Lecture 4: Labour Economics and Wage-Setting Theory

Transcription

1 ecture 4: abour Economics and Wage-Setting Theory Spring 203 ars Calmfors iterature: Chapter 5 Cahuc-Zylberberg (pp ) Chapter 7 Cahuc-Zylberberg (pp and )

2 Topics The monopsony model of age setting and employment Collective bargaining

3 2 The monopsony model Barriers to free entry of firms imited mobility of labour A monopsonist can hold don ages belo the competitive age Examples Single-firm tons ( bruksorter ) The labour-market for nurses - just one hospital in a region - cartel of regions ( landsting ) earlier in Seden

4 3 The basic monopsony model abour supply s () = G() An employed person produces y Decision problem of a monopsonist s Max ( ) = ( )( y ) s s ( y ) = 0 s s y ( ) = 0

5 4 Define Hence: the elasticity of labour supply 0 implies that, i.e. that the monopsonist sets a loer age tha s s y y y = = = = + < < + n the competitive age

6 5 The monopsonistic age coincides ith the competitive age only if in hich case = y = y y + + Otherise the monopsonist gains by loering the age belo the competitive age This reduces the labour supply and hence output and employment. But the loss from this is outeighed by the savings on the age bill. Isoprofit curve = ( y ) = d( y ) d = 0 d d = d y d > 0 for y > Profit maximisation at the tangency point beteen an isoprofit curve and the labour supply schedule A minimum age - if it is not too high raises both the age and employment in a monopsonistic market Non-monotonic relationship beteen minimum age and employment in a monopsonistic market

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8 7 Sources of monopsony poer Workers must have limited mobility - transportation cost - qualifications that cannot be used elsehere Entry costs must prevent entry of competitors Simple game-theoretic model for hy the existence of entry costs can uphold a monopsony N firms can enter c is the entry cost Each orker produces y Stage : entry decision Stage 2: age decision Solve the model backards If only one firm it sets the monopsony age If there are n > competitors, firm i sets its age i so as to maximise its profit i = i (y- i ) taking the ages of other firms as given

9 8 Employment i in firm i depends on all ages ( i, n ) in the folloing ay: i = s ( i ) if i > j, j i i = (/J) s ( i ) if i sets the highest age together ith J- other firms, < J < n i = 0 if there exists one firm j i hich sets i < j All ages equal to y is a Nash equilibrium Then each firm has zero profits and cannot improve its profits - ith a loer age all labour disappears - ith a higher age it makes a loss No single firm can set i < y. - it ould then make a profit - hence it ould pay for a competitor to raise the age above i and capture the hole labour supply - This is so-called Bertrand competition, hich forces the age up to the competitive level

10 9 Stage decision Each firm knos that (i) it ill make zero profits ith competitors present in the market (ii) it ill make monopsony profits if it alone enters Once a firm has entered it does not pay for any other firm to enter - profits ill be zero - but an entry cost c has to be paid - the first firm (if possibilities to enter come sequentially) chooses to enter if ( M ) > c. Extreme assumptions here regarding Bertrand competition but good illustration of ho entry costs may give rise to monopsony and age differences to other sectors unrelated to productivity.

11 0 Collective bargaining Common assumption for unions: identical members N identical members in the union s labour pool Indirect utility function for the individual, increasing in income Every member supplies one unit of labour if the real age exceeds the reservation age (= income of an unemployed person) = abour demand Same probability of getting a job for every union member = /N if < N and unity if N Probability of unemployment ( ) if < N and zero if N. N Union objective Maximise the expected utility of members ν = lν( ) + ( l) ν( ) l = Min (, / N) s If N is exogenous, this is equivalent to maximising the uneighted sum of members utilities: ν( ) + ( N ) ν( ) If orkers are risk-neutral so that ν ( ) = and ν ( ) =, unions maximise the rent from unionisation: l + ( l)( ) = l( ) + If = 0, this is equivalent to maximising the age bill: l

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14 Assumption of identical union members is convenient and has microeconomic underpinnings But in reality members are heterogeneous Restrictive assumptions necessary for collective decisionmaking - majority decisions - sincere voting: no attempts to influence voting by announcing intentions beforehand - voting on a single question - single-peaked preferences - then the median-voter theorem can be applied Restrictive assumption for union decision-making - voting only about the age Conflicts beteen union leadership and membership - leadership may ant to maximise union size - union size may increase ith employment - boss-dominated unions sho more age restraint

15 4 Empirical studies of union goals Stone-Geary utility function ν θ = θ s Special cases θ ( ) ( ) [0,] 0 0 θ = ½, 0 = 0, 0 = 0 i.e. age bill maximisation ½ ½ ν = =, s ½ ½ = ν ( ) = ( ), s θ = ½, 0 =, 0 = i.e. rent maximisation Pencavel (984) used Stone-Geary utility function Decision problem θ Max ν = ( ) ( ) s 0 0 s.t. = α + α ( / r) + α ( r / r) + α x+ α D θ r = output price r 2 = production cost x = output D = Dummy variable FOC: θ α ( ) 0 = θ r( ) 0

16 5 Estimation of labour demand function and FOC gives estimates of θ, 0, 0, α 0, α, α 2, α 3 and α 4. Not rent or age bill maximisation Different θ, but tendency for θ to be lo 0 and 0 increase ith the size of the union Carruth and Osald (985) Rejection of risk neutrality (and age bill and rent maximisation) CRRA = ν"( ) / ν'( ) 0.8 Risk neutrality implies ν"( ) / ν'( ) = 0/ = 0 δ δ ; δ is CRRA δ δ δ = 0 = δ = ν( ) = ln

17 6 ν ( ) δ = 0 δ > 0

18 7 Standard right-to-manage model Bargaining about ages Employer determines employment unilaterally Union objective ν = lν( ) + ( l) ν( ) l = Min (, /N) s Firm profit = R ( ) R' > 0, R" < 0 abour demand from profit maximisation = R'( ) = 0 = R'( ) = R' d ( ) ( ) ( ) In case of disagreement Workers get the utility of unemployed persons Firms get zero profit γ denotes relative bargaining strength of the union: 0 < γ < Apply Nash bargaining solution

19 8 γ γ ν ν s 0 0 Max ( ) ( ) = Profit in case of disagreement 0 ν = union utility in case of disagreement = 0 ν = ν( ) + ( ) ν( ) = ν( ) ν ν = ν( ) + ( ) ν( ) ν( ) = ( ν( ) ν( )) = s 0 d = N [ ν( ) ν( ) ] Max ith s.t. D [ ( ) ] [ ν( ) ν( ) ] [ ( ) ] γ γ γ D [ ] d ( ) = R ( ) ( ) d ( ) N and Solve by taking logs and then differentiate.r.t.

20 9 FOC: d γ d ( ) γν'( ) ( γ) d( ) + + = d ( ) d ν( ) ν( ) ( ) d 0 Note: Mistake in formula on page 394: Second term should be γν '( ) ν( ) ν( ) not γν'( ) ν( ) ν( ) et = ( / )( d / d) = ( / )( d/ d)

21 20 Absolute values of age elasticities of labour demand and profits z Posit = ( z, ) / > 0 z = (, ) / > 0 z γν'( ) φ( z,,, z, γ) = γ ( γ) + = 0 ν( ) ν( ) () (2) (3) () Employment loss from age increase (2) Profit loss from age increase (3) Income gain for employed orkers from age increase Monopoly union assumption γ ν '( ) = + = 0 ν( ) ν( ) Still interior solution Trade union balances income gain for employed orkers against employment loss from age increase

22 2 SOC for a maximum is φ < 0 x = (, z, z, γ) φ d + φ dx = x 0 d = dx φ φ x φ d < 0 sgn = sgn φ dx = + + φ γ ν '( ) ν( ) ν( ) x From FOC e can derive: ν'( ) γ + = ν( ) ν( ) γ Substitution into expression for φ gives γ γ φ = + = > γ γ γ d dγ > 0 arger union bargaining poer raises the age 0

23 22 φ γν'( ) ν = > [ ν( ) ν( ) ] 2 0 An income increase for a jobless person raises the age φ = γ < 0 An increase in the labour demand elasticity loers the age φ = ( γ) < 0 An increase in the profit elasticity loers the age Rerite FOC: ν( ) ν( ) γ = ν'( ) γ + ( γ) μ s No bargaining poer for union: γ = 0 Hence : ν( ) = ν( ) = Employed orkers only get a age equal to the income of the unemployed

24 23 No bargaining poer for the employer: γ = ν( ) ν( ) = ν'( ) The mark-up factor only depends on the elasticity of labour demand. Union indifference curves in, -space [ ν( ) ν( )] U = [ ] 0 = ν'( ) d + d ν( ) ν( ) [ ν( ) ν( )] d = = 0 d U = const ν'( ) 2 [ ] [ ν'( ) ] { [ ] } ν ν d ν( ) ν( ) ν( ) ν( ) = = 2 '( ) "( ) d U = const ν '( ) Union indifference curves are negatively sloped and convex.

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26 25 Isoprofit curves = R( ) R '( ) d d d = 0 d R '( ) = d = [ "( ) ] [ '( ) ] d R d d dr d = = 2 d = d [ ] 2 d R"( ) R'( ) = d d =

27 26 Substitute R'( ) d for d : 2 d d 2 = = R"( ) R'( ) R'( ) = [ ] R "( ) 2 R '( ) 2 Choosing to maximise profit implies R () =. Hence isoprofit curve is horizontal here it intersects the labour demand schedule. At intersection ith labour demand schedule, R () =. Hence 2 d R d 2 "( ) 0 = = <. Isoprofit curves are concave there, hich imply maxima.

28 27 General FOC: γν'( ) γ ( λ) + = 0 ν( ) ν( ) (A), If, γ and are constants, then the real age is constant as ell. It ill not be affected by an iso-elastic shift of the labour demand schedule (for example because of a productivity shock). Constant Douglas. and ill occur if the revenue function is Cobb-

29 28 Simplified model α A = R ( ) = α (0, ) α Profit maximisation gives: α = A = 0 = A α Then: A = α A A α α α α = -α A α α α

30 29 Hence: = = α = = α α Also assume that ν( ) = and ν( ) = Then ν '( ) = FOC (A) then becomes: α γ γ ( γ) + = 0 α α Solving for gives: = γ + α( γ) α

31 30 The age is set as a mark-up on the income of an unemployed, since γ + α(-γ) > α γ(- α) > 0, hich must hold. Especially simple form in monopoly-union case, i.e. if γ = Then = α We have: Hence: = α α = α = =

32 3 Thus: = - = Analogy to monopoly price setting ith price as a mark-up over marginal cost > is alays the case ith Cobb-Douglas production function, as = and 0 < α <. α