Labour SupplyLecture notes

Dan Anderberg

Royal Holloway College

January 2003

1 Introduction

Definition 1 Labour economics is the study of the workings and outcomes of the market for labour.

Most require compensation to work (work for pay).

The agents: buyers and sellers of labour services.

An abstraction: What constitutes a market (geography, sector etc).

1.1 Whats so Special About Labour Markets?

Workers may have discretion over the quality they supply ! Design of contracts.

Wage setting to induce eort (eciency wages) ! Explanation for unemployment.

Quality improvement: Investment in human capital.

Signs of disequilibrium: Involuntary unemployment.

Concern for inequality makes us want to understand how incomes from labour are determined.

This naturally also bring us to a feature of labour markets. Institutions play a key role.

Role of institutions:

Unions

Tax policy

Minimum wages

1.2 Where do we Start?

The wage rate is the price of labour per working hour.

Consider labour supply and labour demand.

Put the two together to obtain equilibrium.

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1.3 Whats in this part of the course?

First, labour supply and labour demand.

Then, a block about unemployment, unemployment insurance and active labour marketpolicy.

Finally, some stu on mobility and the role of the family.

2 What Else?

Web page:

Lecture notes and gures (downloadable).

Seminar material.

Essay topic.

Midterm test (sixth teaching week).

Seminar format

Review questions + student presentation.

My oce hours: ____

3 Measuring the Labour Force

Statics: Labour Force Survey

Classify individuals

employed

unemployed

out of the labour force

Some key features:

Men have reduced participation; women have increased participation.

Hours of work have generally reduced over the recent decades.

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4 The Simple Model of Labour Supply

Question: Where does labour supply come from?

Neo-classical model of labour-leisure choice.

Assumptions of the simple model: Worker obtain satisfaction from

1. consumption C

2. Leisure L

Represented by utility functionU = U (C; L)

Indierence curves

Fig 1.1

Properties:

Downward sloping

Do not cross

Convex to the origin (preferences for balanced bundles).

4.1 Slope of an Indierence Curve

Marginal utility of leisure = MUL Marginal utility of consumption = MUC Consider changing L and C along an indierence curve:

U = MUL L + MUC C = 0

Rearranging yields the MRSCL

= MULMUC

Slope reects a workers taste for labour and leisure.

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4.2 Budget Constraint

Non-labour income V (independent on labour supply).

Assume xed wage w (independent of no. of hours).

Works h hours.C = wh + V

Fig 1.2

Bundles on or below budget line are available (the opportunity set).

4.3 The Hours of Work Decision

Choice a point on the budget line to maximize utility.

Fig 1.3 illustrates an interior choice.

Fig 1.3

Standard tangency condition hold at the interior choice.

Slope of budget line is w; hence at optimumMULM UC

= w

4.4 The Income Eect

Suppose non-labour income increases (holding w constant)

Fig 1.4

Parallell outward shift of budget line.

If consumption and leisure are both normal, the agent will consume more and enjoy moreleisure.

A pure income eect.

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4.5 The Substitution Eect

Suppose the wage increases.

Budget line rotates around the endowment point.

Worker can either increase or decrease hours of work.

Fig 1.5

Decompose into income (E0 to E0) and substitution eect (E0 to E1)

Substitution eect ! increased labour supply.

Income eect ! reduced labour supply (assuming leisure is normal).

Net eect depends on which eect dominates.

4.6 The Participation Decision

Question: How can the model be used to analyse the participation decision?

Think of non-participation as a corner solution (choosing the endowment point).

Definition 2 The reservation wage is the wage where the worker is indierent between participating

and not participating.

Insight: Reservation wage = slope of indierence curve at endowment point.

Fig 1.6

Question: How does the participation decision vary with the wage?

Participation decision is monotonic in the wage!

Fig 1.7

Empirical prediction: The probability that a worker participates is increasing in her wage.

Note that this contrasts the interior solution a wage increase can lead to lower labour supply.

5 The Labour Supply Curve

Definition 3 Labour supply curve: The predicted relationship between the wage and hours of work.

Zero below reservation wage.

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Can be backward bending.

Fig 1.8

Question: How do we obtain the market supply curve?

Definition 4 Labour market supply curve = sum of individual supply curves.

Fig 1.9

Question: How do we measure the responsiveness of labour supply?

Definition 5 Labour supply elasticity:

=h=hw=w

=hw

wh

> 0 as long as the supply curve is upward sloping (h=w > 0)

Usual terminology:

jj < 1 - LS is inelastic (not very responsive)jj > 1 - LS is elastic (quite responsive)

6 Estimates of the Labour Supply Elasticity

One of the most research empirical questions in labour economics.

Method: Using micro-level data, run regression

ln hi = + ln wi + lnVi + Xi

where is the elasticity of hours with respect to the wage, while measure the elasticity of labour supply

with respect to non-labour income.

Findings: For males 0:1.

E.g. a 10 percent increase in the wage ) 1 percent decrease in hours worked.

Points to note:

Income eect dominates!!

Labour supply is inelastic (not very responsive)

Specic to prime-age males.

There are also problems with the estimated elasticities:

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Choice of unit of time: are hours measured weekly, monthly, annual?

Measuring the wage: measurement errors, not observed for those not participating. Measuring non-labour income: Is unlikely to be strictly unrelated to labour supply decision.

If they are correlated,

7 Policy Application: The UK Tax Credits

Support to low income individuals out-of-work through Income Support (IS) Support to low income individuals in-work through Working Families Tax Credits (WFTC). WFTC corner-stone of Labours policy of supporting low income families while still making work

pay.

1,292,600 families and lone parents claim WFTC in the scal year 2001-2002, so its a very largeprogram.

7.1 Some Key Rules of the Policy

Its an in-work benet, meaning you have to work to get it. Must work for 16 or more hours per week, have responsibility for at least one dependent child and

has a suciently low income.

The maximum weekly rate of WFTC is made up of an adult credit, credits for each child, childcarecredits (if applicable) and 30 hour bonus. (See table).

If income is less than 94.50 per week, the maximum WFTC will be paid. If (net) income is greater than 94.50, a taper of 55 per cent of the excess is subtracted from the

maximum WFTC to nd the amount payable.

7.2 An Example

Sue has a (net) wage of 5/hour and works 24 hours/week. She lives alone with her child, aged 6. Since she works more than 16 hours she is eligible for WFTC. She gets the adult element 62.50

plus one child credit 26.45.

However, she earns 5 24 = 120 per week which is above the applicable amount of 94.50. Hence she gets

62:50 + 26:45 :55 (120 94:50) = 74:92in WFTC per week.

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7.3 How does the WFTC Aect the Budget Constraint?

Sues budget constraint:

Slope w = 5 up to 16 hours.

Upward jump at 16 hours.

Comes onto the taper at 18.9 hours, reducing the slope to 2:25

Jumps again at 30 hours

Back to the original budget constraint (no WFTC) if she work 51 hours.

7.4 Theoretical Predictions

Encourage participation ! making at least part-time work pay.

However, may reduce labour supply for those already working.

Fig. 1.10

References

Ehrenberg R. and R.S. Smith (2003) Modern Labor Economics, Chapter 6.

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