Question

Table 15.9 shows the share of income going to each quintile of the income distribution for the United Kingdom in 1979 and \(1991 .\) Use this data to calculate what the points on a Lorenz curve would be, and sketch the Lorenz curve. How did inequality in the United Kingdom shift over this time period? How can you see the patterns in the quintiles in the Lorenz curves? $$\begin{array}{l|l|l} \hline {}{} {\text { Share of Income }} & {}{} {1979} & {}{} {1991} \\ \hline \text { Top quintile } & 39.7 \% & 42.9 \% \\ \hline \text { Fourt quintile } & 24.8 \% & 22.7 \% \\ \hline \text { Middle quintile } & 17.0 \% & 16.3 \% \\ \hline \text { Second quintile } & 11.5 \% & 11.5 \% \\ \hline \text { Bottom quintile } & 7.0 \% & 6.6 \% \\ \hline \end{array}$$

Short answer

In summary, the Lorenz curve for 1991 is further away from the perfect equality line than the one for 1979, indicating increased income inequality in the UK between those years. The bottom and middle quintiles have lower cumulative income shares in 1991, while the top quintile has a higher share. This suggests that the income distribution became more concentrated in the upper income levels over this time period.

Step-by-step solution

Calculate the cumulative share of income for each quintile

To create a Lorenz curve, we need to know the cumulative share of income for each quintile. We will calculate this by adding the income shares successively for both years. $$\begin{aligned} Cumulative\,share\,(1979):&\\ &Bottom\,quintile: 7.0\%\\ &Second\,quintile: 7.0\% + 11.5\% = 18.5\%\\ &Middle\,quintile: 18.5\% + 17.0\% = 35.5\%\\ &Fourt\,quintile: 35.5\% + 24.8\% = 60.3\%\\ &Top\,quintile: 60.3\% + 39.7\% = 100\%\\\\ Cumulative\,share\,(1991):&\\ &Bottom\,quintile: 6.6\%\\ &Second\,quintile: 6.6\% + 11.5\% = 18.1\%\\ &Middle\,quintile: 18.1\% + 16.3\% = 34.4\%\\ &Fourt\,quintile: 34.4\% + 22.7\% = 57.1\%\\ &Top\,quintile:57.1\% + 42.9\% = 100\% \end{aligned}$$

Identify the cumulative population percentages for each quintile

Since there are equal shares of the population in each quintile, the cumulative percentage for each quintile increases by 20%. $$\begin{aligned} Cumulative\,population\,percentage: 20\%, 40\%, 60\%, 80\%, 100\% \end{aligned}$$

Plot the Lorenz curve for both years

We now have all the data we need to plot the Lorenz curve for each year. A Lorenz curve is a graph that shows the cumulative income share (on the y-axis) against the cumulative population percentage (on the x-axis). On the same graph, also plot the perfect equality line: a diagonal line from the origin (0,0) to the point (100,100). The Lorenz curve consists of points obtained by joining the cumulative income share for each quintile in each year. To see how the inequality has changed over time, compare the position of the Lorenz curve in 1979 with that in 1991. The farther away the Lorenz curve is from the perfect equality line, the higher the inequality.

Analyze the Lorenz curve and inequality

We can observe that the Lorenz curve for 1991 is further away from the perfect equality line compared to the curve for 1979. This shows that inequality increased between 1979 and 1991 in the United Kingdom. The patterns in the quintiles can be observed on the Lorenz curves. In 1991, the bottom and middle quintiles have a lower cumulative income share compared to 1979, while the top quintile has a higher share. We can also see that the second quintile's share remains the same in both years. This suggests that the income distribution in the UK became more concentrated in the upper income levels over this time period.

Key concepts

Income Inequality

Income inequality refers to the uneven distribution of income within a population. It highlights the gap between the rich and the poor. To visualize this, economists use tools like the Lorenz Curve. The Lorenz Curve helps in understanding how income is distributed among the population. When a Lorenz Curve is far from the line of perfect equality, this indicates high income inequality. High income inequality means that a large portion of the total income is held by a small percentage of the population.

In the case of the United Kingdom between 1979 and 1991, the Lorenz Curve showed a move away from the equality line. This movement indicates an increase in income inequality during this period. Observing income shares across different quintiles, we note that the top quintile received a larger portion of income over time, while the bottom quintiles received less. This shift signals the growing disparity in income distribution.

Income Distribution

Income distribution involves analyzing how income is spread across different groups within an economy. Typically, populations are divided into quintiles, or 20% segments, for this purpose. Analyzing income distribution helps to identify which segments absorb more wealth.

For the United Kingdom's economic landscape in 1979 and 1991, the income distribution changed. The top quintile's share increased from 39.7% to 42.9%, showing they captured more wealth over the years. Meanwhile, the income share for the lower quintiles decreased, as illustrated by the data. Such changes in income distribution demonstrate a movement towards more wealth being concentrated among the wealthier segments of society.

Cumulative Income Share

The cumulative income share shows the total percentage of income earned by segments of the population when combined progressively. It's a critical component for drawing the Lorenz Curve. A step-by-step cumulative sum helps in identifying how much total income is captured as you move from the poorest to the richest.

In terms of plotting the Lorenz Curve for the UK, starting with the bottom quintile's share, we add each succeeding quintile's share to calculate the cumulative income. For example, in 1979, the cumulative share started at 7% for the bottom quintile and ended at 100% after the top quintile. In 1991, this cumulative calculation showed a slightly different trajectory, signifying shifts in income concentration. These calculations are pivotal to illustrating how income is distributed across the entire population.

United Kingdom Economic History

The economic history of the United Kingdom provides valuable context for understanding shifts in income inequality and distribution. During the late 20th century, the UK experienced significant economic changes influenced by factors like policy shifts, globalization, and technological advancements.

Between 1979 and 1991, a period of notable transformation, the UK saw policies that could potentially impact income distribution, such as deregulation and tax changes. As a result, the income distribution data from that time reflects changes in socio-economic structures. This period marks a shift towards greater income inequality, with more wealth clustering among the higher income quintiles. Understanding this historical backdrop is crucial to fully grasp how and why income distribution manifested as observed during these years.