New Lanark and Efficiency Wages




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Wages, Effort and the Price of Labour Units

At first sight, one may imagine that the wage policy of the business completely determines the price of labour units. However this is not always the case. If the wage the business pays its workers influences their attitude to working hard, then a more complex scenario is involved. Why might such a relationship between the wage paid by the business and the work attitude of workers emerge? The following Examples illustrate.


Example I.8 Suppose the business offers a weekly wage of £ 200 to identical workers on the presumption that they all work hard for 50 hours a week. This policy is dictated by the knowledge that the workers can all earn £ 200 in an alternative occupation (which might be unemployment or an alternative job or both). In other words £ 200 is the rock bottom wage.

If the business can monitor its workforce perfectly then it can ensure that all workers do in fact work hard for 50 hours a week. Workers who "shirk" by working hard for less than 50 hours a week will be detected and fired. The price of labour then is 200/50 = £4 per man hour. But what if monitoring is less than perfect? Suppose that only occasional random checks can be made. Workers will know this and thus each will have an incentive to shirk on the job. If they are not detected, then each one will still collect £ 200 at the end of the week but will have put in less than 50 hours of hard work. If in fact each one only works 40 hours, (twiddling their thumbs for the remaining 10 hours), then in effect the price of labour units is 200/40 = £ 5 per man hour. Note that shirking possibilities have effectively raised the actual price of labour units, even though the wage policy of the business has not changed! To reduce shirking the firm might have to raise its wage above £ 200 per worker. If the wage goes up to say £ 216 per week, each worker may well put in more effort because now the cost of being caught and fired has gone up. Suppose that at £216 per week each worker puts in 45 hours of hard work. What are the consequences as compared to the policy of paying the rock bottom wage of £ 200 ? The results are illustrated in Table I.8 below.


Table I.8 : Rock Bottom and High Wage Policy Compared.




Wage ( £ W)

Effort (E man-hours of hard work)

Price of Labour £(W/E) per man hour

Extent of Shirking (Hours)

Rock Bottom Wage policy

200

40

5

10

High Wage policy

216

45

4.8

5

Even though the wage is higher, the price of labour units has fallen and is now only 216/45 = £ 4.8 per week. The effort of workers has risen and shirking has been reduced (but not eliminated)!


In the above example, all workers were identical and all had an incentive to shirk. The business had to consider the possibility of shirking in designing its wage policy. In the next example, we consider a slightly different scenario.

Example I.8a Suppose there are two types of workers whom the business might hire. Half of these are lazy workers have an outside option of £ 200 per week and are incapable of working more than 40 hours a week. The other half are good workers who have an outside option of £ 216 per week and will work 50 hours a week. The business is seeking to hire 100 workers. What should its wage policy be?
Suppose it offers a rock bottom wage of £ 200. Only the lazy types will apply because the good workers have a better outside option. Hence the effort put in by each worker will be only 40 hours and the price of labour will be £ 5 per man hour. If it follows the high wage policy, then both types will apply. The firm would like to hire only good workers but it cant tell them apart from lazy workers ( unless monitoring or screening is perfect). If it hires on a random basis, it will end up with 50 good workers and 50 lazy ones. The effort expended by the average worker will then be 45 hours, and the effective price of labour £4.8 per hour, exactly as in Table I.8!
The difference between the two examples is that in Example I.8 the high wage policy provides incentives for all identical workers to shirk less and work hard for longer whereas in Example I.8a, the high wage policy induces a better mix of applicants from amongst a pool of diverse workers. But in both cases the common feature is that high wages increase average effort.

Exercise1.8: Construct a numerical example of your own in which high wages affect average effort both because each worker works harder and because a better quality of worker is attracted to the firm. ( Hint: Think of two types of workers, good and bad , and how both good and bad workers put in more effort when the wage rises).

The Efficiency Wage

Do the two examples above suggest that firms should continue to raise wages till effort is at its absolute maximum? The answer is " No" because the wage required for this may simply be too high. A compromise is required to find the optimum wage strategy. Knowledge of the wage-average effort relationship is needed.


The above examples suggest that as the wage rises, the average effort also rises. However, beyond some limit, the rise in effort is small compared to the rise in the wage. In other words, the effort inducing property of the wage tails off as the wage is raised.

Example I.10: A typical profile for the wage-effort relationship is shown in Table I.10 below and in the corresponding diagram, Figure I.10 below.

Table I.10 Weekly Wage (£ per week) and Effort ( man-hours)


Wage

£ per week



Effort

Man-hours



150

0

200

40

216

45

250

46

275

47

Note that the effort does rise continuously as the wage rises but beyond a wage of £ 216 the increases in effort are very small - the tailing off effect. The exact rate at which effort responds to wages depends on a host of factors - but chiefly on alternative income possibilities. A major determinant of these possibilities is the level of unemployment and how much income the unemployed can get. This discussion leads to:


Proposition 1.2: When monitoring is imperfect, wages affect behaviour or applicant quality in such a way that average effort increases as the wage paid rises , but at a diminishing rate. This relationship between average effort and the wage offered is called the Wage- Effort Locus.

Faced with this Effort-Wage Locus, what is the optimum wage policy of the business? Recall that maximising profits implies minimising costs. The price of labour is a cost to the business and hence it would seek to minimise it. But as we have seen in Examples I.8 and I.8a, the effective price of labour units is given by :


Proposition 1.2a : Effective price of labour units = Weekly wage(£W)/Effort (E man-hours).
Hence the firm choses W to minimise W/E. Put another way , the firm chooses W to maximise E/W.

Exercise 1.10: For Table 1.10, find the effective price of labour units for each of the five possible wages.

The effective price of labour calculation forms an integral part of calculating the firms optimal wage strategy as the following example illustrates.


E
xample I.11
If the Effort-Wage Locus is as shown in Table I.10, what is the optimum wage policy of the business?
We simply need to pick the wage for which the price of labour (W/E) is minimised, or equivalently pick the wage for which Effort per man-hour (E/W) is maximised. The results are shown in Table I.11 below and illustrated in Figure I.11 below.

Table I.11: Minimising Labour Price or Maximising Efficiency






Effort

W/E

E/W

150

0

N/A

0.00

200

40

5.00

0.20

216

45

4.80

0.21

250

46

5.43

0.18

275

47

5.85

0.17

From the table we can clearly see that the optimum wage policy is to pay £ 216 per week. Note also that some high wage policies eg £ 250 and 275 are actually worse than the rock bottom policy. We can also use the wage-effort diagram to find the Efficiency wage. Figure I.4 illustrates. Consider a ray drawn from the origin to any point on the W-E curve. The slope of that ray (rise/run) measures E/W. Hence we want to find the steepest ray from the origin to the E-W curve. This is the ray which is just tangential to the curve. In figure II.4, consider a pont like A on the E-W curve. The wage is W1 and the corresponding effort is E1. The slope of the ray OA is E1/W1. By similar geometric construction, the slope of a ray from the origin to any point on the E-W curve measures the value of E/W for that point. In order to maximise E/W, we want to find that ray which is steepest. This is the ray OB which is just tangent to the curve at B. Hence the efficiency wage is W*. To satisfy yourself that this is indeed correct, try other points including some which correspond to wages higher than W *. All of these will involve a ray which is flatter than OB. This example illustrates Proposition 1.3 stated below.





Figure 1.11: The Efficiency Wage



Proposition 1.3: When monitoring is imperfect, so that wages affect average effort, the optimum wage policy is to offer a wage which minimises wage/effort or equivalently maximises effort/wage. The wage which achieves this outcome is called the " Efficiency Wage".
Note also that using Proposition 1.3 solves not only for W* but also for E* and hence for the labour unit price which is W*/E*. thus from Table I.6, we see that W*= £216, E*=45 man-hours, and the optimum price of a labour unit = 216/45 =£ 4.8 per man hour.
Exercise I.11: A business has PF given by Q=100L so that MPL=50/L. The price of its output is £ 2 per ton. Its E-W relationship is shown in the Table below:

EW Relationship

Wage (£ per week)

50

80

100

120

Effort (man hours)

3

5

10

11

Find the optimum wage policy of the business and the associated effort level that this wage policy induces.


Proposition 1.3 provides the missing link which along with Proposition 1.1 and 1.2a enables full solution to the optimum strategy of the firm.

Example 1.12: A business has PF given by Q=100L so that MPL=50/L. The price of its output is £ 2 per ton. Its E-W relationship is shown in the Table below:

EW Relationship

Wage (£ per week)

50

80

100

120

Effort (man hours)

3

5

10

11

Find the complete optimum strategy of the firm:

Solution:

Step 1: Use Proposition 1.3 to find that wage for which E/W is largest. From the EW Table this is W=100. Hence W = 100 and E*=10.

Step 2: Calculate the optimum price of a labour unit=W*/E*=100/10=10

Step 3: Use Proposition 1.1 to find L*. Thus :

2 X 50/L = 10 or L* = 100

Step 4: Since total man-hours (L) = effort (E) X Employment (N), and L*=100, E*=10, then

100= 10 X N, or N* = 10

Step 5: Use PF, i.e. Q = 100L to find Q*= 100 X  100 = 1000 tons.

Step 6: Find total profits =( Revenue - costs) = (output price X output) - (wage X employment)= (1000 X 2) - (100 X10) = £ 1000
Thus the complete profit maximising strategy of the firm is to employ 10 workers at a wage of £ 100 per week (the Efficiency Wage) thereby extracting 10 hours of effort by its workers and thus producing 1000 units of ouput and making a total profit of £ 1000. The flow chart on page 17 illustrates the solution procedure.
Exercise 1.12: (a) Calculate what would happen to the business described in Example I.12 if it paid a wage of (i) £ 80 per week.(ii) £ 120 per week. Comment on your answers.

(b) If the wage effort relationship of a business is as described in Table I.10, the price of its output is £108 per ton and its productive process is characterised by PF given by so that MPL=50/L, find its optimum strategy and maximum profits.(c) What happens if the business described in (b) innovates so that’s its PF is now Q=120L with MPL=60/L? Ilustrate diagrammatically.


Empirical Comparison of firm which pays Efficiency Wage with one that doesn’t


  • EW firm usually pays higher wage, other firm pays rock bottom wage

  • EW firm has longer queue of workers outside its door

  • EW firm has higher output per worker

  • EW firm has higher profits


What changes Efficiency Wage?
Only a change in Effort Wage curve can change the Efficiency wage. Such changes can be brought about by a change in Unemployment level or by a change in Unemployment benefit or by a change in the working environment, for example the reforms at New Lanark. If reforms that increase workers sense of well being and participation in the business are introduced, this will shift the Effort-Wage Locus upwards. For the same wage, the business will now be able to extract greater effort. The efficiency wage may not change but the business will do better from the reforms. Whether such reforms are justifiable from a business point of view depends on the increased profits from the reforms and the cost of implementing the reforms.
Key Concepts: Production Function, Marginal Product of Labour Function, Diminishing Returns, Profit Maximising Strategy, Real and Nominal Prices, Effort -Wage Locus, Effective Price of Labour, Efficiency Wage.
Further Reading:

George Akerlof and Janet Yellen: Introduction in Efficiency wage models of the labor market, ed. by George Akerlof and Janet Yellen, CUP,1986


Exercises

  1. Explain what is meant by the Effort-Wage locus of a firm. What determines its shape? What determines its position?

  2. Explain the difference between a movement along the E-W curve and a shift of the curve itself.

  3. What is the “Efficiency Wage”?

  4. How is the EW curve essential to calculating the “Efficiency Wage”?

  5. A business knows that the wage-effort locus it faces is given by:




Wage (£ per week)


100

120

140

160

180

200

220

240

Effort (man-hours)

20

25

32

39

45

49

53

56

The production function is given by Q= 20√L so that MPL function is given by MPL = 10/ √L where Q is output measured in tons and L is labour measured in manhours. The price of the output is £ 8 per ton.




  1. Sketch the firm’s effort-wage locus. Comment.

  2. Find the firm’s optimal strategy and the value of its profits.




  1. How is your answer to (a) above changed if the Effort level at every wage was to increase by 20 man hours but the price of output and MPL was unchanged? Illustrate by a suitable diagram.




  1. How is your answer to (a) above changed if wage-effort locus and MPL is unchanged but the price of output was to rise by £4 per ton? Illustrate by a suitable diagram




  1. How is your answer to (a) above changed if wage-effort locus and the price of output were unchanged but the production function and MPL were to both change to 30√L and 15/ √L respectively? Illustrate by a suitable diagram




  1. In the light of your answers to (a), (b), and (c) and (d) above, how would you account for a rise in the profits of a company over a period of time?




        1. If two firms had identical technology and faced identical prices for its product, what could you conclude if it was observed that one firm was paying a lower weekly wage than the other?



        1. A firm has production function given by Q=50√L where Q is tons of steel and L is manhours of labour. The corresponding MPL function is given by: MPL=25/(√L). The price of steel is £ 60 per ton. The price of labour is £ 30 per hour.

  1. Calculate the real price of labour stating the units of measurement

  2. Calculate the amount of labour hired stating the units of measurement. Illustrate your answer with a diagram.

  3. Calculate the profits earned stating the units of measurement


    1. The effort wage locus of a firm is given by the following table:




Weekly Wage (£)

50

100

120

150

200

Effort(Hours)

16

40

50

60

64




  1. Would the firm prefer a weekly wage of £ 100 or £ 150? Explain.

  2. Calculate the efficiency wage and explain your answer.



    1. Two firms A and B have the same production function and sell their output at the same world price. However A and B pay different weekly wages ( £ per week). It is known that A pays the efficiency wage. For each of the statements a) to f) below, state whether the statement is true or false with reasons and diagram where appropriate.




  1. Firm B definitely pays a higher wage than A

  2. Workers in Firm B definitely put in more effort compared to workers in firm A

  3. Firm B has lower marginal product than firm A

  4. Firm B hires more labour than firm A

  5. Firm B produces more output than firm A

  6. Firm B has higher profits than firm A


STRUCTURE OF OPTIMAL STRATEGY SOLUTION – Ex. I.6



(A)EW Table

[Unemp rate, Rock Bottom wage]

man-hours - £



1.Opt Wage W* (£ per week)

2.Opt Effort E* (man hours)

Step 1


3. Opt Price of Labour Units W*/E* (£ per man hour) – Step 2
(B) MPL (tons per man hour)

(C) Output Price (£ per ton)



4. Labour units L*, man-hours

Step 3


5. Employment

N* =L*/E*

Step 4

(C) PF


6. Output Q*

Step 5





7.Profits*
Step 6

APPENDIX A: STEPWISE ROUTINE FOR SOLVING WAGE AND EMPLOYMENT POLICY


A Given Environment


  1. Technology- PF, MPL function

PF given by Q=100L so that MPL=50/L.


  1. Output price- given by world market

The price of its output is £ 2 per ton.


  1. Effort wage Relationship

EW Relationship

Wage (£ per week)

50

80

100

120

Effort (man hours)

3

5

10

11


Choice of Strategic Variables



  1. What wage (weekly)to pay them? The Efficiency Wage W

W*=100 ( From EW Relationship)


  1. How Much Labour to Hire? L




  1. How Many workers to hire? N




  1. How much Output to sell? Q


Outcomes
Effort level of workers, E

E*=10 ( From EW relationship, given solution for W*)

Effective price of labour, W/E

(W/E)*= 100/10=10(from previous answers)

Real price of Labour (Effective Wage/Output price)

10/2=5 (from previous answers and Environment)


Labour requirement, L

Use Proposition 1 to get

50/L=5 (previous answer), L*=100

MPL(Environment)=effective real price of labour, ( from previous answers)

Output,Q

Q*=1000{ Environment(PF) and previous answer for L}

Number of Workers hired, N

N*=(L*/E*)=10 (from previous answers)


Profits

Profits= Sales Revenue- Labour Costs=1000(from previous answers )

ENVIRONMENT + STRATEGY →OUTCOMES
: Appendix B: The Optimal Labour Employed and Output Produced.
Consider a firm whose Production Function is given by Q= A√ L. The Marginal Product of Labour Function is then given by MPL= A/[2√ L. ]

To find the profit maximising choice of labour, equate MPL to real price of labour ( wage per hour/ price of bale).



The diagram below illustrates. If money wage is £ W per hour and price of cotton bales is £ P per bale, then real price of labour is (W/P) as shown. Draw horizontal line to meet MPL at J. From J draw vertical line to meet the horizontal axis at L*. Then L* is optimal labour choice. Extend vertical line from L* to meet PF at K. Draw horizontal line from K to meet axis at Q*. Then Q* is the optimal output choice that corresponds to L*
Exercises: By suitable modification of the diagram, show the impact of (a) a rise in wage rate; and (b) an improvement in technology





1Robert Owen: Owen of New Lanark and New Harmony” p97, I. Donnachie (2000)

2 “Owen as a businessman” Butt, p209 cited in I. Donnachie p98, as above

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