Unit 1 The supply side of the macroeconomy: Unemployment and real wages
1.5 The supply side of the macroeconomy
In this section, we will build a model of the supply side of the aggregate economy that can help explain some of the trends and cross-country differences visible in the data.
Building block
For an introduction to economic modelling, read Section 2.8 of the microeconomics volume.
We follow an important principle of economic modelling: to focus on the particular features of the economy we want to understand—the interactions in labour and product markets at the aggregate level—we simplify other aspects of the economy.
In our model, the actors whose decisions affect the supply-side outcomes are:
- the owners of firms that employ workers and sell the output they produce
- the households that purchase those goods and whose members are either employees of firms or unemployed.
The model combines two arenas where households and firms interact:
- the labour market, where the actors are firms as employers and households as workers (both employed and unemployed)
- the product market, where the actors are firms as sellers of goods and services, and households as customers.
People who are self-employed or out of the labour force are left out of the model; another simplification is to ignore differences between the types of work that workers do and the products they produce. Recalling the assumption we made earlier that there is a way of aggregating all of the goods and services produced by the economy, we imagine that all employees and firms produce, and all households buy, ‘units of output’. The total amount of output produced is Y, and the price of one unit of output is P.
- average product
- The average product of an input is the total amount of output divided by the total amount of input. For example, the average product of a worker is the total output divided by the number of workers employed to produce it.
- labour productivity, productivity of labour
- The total output of a production process divided by the labour input (the number of hours of work, or some other measure of the amount of labour).
Similarly, we ignore variation between workers in wages and levels of output. Total employment is N, and all workers earn the same wage, W. The amount of output produced by each worker, Y/N—that is, the average product of labour—is assumed to be constant. Output does not vary across workers or with the level of employment.
Making these simplifying assumptions means that we are effectively concerned only with averages across the whole economy—average wages, prices, and output per worker.
Output per worker, Y/N, gives us a measure of productivity (called labour productivity, because it focuses on workers rather than machinery or other inputs, which are not included in this simplified model).
Remember that what matters for workers’ living standards is the real wage: the wage measured in terms of how much it can buy. When the nominal wage is W per week and the price of one unit of output is P, the real wage is w = W/P; this is the wage measured in terms of something ‘real’—what you can buy with it. The nominal wage is referred to using upper case ‘W’ and the real wage is lower case ‘w’.
Note that productivity, Y/N, and the real wage, w, are both measured in units of output, so we can directly compare workers’ wages with how much they produce.
The outcomes from the model will be:
- employment, N
- the unemployment rate, u
- the real wage, w.
In future units, we extend the supply-side model to analyse the determinants of inequality and inflation. We will also discuss some of the long-term determinants of productivity in Units 8 and 10.
We build the supply-side model using a diagram with employment and unemployment on the horizontal axis, and output per worker and the real wage on the vertical axis. In Figure 1.11, we split the horizontal axis into segments to show the main labour market indicators (as in Section 1.3): farthest on the right is the population of working age. The number of inactive people is the difference between the population of working age and the labour force. When N people are employed, the number unemployed is the difference between N and the labour force.
Figure 1.11 Labour market concepts.
Similarly in Figure 1.12, we use the vertical axis to show output per worker, which is labelled \(λ\) (pronounced ‘lambda’) and the real wage. Remember that output per worker (that is, productivity) does not depend on employment, so we can represent \(λ\) by a horizontal line in this diagram. The figure shows how, if the real wage is w, output per worker is shared between the worker and the owners of the firm: the worker receives w, and the rest is the firm’s profit per worker.
Figure 1.12 Output per worker is shared between firms and employees.
Actors and markets
We often refer to firms as actors. But there are many actors within a single firm.
- The owner or owners hire and fire the managers who conduct the daily business of the firm. They own the property of the firm, its buildings, intellectual property (such as patents or trademarks), and machinery, and receive the profits.
- Managers direct the activities of the employees in the firm and are paid salaries, sometimes with a share of the profits of the firm added on.
- Employees of the firm work under the direction of managers in return for wages.
When we say ‘the firm sets a price’ or ‘hires a worker’, we mean the owners make this decision, or the managers acting on their behalf.
Within the management of the firm, it is helpful to think of important decisions as made by two distinct actors. The first is the human resources department (‘HR’), which makes decisions relating to the labour market. We suppose that HR is in charge of setting wages to ensure that employees can be recruited and will work effectively. The second is the marketing department, tasked with setting a price for the firm’s product that will maximize its profits.
The model of the aggregate economy therefore has two parts:
- In the labour market, the focus is the relationship between employers and workers and on how wages are set by HR departments in firms.
- In the product market, the focus is the relationship between firms and their customers and on how prices for goods and services are set by marketing departments in firms.
The wage-setting curve
- wage-setting curve, WS curve
- A relationship showing, for each level of economy-wide employment, the wage that employers need to set to recruit and motivate workers.
From the firms’ HR departments and the labour market, we get the wage-setting (WS) curve. It is a relationship between the real wage set by HR departments, and the aggregate level of employment in the economy.
In each firm, HR determines the nominal wage, W, that will be just sufficient to recruit, retain, and motivate the firm’s desired number of workers. Given the aggregate price level, P, in the economy, this determines the firm’s real wage, which is what matters for workers’ responses to wage offers. When we add up the effects of the real wage and corresponding employment in all firms, we get the wage-setting (WS) curve for the whole economy, shown in Figure 1.13. It is an upward-sloping relationship between aggregate employment, N, and the real wage, w.
We will examine exactly why the WS curve slopes upward in the next section. But for now, note from Figure 1.13 that when employment is high, unemployment is low. This means that workers have better alternative options: they can easily find other jobs. We say that the labour market is ‘tight’. When the labour market is tight, there is more competition, so firms need to pay a high real wage to get workers to turn up and provide the required effort. The opposite is a ‘loose’ or ‘slack’ labour market when unemployment is high.
We can also think of it as a relationship between the real wage and the unemployment rate, because for every level of aggregate employment, there is an associated rate of unemployment. In Figure 1.13 when employment is NA, the wage is wA, and the corresponding unemployment rate is uA—the number of workers in the labour force who are unemployed, divided by the size of the labour force.
Figure 1.13 The wage-setting (WS) curve.
The WS curve gets increasingly steep as unemployment shrinks toward zero. This reflects an important feature of the model—and of the world. As later sections will explain, there is always unemployment in the economy.
Question 1.3 Choose the correct answer(s)
The graph shows the economy at point A on the wage-setting curve, with 64 people employed (out of a population of 100). Based on the information in the graph, read the following statements and choose the correct option(s). All numbers given are rounded to the nearest whole number.
- Participation rate = labour force/population of working age = 80/90 = 89% (rounded to the nearest whole number).
- Unemployment rate = unemployed/labour force = (80 – 64)/80 = 20%.
- Employment rate = employed/population of working age = 64/90 = 71% (rounded to the nearest whole number).
- Holding employment fixed at 64, the unemployment rate (which can be rewritten as 1 – employed/labour force) would increase because the labour force increases and is in the denominator. The participation rate (labour force/population of working age) increases because the labour force is in the numerator.
The price-setting curve
- price-setting curve, PS curve
- A relationship showing, for each level of economy-wide employment, the real wage that results when firms maximize profits by setting prices as a constant markup on costs.
From the firms’ marketing departments and the product market, we get the price-setting (PS) curve—another relationship between the real wage and the level of employment.
The marketing department does not control wages—it sets the price, P, of the firm’s output to maximize profits. But the price it sets depends on the firm’s production costs, which depend on the nominal wage, W.
What else affects the profit-maximizing price? Production costs depend not only on wages, (W), but also on labour productivity, (\(λ\)). The profit-maximizing price will also depend on how much competition there is in the product market. When there is intense competition from other firms, the firm has to charge a lower price because otherwise it risks losing consumers.
We have already said that \(λ\) doesn’t vary with the level of employment. We also make the ceteris paribus assumption that the intensity of competition in the product and labour markets remain constant irrespective of the firm’s output and employment. Under these assumptions (as we explain further in Section 1.6), each firm sets a price, P, that is proportional to the nominal wage, W. And it sets the same price whatever its level of employment.
Since all firms in the economy will do the same, the prices set by marketing departments lead to a ratio between W and P—that is, an aggregate real wage, w—that doesn’t depend on aggregate employment, N. So the price-setting curve in the aggregate economy is shown in Figure 1.14 as a horizontal line. The difference between the real wage, w, and output per worker is the real profit per worker (profit measured in units of output).
Figure 1.14 The price-setting (PS) curve.
The WS–PS model of the macroeconomy
- 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.
This model of the supply side of the aggregate (or whole) economy (Figure 1.15) is named after the two curves—the wage-setting (WS) curve and the price-setting (PS) curve. We refer to it by its nickname, the WS–PS model.
Figure 1.15 The WS–PS model of the economy’s supply side.
Where the two curves intersect, at point A, the real wage on the WS curve is equal to the wage on the PS curve. At other levels of employment, one is higher than the other. Only at the intersection are the decisions of wage and price setters across the economy consistent: both marketing and HR departments in all firms are satisfied with the wage they are paying (workers are being recruited and are working effectively) and the price they are setting (firms can sell their output at a price that maximizes their profits).
This may seem surprising—how could HR and marketing departments ever make inconsistent decisions? The problem is not that the departments within a firm don’t talk to each other: marketing accepts the decision by HR on the nominal wage. Rather, it is that the choices in each firm—the nominal wage, W, and price, P—depend on what they know or believe will happen in the rest of the economy, which they cannot control. And in turn, what happens in the economy as a whole—the unemployment rate, u, and the aggregate real wage, w—depends on what all firms do. The mutual dependence of their decisions is illustrated in Figure 1.16.
Figure 1.16 The mutual dependence between firm behaviour and the whole economy.
There is just one combination of real wage and unemployment rate at which the outcome in the aggregate economy is the same as the one that firms expected when they made their choices. It is the real wage and unemployment rate where the price-setting and wage-setting curves cross.
The equilibrium of the supply side of the economy
- Nash equilibrium
- An outcome is termed a Nash equilibrium if none of those involved, by individually choosing a different action, could bring about an outcome that they would prefer. In game theory, a Nash equilibrium is a set of strategies, one for each player in the game, such that each player’s strategy is a best response to the strategies chosen by everyone else. See also: game theory.
This outcome is called the Nash equilibrium of the whole economy or, equivalently, the supply-side equilibrium. An outcome is termed a Nash equilibrium if none of those involved, by individually choosing a different action, could bring about an outcome that they would prefer. It is named after the mathematician and winner of the Nobel prize for economics, John Nash.
We often refer to a Nash equilibrium as the ‘result’ or ‘outcome’ of a model. We mean that the equilibrium (in this case the equilibrium real wage and employment level) is what we would expect to observe on average in the economy over a long period of time. The reason we use the equilibrium to predict what we will observe in the economy is that if an outcome is not a Nash equilibrium, at least one of the actors can do better by changing what they do. And if they change what they do, then the outcome will change, so it is not what we would expect to observe over the long run.
Only at the Nash equilibrium—the intersection of the WS and PS curves—do owners have no incentive to change wages or prices or to increase or reduce the size of their firms. We know this because they have set prices, wages, and the level of hiring to maximize their profits given the actions taken by others. Employed workers can do no better than to work at the level required by the employer, given the wage offered by the employer and the prospects of finding work elsewhere; this is what the WS curve tells us.
But what about those without work? Could they not go to some employer and promise to work as hard as HR requires but at a lower wage? HR would not be fooled; they have already figured out the lowest wage needed to motivate people to work at the level they require, and would not believe anyone’s promise to work hard at a lower wage.
The WS–PS model tells us the real wage and unemployment rate we would expect to observe in the economy on average over a number of years as long as there are no shifts in either the WS or PS curves. In the next two sections, we examine each curve in more detail, and what may cause it to shift.
