Labour Supply. Lecture notes. Dan Anderberg Royal Holloway College January 2003

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1 Labour Supply Lecture notes Dan Anderberg Royal Holloway College January Introduction Definition 1 Labour economics is the study of the workings and outcomes of the market for labour. ² Most require compensation to work (work for pay). ² The agents: buyers and sellers of labour services. ² An abstraction: What constitutes a market (geography, sector etc). 1.1 What s so Special About Labour Markets? ² Workers may have discretion over the quality they supply! Design of contracts. ² Wage setting to induce e ort (e ciency wages)! Explanation for unemployment. ² Quality improvement: Investment in human capital. ² Signs of disequilibrium: Involuntary unemployment. ² 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. ² Role of institutions: Unions Tax policy Minimum wages 1.2 Where do we Start? ² The wage rate is the price of labour per working hour. ² Consider labour supply and labour demand. ² Put the two together to obtain equilibrium. 1

2 1.3 What s in this part of the course? ² First, labour supply and labour demand. ² Then, a block about unemployment, unemployment insurance and active labour market policy. ² Finally, some stu on mobility and the role of the family. 2 What Else? ² Web page: Lecture notes and gures (downloadable). Seminar material. Essay topic. ² Midterm test (sixth teaching week). ² Seminar format Review questions + student presentation. ² My o ce hours: 3 Measuring the Labour Force ² Statics: Labour Force Survey ² Classify individuals employed unemployed out of the labour force ² Some key features: Men have reduced participation; women have increased participation. Hours of work have generally reduced over the recent decades. 2

3 4 The Simple Model of Labour Supply Question: Where does labour supply come from? ² Neo-classical model of labour-leisure choice. Assumptions of the simple model: Worker obtain satisfaction from 1. consumption C 2. Leisure L ² Represented by utility function U = U (C;L) ² Indi erence curves Fig 1.1 ² Properties: Downward sloping Do not cross Convex to the origin (preferences for balanced bundles). 4.1 Slope of an Indi erence Curve ² Marginal utility of leisure = MU L ² Marginal utility of consumption = MU C ² Consider changing L and C along an indi erence curve: U = MU L L + MU C C = 0 Rearranging yields the MRS C L = MU L MU C ² Slope re ects a workers taste for labour and leisure. 3

4 4.2 Budget Constraint ² Non-labour income V (independent on labour supply). ² Assume xed wage w (independent of no. of hours). ² Works h hours. C = wh + V Fig 1.2 ² Bundles on or below budget line are available (the opportunity set). 4.3 The Hours of Work Decision ² Choice a point on the budget line to maximize utility. ² Fig 1.3 illustrates an interior choice. Fig 1.3 ² Standard tangency condition hold at the interior choice. ² Slope of budget line is w; hence at optimum MU L MU C = w 4.4 The Income E ect ² Suppose non-labour income increases (holding w constant) Fig 1.4 ² Parallell outward shift of budget line. ² If consumption and leisure are both normal, the agent will consume more and enjoy more leisure. ² A pure income e ect. 4

5 4.5 The Substitution E ect ² Suppose the wage increases. ² Budget line rotates around the endowment point. ² Worker can either increase or decrease hours of work. Fig 1.5 ² Decompose into income (E 0 to E 0 ) and substitution e ect (E 0 to E 1 ) ² Substitution e ect! increased labour supply. ² Income e ect! reduced labour supply (assuming leisure is normal). ² Net e ect depends on which e ect dominates. 4.6 The Participation Decision Question: How can the model be used to analyse the participation decision? ² Think of non-participation as a corner solution (choosing the endowment point). Definition 2 The reservation wage is the wage where the worker is indi erent between participating and not participating. Insight: Reservation wage = slope of indi erence curve at endowment point. Fig 1.6 Question: How does the participation decision vary with the wage? ² Participation decision is monotonic in the wage! Fig 1.7 Empirical prediction: The probability that a worker participates is increasing in her wage. ² 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. ² Zero below reservation wage. 5

6 ² 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: ¾ = h=h w=w = h w w h ² ¾ > 0 as long as the supply curve is upward sloping ( h= w > 0) ² Usual terminology: j¾j < 1 - LS is inelastic (not very responsive) j¾j > 1 - LS is elastic (quite responsive) 6 Estimates of the Labour Supply Elasticity ² One of the most research empirical questions in labour economics. Method: Using micro-level data, run regression ln h i = + ¾ ln w i + lnv i + ¹X i where ¾ 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 ¾ ¼ 0:1. ² E.g. a 10 percent increase in the wage ) 1 percent decrease in hours worked. ² Points to note: Income e ect dominates!! Labour supply is inelastic (not very responsive) Speci c to prime-age males. ² There are also problems with the estimated elasticities: 6

7 Choice of unit of time: are hours measured weekly, monthly, annual? ² Measuring the wage: measurement errors, not observed for those not participating. ² 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 ² Support to low income individuals out-of-work through Income Support (IS) ² Support to low income individuals in-work through Working Families Tax Credits (WFTC). ² WFTC corner-stone of Labour s policy of supporting low income families while still making work pay. ² 1,292,600 families and lone parents claim WFTC in the scal year , so it s a very large program. 7.1 Some Key Rules of the Policy ² It s an in-work bene t, meaning you have to work to get it. ² Must work for 16 or more hours per week, have responsibility for at least one dependent child and has a su ciently low income. ² The maximum weekly rate of WFTC is made up of an adult credit, credits for each child, childcare credits (if applicable) and 30 hour bonus. (See table). ² If income is less than per week, the maximum WFTC will be paid. ² 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 ² Sue has a (net) wage of 5/hour and works 24 hours/week. She lives alone with her child, aged 6. ² Since she works more than 16 hours she is eligible for WFTC. She gets the adult element plus one child credit ² However, she earns 5 24 = 120 per week which is above the applicable amount of ² Hence she gets 62: :45 :55 (120 94:50) = 74:92 in WFTC per week. 7

8 7.3 How does the WFTC A ect the Budget Constraint? ² Sue s 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 ² Encourage participation! making at least part-time work pay. ² However, may reduce labour supply for those already working. Fig References Ehrenberg R. and R.S. Smith (2003) Modern Labor Economics, Chapter 6. 8