Lecture 5: Labour Economics and Wage-Setting Theory

Transcription

1 Lecture 5: Labour Economics and Wage-Setting Theory Spring 2014 Lars Calmfors Literature: Chapter 7 Cahuc-Zylberberg (pp )

2 1 Topics Weakly efficient bargaining Strongly efficient bargaining Wage dispersion Co-ordination of wage bargaining

3 2 Efficient contracts Bargaining over the wage only and letting employers determine employment (right to manage) is not efficient. An efficient solution can be found by bargaining over both the wage and employment. Max w, L [ ] 1 ( ) [ ν( ) ν( )] γ γ γ R L wl w w L s.t. 0 L N and w w Interior solution R'( L) w γ (1 γ) + 0 (I) RL ( ) wl L L γν '( w) (1 γ) + 0 (II) RL ( ) wl ν( w) ν( w) Eliminate γ between the two equations to get w R'( L) ν( w) ν( w) ν '( w) (III)

4 3 This is the equation of a contract curve (Pareto-efficient combinations of w, L) connecting tangency points of indifference and isoprofit curves. The same equation would be obtained by maximising [ ] L ν( w) ν( w) s.t. π π Differentiation of the contract curve equation gives: dw R"( L) dl ν "( w) w R '( L) [ ] γ 0 R '( L) w according to (I) R '( L) w ν( w) ν( w) and w w according to (III) Hence the contract curve starts on the labour demand schedule at w If w R'( L) > and workers are risk averse, i.e. ν " < 0, then dw / dl > 0 for w > R '( L). w γ 0 gives the competitive level of employment L Lw ( ) With γ > 0, the union uses its bargaining power to raise both the wage and employment over the competitive levels. dw If workers are risk-neutral, then ν " 0 and. Hence the contract dl curve is vertical. Employment is at the competitive level.

5 4 Overemployment if workers are risk-averse weak efficiency as R '( L) < w due to employment being higher than L defined by R'( L ) w c c

6 5 Strongly efficient contracts Efficiency gain for union if utility of employed and unemployed are equated Incentive to bargain with firm over unemployment benefit paid by the firm Union objective Lν( w) + ( N L) ν( b + w) Firm profit π R( L) wl ( N L) b Max Lν( w) + ( N L) ν( b+ w) w, b w, b s.t. π π 0 [ ] Max Lν( w) + ( N L) ν( b+ w) + λ R( L) wl ( N L) b π 0 FOC Lν'( w) λl 0 ( N L) ν'( b + w) λ( N L) 0 ν '( w) λ ν '( b + w) λ

7 6 Hence: ν '( w) ν'( b + w) w b + w Pareto efficiency requires a wage for the employed that is equal to the income as unemployed. The firm pays a benefit b to all unemployed. It pays a wage w + b to the employed. Employment does not matter to the union, since members are insured against unemployment. The bargaining problem Max b FOC: 1 γ [ R( L*) wl* bn] [ ν( w + b) ν( w) ] [ ] ν( w + b) ν( w) γ R( L*) wl* bn ν'( w+ b) 1 γ N with w w+ b γ R'( L*) w Employment equals the competitive level Union members appropriate a share of the firm s profit without this having negative effects on employment

8 7 Diagrammatical illustration Indifference curves: ν ν 1 1 υ s dw dw dl dw dl ν( w) The indifference curves are horizontal lines. Isoprofit curve π R( L) wl bn R( L) wl N( w w) dπ 0 R'( L) dl wdl Ndw dw R '( L) w dl N Tangency points between isoprofit curves and indifference curves give a vertical contract curve (at the competitive level of employment) Bargaining over wages, employment and unemployment benefits from firms is strongly efficient.

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10 9 Collective bargaining and wage dispersion Heterogeneous workers Collective bargaining reduces wage dispersion Two types of workers, indexed by i 1, 2 Revenue of the firm R(L 1, L 2 ) Type -1 workers are more productive with a higher reservation w > w wage 1 2 N i workers of type i in the firm s labour pool The union utility function 2 υ υ υ L ( w ) + ( N L ) ( w + b ) L N s i i i i i i i i i1 Strongly efficient bargaining over employment, wages and unemployment benefits Optimal contract implies w w + b i i i

11 10 Bargaining problem γ 2 2 RL (, L) ( wl bn) N { ( w b ) ( w )} ν + ν i i i i i 1 i 1 Max i i i i b, b, L, L γ s.t. 0 L N i 1, 2 i i FOCs (11) (12) RL (, L) L ν'(w + b ) w i 1 γ i i 2 γ γ 2 i1 [ ν( ) + ) ν( )] N w b w i i i i RL (, L) ( wl + bn) 1 2 i 1 i i i i Equation (11): Productive efficiency, i.e. the marginal productivity of each type of worker equals the reservation wage. This implies the competitive level of employment. Equation (12): RHS is independent of i. Hence the same wage for the two types of labour. Wage equality follows from the assumption of a utilitarian union and identical preferences.

12 11 N N N N ν( w ) + ν( w ) ν w + w N + N N + N N + N N + N Because of concavity the union is better off with a wage N N 1 2 w + N + N N + N w for everyone than with separate wages w 1 and w 2.

13 12 Two-stage bargaining over employment (Manning 1987) Stage 1: Bargaining over the wage Stage 2: Bargaining over employment Different bargaining strengths in the two negotiations Bargaining over employment (given the wage) Max L 1 [ ] [ ν ν ] γ γ γ L L L R( L) wl ( w) ( w) L s.t. 0 L N The solution gives L L( γ, w, w) L Bargaining over the wage (takes the outcome of second-stage bargaining over employment into account) Max w s.t. 1 [ ( ) ] [ ν( ) ν( )] R L wl w w L L L( γ, w, w) and w w L γ γ γ Different cases γ 0 and γ > 0 gives the right-to-manage model L γ γ gives (weakly) efficient bargain model L Otherwise solution on neither labour-demand schedule nor contract curve

14 13 Motivations Efficient bargaining is complex Wage bargaining precedes employment bargaining Wage bargaining is often at more centralised level Strongly efficient bargaining is improbable because of moral hazard problems: unemployed being fully insured will not search effectively for jobs - argument for partial insurance - individual firm (sector) offering full insurance would be swamped by labour inflow One does not find many examples of contracts with unemployment benefits paid by firms Unclear empirical results on right-to-manage model and (weakly efficient) bargaining

15 14 Different degrees of co-ordination Employment is determined by the product real wage w p W Nominal wage P Output price L L (w p ), where L Employment The union maximises expected utility for a representitive member: U w c + (1 ) b, where M number of union members w p w c Consumption real wage P c CPI b Real unemployment benefit

16 Maximisation of the union utility function 15

17 Effects of different degrees of co-ordination 16

18 Conclusions on co-ordination and real wages 17

19 The degree of co-ordination and the real wage in a closed economy (the Calmfors-Driffill curve) 18

20 The degree of co-ordination and the real wage in an open economy 19

21 An extended model 20

22 The degree of co-ordination and the real wage in reality 21

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