Unit 2 Unemployment, wages, and inequality: Supply-side policies and institutions
2.3 Unemployment and inequality: WS–PS model and Lorenz curve
- WS–PS model
- Model of the aggregate economy that combines wage-setting (WS) and price-setting (PS) decisions. Where the WS and PS curves intersect is the Nash equilibrium and determines structural unemployment and the real wage. See also: wage-setting curve, price-setting curve, structural unemployment.
The wage-setting and price-setting model (WS–PS model) for the aggregate economy developed in Unit 1 determines not only the level of employment, unemployment, and the real wage, but also the division of the economy’s output between workers (both employed and unemployed) and employers. It is therefore also a model of the distribution of income in a simple economy in which labour is the only input to production, and there are just two types of people, namely, employers—who are the owners of the firms—and workers—some of whom are without work. We can illustrate this by putting a Lorenz curve diagram alongside the diagram showing the wage-setting and price-setting curves.
The distribution of income at the Nash equilibrium
Imagine an economy with 80 identical employees of 10 identical firms, each with a single owner. As in Unit 1, each worker produces an amount of output, \(λ\), per day, and output is divided between the worker and the firm so that the firm receives a constant fraction, \(σ\)—the profit share, which depends on how much competition the firm faces. Writing w for the real wage per day:
\[\text{wage share}=\frac {w}{\lambda} = 1-\sigma\]The left-hand panel of Figure 2.7 shows the wage- and price-setting curves for this economy when the profit share, \(σ\), is 40%. The economy is in equilibrium at point A, where the real wage is both sufficient to recruit workers and motivate them to work, and consistent with the firm’s profit-maximizing price markup over costs. At A, workers receive 60% of output and their employers receive the rest, and there are 10 unemployed people.
Figure 2.7 The distribution of income at supply-side equilibrium.
The right-hand panel shows the Lorenz curve for income in this economy, including the owners as well as the workers. We assume there are no unemployment benefits, so the 10 unemployed people receive no income. So the Lorenz curve (the solid blue line) is a flat line at zero up to the 10th person. The 80 employed workers each earn the same wage equal to 60% of their output; so the Lorenz curve then slopes upward, reaching 60% of total income at the 90th person. The 10 owners receive the remaining 40% of income. The size of the shaded area indicates the extent of inequality, and the Gini coefficient is 0.36.
The Lorenz curve is made up of three line segments, between the starting point (0, 0) and the endpoint (1, 1). The first kink in the curve occurs when we have counted all the unemployed people.
The second kink is the point whose coordinates are the size of the labour force as a fraction of the population (90%), and the fraction of total output received in wages—the wage share, \(1 \ – \ σ\) (60%).
In the right-hand panel, the shaded area—and hence inequality measured by the Gini coefficient—will increase if:
- a larger fraction of the employees is without work (higher unemployment rate): the first kink shifts to the right
- the real wage falls (or equivalently, the markup rises) and nothing else changes: the second kink shifts downwards
- productivity rises but real wages do not rise: this implies that the markup rises, so again the second kink shifts downwards.
What can change the level of employment and the distribution of income between profits and wages in equilibrium? Below, and in the following sections, we examine how changes in economic conditions and policies lead to changes in employment and inequality.
Question 2.2 Choose the correct answer(s)
Figure 2.7 is the Lorenz curve associated with a particular supply-side equilibrium. In a population of 100, there are 10 firms, each with a single owner, 80 employed workers, and 10 unemployed workers. The employed workers receive 60% of the total income as wages. The Gini coefficient is 0.36. In which of the following cases would the Gini coefficient decrease, keeping all other factors unchanged?
- A fall in the unemployment rate would shift the first kink of the Lorenz curve to the left, decreasing the Gini coefficient.
- A fall in the real wage would lower the second kink of the Lorenz curve, increasing the Gini coefficient.
- A fall in worker productivity while the real wage is unchanged implies a fall in the markup, or equivalently, a rise in the wage share in total income. This shifts the second kink of the Lorenz curve upwards, decreasing the Gini coefficient.
- A fall in the degree of competition would lower the price-setting curve in the model of the labour market, resulting in lower employment and a lower wage share. This shifts the first kink of the Lorenz curve to the right and the second kink downwards, increasing the Gini coefficient.
The effect of increased competition in the product market
Follow the analysis in Figure 2.8 to examine what would happen if there were an increase in the degree of competition faced by firms, perhaps as a result of a fall in the barriers preventing firms from other countries competing in this economy’s markets.
Figure 2.8 The effect of an increase in the extent of competition faced by firms: the price-setting curve shifts upwards and inequality falls.
The initial equilibrium
A new equilibrium
A new, lower Gini coefficient
The markup would decrease and, as a result, the real wage shown by the price-setting curve would increase, leading to a new equilibrium at point B with a higher wage and a higher level of employment. The share of output going to profits falls, and the share going to wages rises—inequality falls.
Exercise 2.2 An increase in the wage share
Suppose that in the economy shown in Figure 2.7, the degree of competition faced by firms decreases, so the share going to wages decreases to \(0.4\lambda\), resulting in an employment level (N) of 72. Use a diagram like Figure 2.8 to illustrate this scenario and calculate the Gini coefficient.
Great economists Michał Kalecki
Michał Kalecki (pronounced Ka-LET-ski) (1899–1970) was a Polish macroeconomist whose writings in the early 1930s on aggregate demand, business cycles, and investment anticipated the later work of John Maynard Keynes. He was distinctive, however, in emphasizing the central role of conflicts between owners and workers in his models.
Although trained as an engineer in Poland, his first job was to collect data on companies seeking credit. He also tried his hand at economic journalism for a few Polish weeklies. This cemented his belief that data is the foundation for useful economic models. And to him the data suggested that among the primary questions to be answered were those concerning the distribution of income among classes (‘capitalists and workers’) and the level of employment.
Although he lacked a formal training in economics, Kalecki’s stint at the Polish Institute for Research on Business Cycles and Prices gave him the opportunity to develop models of ‘laissez-faire’ economies. In the mid-1930s, he left Poland, first teaching in the UK and then working for the United Nations in New York. During the early 1950s, at the height of McCarthyism and the ‘red scare’ in the US, Kalecki feared persecution for his advocacy of the interests of workers and so, in 1955, he returned to Poland, where he taught and spent the rest of his life.
In 1943, in his article ‘The Political Aspects of Full Employment’, he showed that even if the elimination of unemployment were possible by means of government spending along the lines proposed by Keynes, it would not be sustainable. He reasoned that owners of firms would oppose eliminating unemployment because it would lead to a reduction of their ability to exert control in the workplace.
He wrote, ‘… if attempts are made [by the government] to … maintain the high level of employment, a strong opposition of “business leaders” is likely to be encountered … [L]asting full employment is not at all to their liking. The workers would “get out of hand” and the “captains of industry” would be anxious to “teach them a lesson”.’ The idea that the threat of losing your job would affect worker behaviour when jobs are hard to find was later taken up by economics Nobel prize winner Joseph Stiglitz in his model of ‘unemployment as a labour discipline device’. According to Kalecki (and Stiglitz), higher levels of employment would require employers to pay higher wages to secure a motivated workforce, an insight that we express in our wage-setting (WS) curve.
His article ‘Determinants of the distribution of national income’ was written in 1938, not long after the introduction of theories of monopolistic and imperfect competition by Edward Chamberlin and Joan Robinson. As with our approach to the price-setting (PS) curve here, Kalecki’s model is based on the market power of owners of firms as sellers of the goods that workers as consumers purchase. Therefore, to Kalecki, the price markup over costs is a determinant of the distribution of income between owners and workers. He showed that ‘the relative share of gross capitalist income and salaries is equal … to the average degree of monopoly’ consistent with our representation of inequality using the Lorenz curve derived from the WS–PS model.
His models also took account of the difference between workers, who saved little or nothing from their wages, and the owners of firms, who saved substantial portions of their income from profits. The result was a theory of demand in the economy as a whole (which we take up in Unit 3) that depended on the distribution of income between the two classes, anticipating the later and more widely known work of Nicholas Kaldor.1 Recent macroeconomic policy models have recognized the importance of taking account of these differences in the fraction of income consumed or saved among workers, owners, and others.
Kalecki’s marriage of macroeconomics with the study of inequality about 80 years before it became popular to do so among other economists is a testament to this visionary economist who lacked appreciation in his own time.
Question 2.3 Choose the correct answer(s)
Read the following ideas and choose the one(s) that Kalecki proposed.
- He reasoned that full employment would not be a sustainable outcome because the owners of firms would not be able to exert control over workers (to incentivize them to work hard).
- This insight is expressed in the wage-setting (WS) curve.
- He showed that price markup over costs is a determinant of the distribution of income between owners and workers.
- His theory of demand in the economy as a whole depended on the distribution of income between workers and owners, who saved different proportions of their income.
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Nicholas Kaldor. 1956. ‘IV The Keynesian theory’ of ‘Alternative Theories of Distribution’. Review of Economic Studies 23: pp. 83–100. ↩
