# 1  Market for (homogenous) labour WEWE E W1W1 W2W2 SESE DEDE.

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1  Market for (homogenous) labour WEWE E W1W1 W2W2 SESE DEDE

2  For the seller – labour is different from other commodities.  For the buyer?  Starting assumption: For the firm, labour is bought like other inputs.  Input demand is  DERIVED DEMAND not consumption demand.

3  Basic assumption:  The firm hires workers in order to MAXIMISE ITS PROFITS  The firm’s makes two decisions: ◦ Produce what (how much)? ◦ Produce how (with what technology/what inputs)?

4  E – units of labour (hours or full time weeks or full-time worker years)  K – capital (machines, buildings, land, stocks etc.)  Production function:  Q = Q(E, K).  A more complex function would be  Q=Q(E 1, E 2,…, K,N,…) or Q=Q(x 1, x 2,…, x n )

5 Production as a function of labour at ONE particular level of all other inputs

6  The slope of the production function shows how production changes with a change in (only) labour input.  The marginal product of labour (MP E ): ◦ The increase in production when E increases by a small amount (Q(E+ΔE, K 0 ) – Q(E, K 0 ))/ ΔE Or mathematically ◦ the (partial) derivative of Q with respect to E at K = K 0  At a fixed level of K  MP E is different at different levels of E  Marginal productivity may increase at small levels of E but will eventually start to decline.  THE LAW OF DIMINISHING RETURNS

 Please note:  The Law of diminishing returns is not a low of diminishing returns to scale (when use of all factors is increased.) 7

8 Q E

9 If MP E > AP E, AP E If MP E < AP E, AP E AP-curve MP-curve The decreasing part of the MP-curve cuts the AP-curve in the AP-curve’s maximum

10 Remember: With a different level of K, we get a different Q and a different MP E for each E To each value of K corresponds another function Q(E) and another function MP E (E) Analogously To each value of E corresponds a function Q(K) and a function MP K (K)

11  VMP E = p MP E (if the firm is a price taker in the product market)  A profit maximising firm employs until:  VMP E = MC E  Under perfect competition the firm is a ”price taker in the labour market”.  It takes w as given and MC E = w

12 The firm’s demand for labour The price of the product(Physical) marginal product of labour The marginal cost of labour Marginal revenue product of labour

13 W1W1 W2W2 W VMP E E2E2 E1E1 Why is only the decreasing part of the VMP.curve relevant? If the ”going wage” is w 2 the firm hires E 2 workers – AP E > MP E E3E3

14  Perfect competition:  The marginal cost of increasing E by one unit is w  The marginal revenue of increasing E by one unit is p MP E  The firm increases employment up to where w = p MP E (1)  How many are hired depends on ◦ the marginal productivity of labour ◦ the wage ◦ the price of the product.

15  In labour market:  MC E ≠ w  In product market:  MR Q ≠ p  The firm employs and produces until:  MC E = VMP E = MR Q *MP E (2) ◦ (1) is a special case of (2)

16  If wages increase, each employer hires less workers  If each employer hires less workers, each employer produces less.  If all employers produce less, the aggregate supply curve for the product shifts to the left.  Equlibrium price increases and the aggregate decrease in demand for labour is less than the sum of the decreases each firm would have made if it had been alone paying the higher wage.

17 The wage elasticity of labour demand

18  Both E and K can vary.  The firm has a choice between technologies.  The same output can be produced with different proportions of E and K  An ISOQUANT shows the different combinations of K and E that produce the same output

19  Ex:  Let be a production function. Q(64, 225) = 240 Q(144, 100) = 240 Q(72, 200) = 240 Q(200, 72) = 240 Q(100, 144) = 240 Q(225, 64) = 240 It is possible to substitute labour and capital for each other at a given level of production

20 E K

21

22 Leontief production function

23 Isoquants are negatively sloped and convex to the origin. Inputs can be substituted but MP is decreasing Q increases

24  The slope of an isoquant shows how much capital is needed to replace each unit of labour without decrease in production This is (minus) the Marginal Rate of Technical Substitution, MRTS

25  An isocost shows the combinations of inputs that cost the firm the same amount.  If the cost of production is C = wE+rK the isocosts are linear with slope –w/r K E

26  To maximise profits firms must: ◦ minimise the cost of producing the chosen output ◦ maximise production at the chosen level of cost.  This happens only at a point of tangency between an isoquant and an isocost.  These points are on the EXPANSION PATH of the firm.  Which point on the expansion path the firm chooses depends on the price of the product.

27

28  The firm will choose input combinations on the expansion path.  Each point on the expansion path represents one level of production.  The cost of inputs at that point is the minimum cost of producing that output.  The cost function of the curve C(Q) shows this minimum for each Q.  MC is the slope of this cost function – the change in cost as the firm moves outwards along the expansion path.  The firm will choose the level of production, Q*, where MC = MR and the input combination where the isoquant for Q* is tangent to an isocost

29 (Assume perfect competition & r and p constant.)  The isocosts become steeper.  More capital intensive technology becomes more profitable.  At every point on every isoquant, cost and marginal cost increases.  The MC-curve moves upwards-leftwards.  The firm will decrease production. It will choose the tangency point of another isoquant with another isocost.

30 A wage increase has two effects on employment:  1. Changed relative prices will make the firm change the capital/labour ratio  2. Changed MC will make the firm decrease output. Decreased output will make the firm use less inputs. There will be SCALE SUBSTITUTION EFFECTS and SCALE EFFECTS

31 P R S Q1 Q2 P is choice with lower wage R is choice with new higher wage E2E1E* E*-E1 is scale effect E2-E* is substitution effect Employment when w increases

32 P R S Q1 Q2 P is choice with lower wage R is choice with new higher wage K2 K1 K* K*-K1 is scale effect K2-K* is substitution effect Use of capital when w increases

33  If both capital and labour are ”normal” inputs the scale effects of both are negative.  The substitution effect increases K and decreases E.  The total effect on E must be negative, the total effect on K depends on the size of the effects.

34 The long run labour demand elasticity > short run labour demand elasticity Estimates of labour demand elasticity vary depending on the time and place, the level of aggregation, the method used (assumptions about the production function) Hamermesh’s survey: Many studies find ε  -0.3 Swedish studies (Ekberg, Walfridsson) -0.3 & -0.2 Scale effects included: -0.65 Lower elasticity for highly educated workers Lower for white collar than for blue collar Higher for young than for older workers

35  The elasticity of substitution between two factors of production is The size depends on the shape of the isoquants.  If they are perfect substitutes a change in relative price leads to no change at all or a total switch  If they are perfect complements, the elasticity is zero. q i, and p i are quantitites and prices of the two inputs

36  Empirical estimates of capital/labour substitution elasticities vary: ◦ For whole or large parts of economies 0-1, most often 0.4-0.8 ◦ Swedish estimates: wide range at different times and different industries and different for different groups of workers.

37  Factor i will be employed at the level where VMP i =MP i *p  If the price of one factor goes up, what happens to demand for the others?  The cross-elasticity of demand between factor i and k =

38  If δ ik < 0 factors i and k are complements in production ◦ An increase in the price of k shifts the demand curve for i leftwards  If δ ik > 0 factors i and k are substitutes in production ◦ An increase in the price of k shifts the demand curve for i rightwards

39  Many studies find that skilled labour (or white collar) and capital are complements while unskilled (or blue collar) labour and capital are substitutes.  Worker groups with different skills and characteristics can be substitutes or complements.

40  Demand for labour/one type of labour is less elastic: ◦ If it is very essential to production and difficult to replace either by capital or other labour. ◦ If demand for the final product is inelastic. ◦ Their wages make up a small part of total costs of production. ◦ If the supply of complements to it is inelastic and that of substitutes elastic. The less elastic demand is, the greater the scope for unions to increase wages with small loss in employment.

41  Assume: Two groups of workers, A & B, are complements ◦ wages of group A   demand  for both groups ◦ Demand for labour of type B   their wage w B . If supply is inelastic, w B  much and the firm reduces output less.  Assume: Labour of type A and capital are substitutes. ◦ w A   firm wants to substitute capital for labour ◦ If supply of capital is elastic, increase in demand  price of capital , reducing the incentives for the firm of substituting from labour to capital

42 D1D1 D2D2 Inelastic supply Elastic supply

43  Perfect competition VMP W2W2 W1W1 E1 E2 W E

44  Can occur due to:  A very restricted local labour market (”company town”, ”bruksort”)  Very high degree of specialisation (perhaps unique to the firm)  Segregation/discrimination  Monopoly (public or private)

45  A discriminating monopsonist pays each worker his/her reservation wage. Employment is = E Perfect comp. but all workers except the last get less than w PC  A non-discriminating monopsonist pays all workers the same wage. Therefore the cost of hiring an additional worker > the wage of that worker (if labour supply is upward sloping). Both employment and wage will be less than under perfect competion.

46 W W PC W WMWM E E PC EMEM LSLS VMP MC E

47  Can be set by legislation or in collective agreements.  Effects: ◦ On distribution of income (tend to equalise) ◦ On employment (usually negative but the evidence is mixed and disputed). ◦ Encourages structural change

48 SLSL SLSL

49 W min VMP S MLC S VMP Employment  Wage  Unemployment  Perfect competition: Monopsony Employment  Wage  Unemployment 

50  A firm dominates employment in a small town. The price of its product is 10 SEK. The firm’s production function is : Q = 20E – 0.005 E 2  Q = production  E = Employment.  a) What is the firm’s labour demand function D E ?  What is its labour demand if w= 150 SEK?  b) Assume that the firm is a monopsonist in this labour market and that labour supply is given by.  w=50+0.2E  What is MC E  Calculate the firm’s D E and the wage, w.  c) The state sets a minimum wage w=150, How many workers will the firm employ?  a) VMP E =p*MP E =10*(20-0,01E)=200-0,1E  Profit maximisation requires that VMP E =MC E =w  D E is given by: w=200-0,1E  E=2000-10w  w=150 => E=500  b) The labour cost of the firm :  E*w = E*(50+0.2E) = 50E+0.2E 2  MC E : 50+0.4E  MC E =MRP E  50+0.4E= 200-0.1E  E = 300  To employ 300 workers the firm has to pay  w=50+0.2L=50+60=110  c) With a minimum wage S E =0 for w<150  MC E =150  ´Profit maximisation requires that VMP E =150 =>E=500

51  Transaction costs  Search and hiring costs  Training costs for new employees  Severance pay  Negotiations, law suits  Loyalty, work climate  Reputation as an employer  Uncertainty about how lasting and how big an up/downturn in product demand/business cycle will be.

52  Economic downturn ◦ Decrease in overtime ◦ No new hirings ◦ No short replacements for absent workers ◦ No temporary workers ◦ ”Natural wastage” ◦ Temporary lay-offs ◦ Dismissals  Economic upturn ◦ Increase overtime ◦ Less liberal with leave of absence ◦ Use temporary workers ◦ New hirings

53  Reasons to want part-time/seasonal workers ◦ Demand for the good or service produced may vary over the day, week or year. ◦ A temporary job (fixed term contract) can function as a work trial ◦ A temporary worker may replace a temporarily absent employee ◦ Productivity per hour can be higher with fewer hours per day/week   Reasons to prefer full time/long term workers: ◦ Overhead-costs for every (new) employee. ◦ Productivity is higher if workers learn on the job.

54 TotalMenWomen 198712.09.714.2 200415.113.117.1 4th quarter 2010 15.413.817.2

55 MenWomen LO1112 TCO68 SACO912 Not organised2434 LO – blue collar TCO – lower to middle level white collar SACO – higher level white collar

56 AgeMenWomen 15-24 51,163,2 25-54 9,412,7 55-74 8,78,2

57  The public sector is an important employer, particularly for women ◦ On the one hand, has some monopsony power ◦ On the other, not necessarily profit maximising! ◦ * Municipal and county council WomenMen Local government* 6.36.0 Central government 41.411.7 Private52.382.3

58  We know numbers employed and wages. When they change is that supply or demand?? If both supply and demand functions shift we observe two points but we don’t know anything about the underlying curves! D2 D1 S2 S1

59  Solution to the IDENTIFICATION PROBLEM?  Find instrumental variables that make one curve shift but not the other.  But it is always a matter of the researcher’s judgement if the instrumental variables are well chosen.

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