0
1 2
Effort or productivity curve
Unit labour costs
Real wage w Real wage w
(b) 1/x′ Unit labour costs w/x′
x′ Effort 2/x′
Unit labour costs rise as real wage rises
Figure 6.14 Panel (a) illustrates the assumption employed so far, that work effort measured, say, as pieces produced per hour, is at xœ, independent of pay. Unit labour costs are wNxœ, and thus vary with the wage. They are represented by the slope of a ray from the origin to the point of intersection between the vertical line over xœand the horizontal line at the current wage. Panel (b) illustrates that unit labour costs increase linearly with the real wage w.
Labour productivityor efficiencyor effortxcan be measured as output produced per work hour, x = Y>L.Unit labour costsULCare wage costs per unit of output. The manipulations ULC K wL>Y = w/(Y>L) = w/x show that ULC can also be expressed as the real wage divided by labour productivity, w>x.
worked so far. Panel (a) shows that labour productivityor efficiency or effort, which we use as synonyms in this context, is at œfor all wage levels. Unit labour costs, the real wage costs of one unit of output produced, œ, are simply marked by the slope of a ray through the origin which intersects the vertical efficiency line at a given real wage. Since efficiency is constant, unit labour costs obviously double as wages rise from 1 to 2. Panel (b) shows the general relationship between unit labour costs and the wage rate to be a pos-itively sloped straight line through the origin. Employers who want to mini-mize unit labour costs thus will try to pay the lowest wage they can.
Next, Figure 6.15 contrasts this orthodox view with the efficiency–wage ar-gument. The innovation in panel (a) is highlighted by comparing it with panel (a) of Figure 6.14: work effort is positively related to the wage rate. It is zero if the wage is zero. As long as pay is low, effort rises faster than the wage rate.
Beyond some threshold saturation sets in, and additional wage increases yield smaller and smaller efficiency gains. The consequence of this relationship between effort and wage rates for unit labour costs can be traced again by fol-lowing the slope of a ray from the origin to the effort curve (see Figure 6.15, panel (a)). Initially, since for low pay levels effort rises faster than the wage rate, the slope of this ray becomes smaller as firms raise wages. Beyond the wage rate , however, unit labour costs rise. Panel (b) illustrates how this translates into a C-shaped relationship between unit labour costs and the wage rate. The wage rate that minimizes unit labour costs is called the efficiency wage.
A simple model
A simple model may illustrate how the efficiency wage considerations intro-duced above fit into our previously developed picture of the labour market, and how they account for the existence of involuntary unemployment in equilibrium.
wx wx
wx
w>x x
The efficiency wageis the wage that minimizes unit labour costs.
6.2 Why is there unemployment in equilibrium? 167
Let output Y depend on physical labour input L and on labour effort or efficiency x (which depends on the real wage w):
Partial production function (6.5) Then the firms’ profits ⌸ are given by the difference between output (which equals the firms’ revenue) and wage costs.
Profits (6.6)
This innocent-looking modification of the production function can have dra-matic consequences for a firm’s behaviour in the labour market. This is the case if labour efficiency responds strongly to a change in the wage rate, mean-ing that its elasticityis very high. Suppose labour efficiency increases by 2% if the real wage rises by 1%. Then currently employed labour becomes 1%
more expensive, but it produces 2% more. Costs go up by 1%, but revenue rises by 2%. So profits increase. Figure 6.16 shows how this affects iso-profit lines and the labour demand of firms.
What remains unchanged is that for each wage rate there is an optimal, profit-maximizing level of employment, just as explained in our discussion of the conventional classical labour demand curve in Figures 6.4 and 6.5. If the wage rate is , employment maximizes profits, as identified by point A.
The iso-profit line for the corresponding level of profits ⌸1passes through A.
Of course, profits fall if we move to the left of A, say into œ, or to the right of A, into –, for reasons already discussed earlier in this chapter. But this time, a drop in the wage rate does not help to restore profits to . The rea-son is that while a lower wage rate indeed reduces costs, it reduces labour efficiency and, hence, output and revenues even further. Thus profits actually
⌸1
A
A L1
w1
Profits = Output - Wage costs
⌸ = Y[x(w)L] - wL Y = Y[x(w)L]
Elasticitymeasures by how many percentage points one variable responds if some other variable changes by 1%.
Effort x2
xx
x1
Real wage w Real wage wEffort or
productivity curve
wx
wx
xx
(a) w1
w2
(b) Unit labour costs
Unit labour costs
Here unit labour costs fall as wage rises
Here unit labour costs rise as wage rises
w1
x1
w2
x2
Figure 6.15 Panel (a) proposes that work effort (that is, productivity) may be related to the real wage. As the wage increases, productivity first increases at an accelerating and then at a decelerating pace. Unit labour costs, w/x, vary with the wage. They are represented by the slope of a ray from the origin to the point of intersection between the horizontal line at the current wage and the effort curve. Panel (b) illustrates that unit labour costs initially fall as firms raise wages, but increase again as wages move beyond wx, yielding a C-shaped unit labour costs curve.
Iso-profit lines when labour efficiency is very elastic
L3 L1 L2 Labour
w3
w2
w1
Real wage
Labour demand curve
A’
A”
C
B
A
Figure 6.16 This shows the non-standard case, when labour efficiency (or productivity, or effort) depends positively on the real wage, and its real-wage elasticity exceeds 1. Then efficiency rises faster than wages, and unit labour costs, the wage cost of one unit of output, actually fall as wages go up. This makes iso-profit lines U-shaped (compare with the standard case shown in Figure 6.5). Iso-profit lines positioned further up are associated with higher profits. When facing a given wage demand, say w1 or w2, firms extend employ-ment to the point where they reach the highest iso-profit line possible. This puts the bottom of each iso-profit line at the point where it intersects the ‘labour demand curve’.
However, this labour demand curve existed only if firms were prohibited from paying higher wages than trade unions demand. If wages are free to rise, they begin to drift upwards until labour efficiency can no longer increase faster than real wages, and this segment of the labour demand curve vanishes.
drop even further when wages go down. The logical conclusion is that wages actually have to move in the opposite direction to restore profits. When, starting in Aœ(A–), the wage rate rises to , output and revenue rise more than wage costs, and profits go up. At point C (B) profits are back at the level ⌸ . This is why the corresponding iso-profit line passes through points C, A and B.
So when labour efficiency depends on the wage rate and the wage elasticity of labour efficiency exceeds 1, iso-profit curves are U-shaped, and the labour market diagram is actually filled with an infinite number of such U-shaped indifference curves. And, since profits rise when the wage rate goes up, the further up an iso-profit line sits, the higher is the associated level of profits.
This has the important implication that firms would like to end up as far up to the left on their labour demand curve as they possibly can. In other words, they would constantly beg their workers to accept higher and higher wages!
Is this realistic? Of course not.
The reason why we ended up with a somewhat unconvincing result is that we postulated that rising wages could increase labour efficiency without lim-its. This is not feasible. Realistically, as postulated in Figure 6.15, the wage elasticity of labour efficiency may be very high indeed as long as wages are low. At such wage levels iso-profit lines are really U-shaped as depicted in
1
w3 (w2)
6.2 Why is there unemployment in equilibrium? 169
Figure 6.16. But beyond some threshold saturation takes over and effi-ciency gains cannot keep up with wage increases any longer. The iso-profit lines change their shape to an inverted U, the conventional case covered in Figure 6.5. When we merge cases onto a single diagram, iso-profit lines become concentric, looking like squeezed circles or ellipses, with a clearly defined maximum in the centre (Figure 6.17). In the region above the wage elasticity of labour efficiency is smaller than 1. Below it exceeds 1. In striv-ing for the highest profits, firms want to move down their labour demand curve to the point of maximum profits when wages exceed , but move up their (dashed, fictional) labour demand curve when wages are below .
Firms maximize profits by voluntarily paying the efficiency wage and setting the employment to . Firms do not want to employ more labour, since at the level of labour productivity determined by additional labour would cost more than it produces. Also, while firms could obtain labour input at a lower wage rate, they refrain from doing so. The reason is that if wages drop below , productivity falls faster than the wage.
The unintended side effect of the firms’ profit-maximizing behaviour is that we end up with involuntary unemployment in the amount .
Mismatch
The concept of the classical labour market rests on various simplifying as-sumptions. The more important ones are as follows:
■ All transactions are done in one place. There is no geographic dimension.
■ Labour is homogeneous. There are no particular skills, experiences or tal-ents needed to fill a specific job opening. Hence, any unemployed worker can be hired by any firm with a job vacancy.
■ All participants in the labour market possess perfect information. Firms know where to find unemployed workers, and workers are always aware of job openings.
LS - Lx wx
Lx wx
Lx
wx wx wx
wx
wx wx
Labour LS
Lx
Individual labour-supply curve Labour
demand curve
Iso-profit lines
Real wage
wx
Involuntary unemployment
Figure 6.17 If work effort increases with the real wage, unit labour costs are minimized (and profits are maximized) by paying wxand employing Lx. Moving away from wxor Lxin either direction re-duces profits. Hence iso-profit lines are concentric around the profit maximum marked by the blue dot. Workers who do not find employment at wxcannot bid down wages since firms voluntarily pay wxin order to minimize costs. As a result, involuntary unemployment in the amount LS-Lxpersists.
Figure 6.18 shows how the labour market is affected if we give up these assumptions. The two light blue lines give the gross employment supplied and demanded at various wage levels. As the real wage differs from w*
supply and demand are not equal. Employment is now determined by whichever of the two is smaller. For this is demand, for it is supply.
Now assume that because of geographical or vocational mismatch, or because of imperfect information, at any wage level a certain fraction of supply and demand remains ineffective. Then effective supply and demand curves are given by the dark blue lines. These are obtained by subtracting
w 6 w*
w 7 w*