Labour Demand Lecture notes Dan Anderberg Royal Holloway College January 2003 1 The Simple Model of Labour Demand Question: Where does labour demand come from? ² Labour demand is a DERIVED DEMAND: rms only hire (rent labour services) in order to produce. Assumptions of the simple model 1. pro t maximisation 2. homogeneity of factors of production 3. perfect competition 2 De nitions (refreshing your memory) ² Marginal analysis: look at incremental changes when all else is constant. ² Marginal product: the extra output produced by an extra unit of input. ² Marginal revenue: the price an extra unit of output can command when sold (Nb. this is true for perfect competition only). ² Marginal revenue product the extra income due to the extra unit of input (MRP = MR MP ) ² Marginal cost: the extra cost of the extra unit of input (MC = W in simple model) 3 Labour Demand in the Short Run Definition 1 Short-run: A period so short, only L can change (capital is xed). Question: What is the condition implied by pro t maximisation? ² Pro t maximisation requires MRP = MC (= W ) (Why?) 1
² Implication: Marginal product equals the real wage. Why? MRP = MP P and MC = W. Hence MRP = MC implies MP = W=P ² Recall: Marginal product of labour is downward sloping when capital is xed. (Congestion e ect). ² PLOT: marginal product (real wages) against employment. Fig 2.1 Insight!! The MP curve gives the relationship between W and L for the rm; it is thus the rm s labour demand schedule (LD curve). Question: How do we go from the rm s labour demand to market labour demand? ² Market labour demand is the sum of all rm-level demand curves. 4 Labour Demand in the Long Run Definition 2 Long-run: a period so long, where all factors of production can be adjusted. Question: What are the conditions implied by pro t maximisation? ² Pro t maximisation now requires: MRPL = MCL(= W ) and MRPK = MCK(= C); or P = W=MPL and P = C=MPK ² Combining the two conditions, we get W=MP L = C=MPK or MP K=MPL = C=W Interpretation: The product of an extra unit of L, relative to that of an extra unit of K, should equal the cost of an extra unit of L, relative to that of K. Question: What would happen if the wage rate went up? ² Scale e ect on labour: more expensive! lower employment ² Scale e ect on capital: less product! less capital ² Substitution e ect: capital is relatively cheaper! more capital ² Overall: employment declines impact on capital is ambiguous 2
5 Labour Demand in Monopoly Definition 3 Monopoly: When there is only one producer in the (product) market. ² Assume short-run for simplicity ² Slightly di erent pro t-max condition: Still MRP = MC (= W), but now MR < P. Hence MR MP = W ) MP = W P Perfect Comp. ) MP = W P Monopoly ) MP = W P P MR > W P Since MP decreases with employment we nd that that: ² Labour demand will be lower under monopoly. P MR 5.1 Labour Demand in Monopsony Definition 4 Monopsony: when there is only one buyer in the (labour) market. ² Upward-sloping labour supply curve (not xed to the market wage). ² Slightly di erent pro t-max condition (note MC 6= W). Now MRP = P MP, and MRP = MC, but MC > W: Hence MP = W P MC W Hence Perfect Comp. ) MP = W P Monopsony ) MP = W P Again since MP decreases with employment, we nd that MC W > W P ² In monopsony there is lower output, employment (and wages). 6 Elasticity ² The responsiveness of labour demand to a change in the wage rate is normally measured as a elasticity. Question: What is the own-wage elasticity? 3
² The responsiveness of LD to a change in W for a category of labour i ii = % L i % W i = L i=l i W i =W i = L i W i W i L i Question: What do we know about the own-wage elasticity? ² Own-wage elasticity is always negative (since L i = W i < 0). ² The greater the elasticity (in abs. terms) the atter the LD curve. Terminology typically used: j ii j = in nite! perfectly elastic (totally at) j ii j > 1! elastic j ii j = 1! unit elasticity j ii j < 1! inelastic j ii j = 0! perfectly inelastic (vertical) 7 The Hicks-Marshall Laws of Derived Demand Question: When is the own-wage elasticity of labour demand high? The Hicks-Marshall laws of derived demand identify four cases. 7.1 Demand for Final Product Law 1: The own-wage elasticity of labour demand is high when price elasticity of product demand is high. ² This is due to a scale e ect: W "! MC "! P "! D #! Q #! LD #. Implications: ² higher at rm-level than at market-level. ² higher for perfectly competitive rms than for monopolists. ² higher in long-run than in short-run. 7.2 Substitutability of other Factors Law 2: The own-wage elasticity of labour demand is high when other factors of production can easily be substituted. Implications: ² higher in long-run than in short-run. ² can depend on institutions (unions, safety regulations etc.) 4
7.3 Supply of Other Factors Law 3: The own-wage elasticity of labour demand is high when the supply of other factors of production is highly elastic. Implications: ² higher in long-run than in short-run. 7.4 Share of Labour in Total Cost ² E.g. suppose that wages are only 10% of total costs; then if % W = 20%! % (TC) = 2% (only) ² Suppose instead wages are 90% of costs, if % W = 10% (half!)! % (TC) = 9% (much larger). ² Larger scale e ect in the second case. Law 3: The own-wage elasticity of labour demand is high when wages area large share of total production costs. 8 Estimates of Elasticity of Demand ² Many empirical attempts to estimate the elasticity of labour demand. ² Some consensus that short-run elasticity is around 0:4 to 0:5: ² Long-run elasticity is, as predicted, larger: around 1: 9 Application: Minimum Wage 9.1 The Minimum Wage in the UK ² Stated objective: create a minimum pay level, protecting workers from unacceptably low rates of pay. ² Number a ected: 1.8 million adults and 0.1 million youth. ² Since when: National minimum wage came into force April 1999. ² Generosity: Increasing over time Fig 2.2 Question: Who is particularly a ected? ² Certain sectors: retail; childcare; textile industry etc. ² Certain gruops: women; ethnic minorities etc. 5
9.2 Theory ² Assume: coverage is complete. labour and product markets are competitive. ² Original equilibrium: E employed. ² When minimum wage W mw is imposed: Fig 2.3 rms reduce demand to E mw more labour is supplied (movement along LS curve) Result: Unemployment E s E mw. 9.3 Incomplete Coverage ² Not all workers are covered by the minimum wage: self-employed, some apprentices, (in the US) certain occupations. ² Suppose there a covered and an uncovered sector. ² Before the minimum wage, a unique equilibrium in each sector with wage W. Fig 2.4 ² Minimum wage W mw is then imposed in the covered sector. ² Employment in the covered sector reduces to E mw ² Some displaced workers move to the uncovered sector. ² New equilibrium in the uncovered sector with lower wage W 0 and more employmen E 0. ² Thus, less total unemployment generated by the minimum wage; however, creates even lower pay in the uncovered sector. 6