Topic 3.1b Long-Run Labour Demand. Professor H.J. Schuetze Economics 370

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1 Topic 3.1b Long-Run Labour Demand Professor H.J. Schuetze Economics 370 Long-Run Labour Demand In the long-run the firm can now vary both inputs and. Typically the firms production and employment decisions are examined in 2 stages: (i) Cost minimization: firm determines the minimum cost of producing a given level of output (choose and ). (ii) Profit maximization: choose Q to maximize profits. Professor Schuetze - Econ

2 Cost Minimization Production function: Q = Q (,) Isoquants: the combinations of labour and capital required to produce a given level of output i.e. how technology allows labour and capital to be combined to produce output. MP slope MRTS MP Q 1 Q 1 > : requires more of both capital and labour to produce Q 1. Professor Schuetze - Econ Isoquants A B Q 1 Downward sloping: The more labour you use to produce (fixed level of output) the less capital you need. True if production is technically efficient Convex: At A: using lots of capital (perhaps too many machines), could produce the same amount giving up a lot of capital using just a little more labour. At B: labour and capital are pretty good substitutes. Professor Schuetze - Econ

3 Iso-Cost Curve Iso-cost curve: The combinations of capital and labour the firm can employ given their market price for a given expenditure level (C). C = r k + w, where r = price of capital w = wage C/r w / r C r Slope = -w/r c/w Professor Schuetze - Econ Cost Minimizing and E Given a chosen level of output the firm will minimize the cost of producing it. E E C 1 A C 0 Firm chooses to produce What is the least cost combination of and? Could produce at A (at a cost of C 1 ) Could also produce at E (at a cost of C 0 <C 1 ) In fact C 0 is the lowest cost the firm can produce at Cost minimization occurs at a point of tangency between the isoquant and the isocost curves Professor Schuetze - Econ

4 Deriving the Long-Run Labour Demand Curve All we need to do is vary the wage and trace out the new equilibrium amounts of labour Start with relatively low wage (w 0 ) Q 1 Suppose the wage increases to w 1 The isocost will rotate in The firm now maximizes profits choosing a lower level of output E 1 E 0 1 C 1 0 C 0 The firm will employ fewer units of labour after the increase in the wage Professor Schuetze - Econ Deriving the Long-Run Labour Demand Curve This implies that the long-run labour demand curve will be downward sloping W Labour Demand W 1 W 0 D 1 0 Let s now consider why output falls and what happens to overall costs Professor Schuetze - Econ

5 Why will the firm choose to lower output? Output Market Industry S 1 S 0 P 1 P 1 Firm MC 1 MC 0 ATC1 ATC P 0 P 0 Q 1 D Q q 1 q 0 q The increase in the wage will shift the firms marginal cost curve up to MC 1 Thus, the industry supply curve will shift left and price will rise to P 1 The new equilibrium has each firm reducing output Professor Schuetze - Econ Total Costs and Capital Total cost could increase (as shown) or decrease Decrease in output reduces cost Increased price of labour increases cost Costs are endogenous for the firm Capital Use could also increase or decrease as we shall see. However, the amount of labour will decrease for a wage increase We can prove this using scale and substitution effects Professor Schuetze - Econ

6 Scale and Substitution Effects: Substitution Effect: Capital becomes relatively cheaper Thus, the firms substitutes away from labour ( falls, rises) Scale Effect: The firm reduces its scale of operation ( and decrease) Overall: Amount of Labour demanded falls Amount of capital demanded is indeterminate Professor Schuetze - Econ Scale and Substitution Effects Graphically: C B A Q Substitution Effect: Allow the prices to change but hold output constant Substitute away from labour ( 0 1 ) Scale Effect: Hold prices fixed at new levels but allow output to change Reduces labour requirements ( 1-2 ) Professor Schuetze - Econ

7 Comparing Short and Long-Run Labour Demand Can think of the difference between the two in terms of scale and substitution effects Short-Run: Capital is fixed Therefore, no substitution effect *Labour demand is downward sloping because of scale effect and diminishing marginal product of labour Long-Run: Firm has more flexibility Added substitution effect Therefore, the response to a wage change will be larger in the long-run Professor Schuetze - Econ Comparing Short and Long-Run Labour Demand W W 1 W 0 MRP (= 1 ) E 1 MRP (= 0 ) E s E 0 MRP (LR) = marginal revenue product of labour in the long-run Flatter because a given wage change will evoke a larger response in the long-run. MRP (LR)=D(LR) 1 s 0 Suppose initially at long-run equilibrium E 0 and wage rises to w 1 Short-Run: ew equilibrium is at E s Long-Run: Firm can adjust capital (substitution effect) Shifting the short-run demand curve left ew equilibrium is at E 1 Professor Schuetze - Econ

8 Long-Run Labour Demand Curve: The locus of points (E 0, E 1 ) at which the firm optimally adjusts employment of both labour and capital Elasticity of Demand for Labour: It is important to know how responsive Labour demand is to changes in the wage i.e. to have an estimate of the elasticity = % /% w It is important to know so that the effects of policies (such as the minimum wage which increases the wage) will be known. elastic big negative employment effect inelastic small negative employment effect Professor Schuetze - Econ Elasticity of Demand for Labour: The main determinants of the elasticity of demand are (Marshall s rule): (i) The availability of substitute inputs (ii) The elasticity of supply of substitute input (iii) The elasticity of demand for the output (iv) The ratio of labour cost to total cost We will discuss these separately discussing the case where the elasticity of demand is likely to be inelastic. Professor Schuetze - Econ

9 (i) Availability of Substitute Inputs Labour demand will be inelastic if alternative inputs are not easily substituted for labour 0 extreme case can t substitute easily MRTS is small must use 0, 0 0 Availability of substitutes affects the substitution effect Could be determined by 1.Technology: Can only use labour to complete a process Professor Schuetze - Econ Factors Affecting the Availability of Substitutes 2. Institutions: Union does not allow for non-union workers Examples of workers not easily substitutable: construction trades people teachers software engineers 3. Time: In the long-run substitutes are more likely to be available (could consider an alternative production process) Professor Schuetze - Econ

10 (ii) Elasticity of Supply of Inputs Alternative inputs are also affected by changes in the price of the input e.g. if the supply of capital is inelastic demand for substitute big price Therefore, the more inelastic is the supply of substitutes the more inelastic is the demand for labour Professor Schuetze - Econ (iii) Elasticity of Demand for Outputs The demand for labour is tied to the demand for the output as we have seen The elasticity of demand for the product determines the size of the scale effect If demand for the output is inelastic then the derived demand for labour will be inelastic. Increase in price because of increase in w leads to small decrease in demand for output The wage increase is passed on to consumers in the form of higher product prices but product demand does not change much e.g. on-residential construction Few alternatives to building in a particular location Professor Schuetze - Econ

11 (iv) Ratio of Labour Cost to Total Cost Measures the extent to which labour cost is an important component of total cost Demand for labour will be inelastic if Labour is a small portion of total cost The firm will not have to cut output by much because the increased cost from the wage increase would be small i.e. If the ratio is small then the scale effect is likely to be small Importance of Being Unimportant e.g. Airline pilots Probably a small portion of overall costs given the price of airplanes Professor Schuetze - Econ Empirical Evidence How elastic is the labour demand curve? Hammermesh (1986, 1993) Estimates for different types of labour United States data (Private Sector): Ranged from 0.15 to 0.75 Median estimate over 1 year. i.e. 1% increase in wages leads to one third of a percent reduction in employment after a year ( ½ subs effect, ½ scale effect) There are several Canadian studies which find industry level elasticities to be within this range Professor Schuetze - Econ