequality 1 in economics the lorenz curve denotes inequality in the distribution of either wealth or income these are not synonymous since it is possible to have either high earnings but zero or negative net worth or low earnings but a large net worth a lorenz curve usually starts with an empirical measurement of wealth or income distribution across a population based on data such as tax returns which report income for a large portion of the population a graph of the data may be used directly as a lorenz curve or economists and statisticians may fit a curve that represents a continuous function to fill in any gaps in the observed data the closer the lorenz curve is to the line of equality the less inequality exists the further the lorenz curve is to the line of equality the more inequality exists components of the lorenz curvethe united states federal reserve collected net worth statistics from u s households it then graphically depicted the inequality distribution of wealth the latest data collected by the survey of consumer finances is from 2019 per the federal reserve the underlying data demonstrates that the bottom 50 of households hold just 1 5 of overall household wealth 2there are several important components to understand when analyzing a lorenz curve the lorenz curve and the gini coefficientthe gini coefficient is used to express the extent of inequality in a single figure it most often ranges from 0 or 0 to 1 or 100 complete equality in which every individual has the exact same income or wealth corresponds to a coefficient of 0 plotted as a lorenz curve complete equality would be a straight diagonal line with a slope of 1 the area between this curve and itself is 0 so the gini coefficient is 0 a coefficient of 1 means that one person earns all of the income or holds all of the wealth 3 in theory the gini coefficient can exceed 100 in extreme situations for example when handling negative wealth or income the figure can theoretically be higher than 1 in that case the lorenz curve would dip below the horizontal axis the gini coefficient is equal to the area below the line of perfect equality minus the area below the lorenz curve divided by the area below the line of perfect equality in the graph above the gini coefficient is the area below the dashed line but above the solid line the gini coefficient is used to measure the extent of inequality it can also be used to compare two different nations or countries to see which has more inequality for data sets demonstrating inequality it may be difficult to property analyze certain sections of data for example the graph above has a very long left skewed tail this makes it difficult to exam changes in equality for this section of data advantages and disadvantages of the lorenz curvea lorenz curve gives more detailed information about the exact distribution of wealth or income across a population than summary statistics such as the gini coefficient or the lorenz asymmetry coefficient because a lorenz curve visually displays the distribution across each percentile or other unit breakdowns it can show precisely at which income or wealth percentiles the observed distribution varies from the line of equality and by how much the underlying data for a lorenz curve is necessary to calculate the gini coefficient a primary means of mathematically measuring inequality assuming sufficient data can be collected a lorenz curve can be prepared for any geographical region i e by country by state by city etc this may be especially important for governments relying on a lorenz curve to better understand how to most appropriately assess tax brackets though the lorenz curve often displays sensitive financial information it also maintains the anonymity of the underlying surveyed individuals in addition the lorenz curve can be layered on top of itself over time demonstrating how public policy has changed the level of inequality at various points along the lorenz curve because constructing a lorenz curve involves fitting a continuous function to some incomplete set of data there is no guarantee that the values along a lorenz curve other than those actually observed in the data actually correspond to the true distributions of income this is also true because it may be too expensive or demand too many resources to collect enough data points to fill all gaps most of the points along the curve are just guesses based on the shape of the curve that best fits the observed data points therefore the shape of the lorenz curve can be sensitive to the quality and sample size of the data and to the mathematical assumptions and judgments as to what constitutes a best fit curve and these may represent sources of substantial error between the lorenz curve and the actual distribution the lorenz curve or gini coefficient may also be insufficient to clearly demonstrate the extent of change of inequality over time consider a situation where two gini coefficients are calculated to be the exact same it is possible for the slope of the lorenz curve to be radically different yet the underlying aggregated inequality level is calculated to be the same visually depicts inequality across a population in a manner easy to understand and analyze