Labour Demand Borjas ch 3 4 9 Not included

Labour Demand (Borjas ch. 3+4. 9) (Not included: 3 -6, 3 -10, + pp 139 -141) Market for (homogenous) labour SE DE W 1 WE W 2 EE

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.

Short repetition of theory of production… Basic assumption: The firm hires workers in order to MAXIMISE ITS PROFITS The firm’s demand for factors of production involves two decisions: ◦ Produce what (how much)? ◦ Produce how (with what technology/what inputs)?

The production function 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, …, xn)

If all other inputs are held constant we can see production as a function of labour. Production as a function of labour at ONE particular level of all other inputs

Marginal productivity of labour The slope of the production function shows how production changes with a change in (only) labour input. The marginal product of labour (MPE): ◦ 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 MPE 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

The average product of labour = Q E

Average and marginal product If MPE > APE , APE If MPE < APE , APE MP-curve AP-curve The decreasing part of the MP-curve cuts the AP-curve in the AP-curve’s maximum

Remember: With a different level of K, we get a different Q and a different MPE for each E To each value of K corresponds another function Q(E) and another function MPE Analogously If labour input is constant, you can see production as a function of capital and define the marginal productivity of capital.

The employment decision in the short run = with a fixed level of K VMPE = p • MPE (if the firm is a price taker in the product market) A profit maximising firm employs until: VMPE = MCE Under perfect competition the firm is a ”price taker in the labour market”. It takes w as given and MCE = w

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

VMP Why is only the decreasing part of the VMP. curve relevant? W W 2 W 1 E 2 E 1 If the ”going wage” is W 2 the firm hires E 2 workers – APE > MPE E

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

If competition might not be perfect: In labour market: MCE ≠ w In product market: MRQ ≠ p The firm employs and produces until: MCE = MRQ *MPE (2) ◦ (1) is a special case of (2)

Aggregate labour demand in the industry (still short run) If wages increase, each employer hires less labour power. 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.

The wage elasticity of labour demand

In the longer run: 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

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

Isoquant of Q when Q=240 K E

A special case: Inputs are perfect substitutes

Another case: Inputs are perfect complements Leontief production function

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

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

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

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.

The expansion path of a firm

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

What happens to factor use if w increases? (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.

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 SUBSTITUTION EFFECTS and SCALE EFFECTS

Employment when w increases P is choice with lower wage R is choice with new higher wage E*-E 1 is scale effect E 2 -E* is substitution effect P R S Q 1 Q 2 E* E 1

Use of capital when w increases P is choice with lower wage R is choice with new higher wage K 2 K 1 K* K*-K 1 is scale effect P R S Q 1 Q 2 K 2 -K* is substitution effect

w , r constant 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.

Elasticity of labour demand: 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 production the 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

Elasticity of substitution: 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. qi, and pi are quantitites and prices of the two inputs

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.

With many inputs: Q=Q(E 1, E 2, …, K, N, …) Factor i will be employed at the level where VMPi=MPi*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 =

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

Empirical studies: 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.

Marshall’s rules: 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.

Why “If the supply of complements to it is inelastic and that of substitutes elastic. “ 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

Two groups of workers, A & B, are complements D 1 D 2 Inelastic supply Elastic supply

Labour market structure and labour demand Perfect competition W W 2 VMP W 1 E 2 E 1 E

Monopsony MCE W 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)

A discriminating monopsonist pays each worker his/her reservation wage. Employment is = EPerfect 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.

Labour demand with (nondiscriminating) monopsonist: W W MCE LS WPC WM VMP EM EPC E

Minimum wages 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

Labour supply with and without minimum wage SL SL

Effects of minimum wage under perfect competition and monopsony Monopsony Perfect competition: Wmin MLC S S VMP Employment Wage Unemployment

A firm dominates employment in a small town. The price of its product is 10 SEK. The firm’s production function is : Q = 20 E – 0. 005 E 2 Q = production E = Employment. a) What is the firm’s labour demand function DE ? 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. 2 E What is MCE Calculate the firm’s DE and the wage, w. c) The state sets a minimum wage w=150, How many workers will the firm employ? a) VMPE=p*MPE=10*(20 -0, 01 E)=200 -0, 1 E Profit maximisation requires that VMPE=MCE=w DE is given by: w=200 -0, 1 E E=2000 -10 w w=150 => E=500 b) The labour cost of the firm : E*w = E*(50+0. 2 E) = 50 E+0. 2 E 2 MC E : 50+0. 4 E MC E =MRP E 50+0. 4 E= 200 -0. 1 E E = 300 To employ 300 workers the firm has to pay w=50+0. 2 L=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

Adjustment costs – labour as a quasifixed factor of production 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.

Labour demand adjustment over the business cycle: 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 ◦ ◦ ◦

Demand for hours of work or demand for number of workers? 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.

Percent workers with fixed term contracts by gender Total Men Women 1987 12. 0 9. 7 14. 2 2004 15. 1 13. 1 17. 1 4 th quarter 2010 15. 4 13. 8 17. 2

Percent workers with fixed term contracts by union affiliation Men Women LO 11 12 TCO 6 8 SACO 9 12 Not organised 24 34 LO – blue collar TCO – lower to middle level white collar SACO – higher level white collar

Percent workers with fixed term contracts by age Age 15 -24 25 -54 55 -74 Men Women 51, 1 63, 2 9, 4 12, 7 8, 2

Employment, Sweden 2005 Percent of employed 20 -64 years Women Men Industry Social work 17 3 Health care 13 3 1 0 20 8 Retail trade 7 3 Recreation, hotels, restaurants 5 4 12 15 Wholesale trade and communications 7 19 Agriculture, forestry, fishing 0 1 Manufacturing 8 26 Construction 1 10 Other 9 8 Personal Service Education and science Financial and insurance

Employment, Sweden 2005 Percent of employed 20 -64 years 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! Women Local government* 6. 3 6. 0 Central government 41. 4 11. 7 Private ◦ Men 52. 3 82. 3 * Municipal and county council

Supply or demand? We know numbers employed and wages. When they change is that supply or demand? ? S 1 S 2 D 1 If both supply and demand functions shift we observe two points but we don’t know anything about the underlying curves!

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.