Topic 3.1a Short-Run Labour Demand. Professor H.J. Schuetze Economics 370

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1 Topic 3.1a Short-Run Labour Demand Professor H.J. Schuetze Economics 370 Labour Demand Let s turn our attention away from employees to focus on the behaviour of employers or firms. Recall that labour demand is: the amount of labour that would be demanded by firms at any given overall wage rate (w) Unlike goods and services the demand for labour is a derived demand Labour is not demanded for final use or consumption but as an input into production. The demand for construction workers is linked to the demand for new buildings. Professor Schuetze - Econ

2 Basic Neoclassical Model There are a few assumptions that are fundamental to the model. (i) Employers and employees are rational and well informed. (ii) Employees wish to maximize utility. (iii) Employers wish to maximize profits. The predictions of the model also depend upon the degree of competition in the market Professor Schuetze - Econ Competition The four main degrees of competition are: Product Market 1. Perfect Competition 2. Monopolistic Competition 3. Oligopoly 4. Monopoly Labour Market 1. Perfect Competition 2. Monopsonistic Comp. 3. Oligopsony 4. Monopsony Let s start with the case where there is perfect competition in the product and labour markets Professor Schuetze - Econ

3 Perfect Competition What does perfect competition imply? Product Market: Large number of sellers Sellers produce a homogeneous product Sellers and buyers have perfect information No barriers to entry These imply: horizontal demand for product Labour Market: Large number of workers Workers are homogeneous Large number of homogeneous Employers Workers and employers have perfect information No barriers to entry These imply: horizontal supply of labour Professor Schuetze - Econ Short and Long Run Finally we will also need to distinguish between the short-run and the long-run. Short-Run: Period during which one or more factors of production cannot be varied (in our case capital). Long-Run: Period during which all factors can be adjusted. Professor Schuetze - Econ

4 Short-Run Demand for Labour Firm produces single output (Q) using 2 inputs, capital (K) and labour (N). In the short-run capital is fixed so K = K 0. The number of workers a firm is willing to hire depends upon: (i) The quantity of output that its workers are able to produce. (ii) The price the firm is able to charge for the finished goods. To see this, consider the following: Professor Schuetze - Econ Marginal Product of Labour (MP N ) The change in output that results when one unit of labour is added to the production process (holding all other inputs fixed) MP N = Q/ N Usually assume diminishing returns set in at some point Example: Production line built for 10 people If you only have one worker he/she will not be very productive Adding another worker will certainly increase production by a lot since tasks can be shared Eventually adding workers will increase production by a lesser amount than the preceding workers Professor Schuetze - Econ

5 Basic Neoclassical Model We can depict this relationship as follows: MP N MP N increases up until 10 workers Diminishing marginal product beyond 10 workers MP N MP N 1 10 N The MP N curve could shift if the firm is able to increase capital (i.e. a different short-run) Professor Schuetze - Econ Average Product of Labour (AP N ) Equals total output (Q) divided by the total number of workers employed (N) AP N = Q/N MP N is related to AP N as follows: If the amount produced by adding an extra worker (MP N ) is greater than the average product (AP N ) then AP N will rise. If MP N is less than AP N then AP N will fall e.g. grades in this course Professor Schuetze - Econ

6 Average Product of Labour (AP N ) Thus, MP N will intersect AP N at the maximum of AP N AP N MP N AP N rising when MP N is above it. AP N falling when MP N is below. MP N AP N AP N must be flat at point of intersection average = marginal (no change in average). N Professor Schuetze - Econ Marginal and Average Revenue Product of Labour The profit maximizing firm is only indirectly interested in the number of units of output each worker adds. The direct determinant of labour demand is the effect an additional worker has on the firms total revenue (MRP N ). Marginal Revenue Product of Labour equals the additional units produced by a worker (MP N ) times the increment in total revenue each of those units would produce (MR). MRP N = TR/ N = TR/ Q Q/ N = MR MP N Professor Schuetze - Econ

7 Marginal Revenue Product of Labour However, under perfect competition MR =? MR = P, so MRP N = P x MP N e.g. One more labourer in an apple orchard increases annual production by 3,000 bushels. Each bushel is worth $10 MRP N = $10 x 3,000 = $30,000 Average Revenue Product of Labour (ARP N ) equals the firms total revenue divided by the number of workers ARP N = TR/N = {P Q}/N = P Q/N = P AP N Professor Schuetze - Econ Marginal and Average Revenue Product of Labour MRP N and ARP N equal MP N and AP N multiplied by a constant (P). So, the same relationship holds for MRP N and ARP N as did for MP N and AP N : MRP N ARP N MRP N ARP N Professor Schuetze - Econ

8 Deriving the Short-Run Demand Curve For the firm, two decision rules follow from the assumption of profit maximization 1. Because fixed costs (capital costs) must be paid whether or not producing, the firm will operate as long as total revenue exceeds total variable costs. TC = FC + VC if TR = VC, = TR - TC = - FC Total losses = fixed costs. firm would lose this by shutting down. if TR > VC > - FC Better off operating than shutting down. Professor Schuetze - Econ Deriving the Short-Run Demand Curve 2. If producing at all, the firm should produce the quantity at which marginal revenue = marginal cost These decision rules can be stated in terms of inputs rather than output. First define Total Revenue Product of Labour: The total revenue associated with the amount of labour employed = TRP N 1a. Produce providing the total revenue product of Labour exceeds the total costs of labour; other wise shut down. 2a. If it produces at all, the firm should expand employment up until the point at which MRP N = MC N Professor Schuetze - Econ

9 Deriving the Short-Run Demand Curve wage With perfect competition MC=AC=wage So, the firm hires up to w 1 the point where MRP N = w 0 ARP wage N If the wage = w 0 the firm MRP N will hire N 0 workers. N 1 N 0 N The firm will shut down in the short-run if total cost of labour (VC) exceeds the total revenue product of labour (TR) i.e. if VC > TRP N or if VC/N > TRP N /N w > ARP N So at wages higher than w 1 the firm would choose to shut down. The demand curve is downward sloping because of diminishing returns. Professor Schuetze - Econ Implications of Equilibrium Says something about how MP N is associated with wage. Firms produce up until MRP N = w or P MP N = w Therefore, implies that at equilibrium MP N = w/p The marginal product of labour equals the real wage. * The more productive you are the higher the real wage you will receive in the short-run (PC). Professor Schuetze - Econ

10 Monopsony Suppose instead, that there is imperfect competition in the labour market but competition in the output market For example, suppose that there is only one firm purchasing labour in the input market The firm s labour supply curve is no longer perfectly elastic at the going wage Instead, the firm s labour supply curve is the upward sloping industry labour supply curve Thus, the marginal cost of labour will vary with the number of employees Exactly how, depends on the type of monopsonist Professor Schuetze - Econ Perfectly Discriminating Monopsonist w w PM Suppose the monopsonist is able to price discriminate i.e. pay each worker his/her reservation wage By concealing the higher wages of new workers Using non-wage mechanisms to pay new workers Thus, the firms MC equals its supply curve N PM MRP N S=MC N The firm still hires up to where MRP=MC The firm hires N PM workers Similar outcome to perfect competition Unlike perfect competition, however, the monopsonist earns profits Professor Schuetze - Econ

11 2. Non-Discriminating Monopsonist In the more likely case where the monopsonist can t price discriminate we need to think harder about what MC N will be The MC N curve will lie everywhere above the labour supply curve This is because as the firm raises wages to attract more workers (marginal workers) it also pays those extra wages to existing (intramarginal) workers Professor Schuetze - Econ Non-Discriminating Monopsonist w MRP M w C w M N C MC N MRP N S Hire up to the point where MC N equals MRP N (N M ) Read the wage off of the supply curve (w M ) Implications? N M N Compared to the perfectly competitive equilibrium less labour is hired at a lower wage. Monopsony implies w<mrp N Monopsony profit = (MRP M -w M ) N M Sometimes referred to as monopsonistic exploitation However, intramarginal workers receive sellers surplus Professor Schuetze - Econ

12 Bruggink and Rose (1990) Paper Basic idea: owners accused of colluding in free agent market after 85 and 86 seasons Gained monopsony power which suggests that players paid under MRP Uses econometrics to estimate MRP Premise: winning teams more popular (more revenue) and player performance leads to wins? Implies fans go to see teams not players Still allows players to be a draw to the extent that their play helps team win Professor Schuetze - Econ Empirical Model Estimate how player performance affects winning and hence revenue Step 1. Estimate effect of team performance on wins pctwin= (tsa)+72.47(tsw)+63.54(cont)-50.10(out)+e pctwin mean = 500 TSA=relative slugging avg (bases/at bats) TSW=rel strikeout/walks, and in/out pennant race relative means team avg./league avg. Says that for every percent above average in slugging, winning pct goes up 0.4 percentage points For strikeout/walk ratio, every percentage point above average leads to a 0.1 percentage point increase in the win percentage cont/out - if average team finishes around 500; team in contention finishes at 564 and one that is out at 450 Professor Schuetze - Econ

13 Empirical Model Step 2. Estimate effect of winning etc. on team revenue REV= (PCTWIN) (SMSA) (STD) (TWOTM)+e REV mean = 30,935,231 STD=old stadium is insignificant Says adding 100 pts to win(going from ) adds about 5 million to revenue Step 3. Estimate effect of individual performance on revenue If subs step 1 into step 2 get effect of team performance on revenue For hitting: 53070*426*TSA = 22,607,820*TSA For pitching: 53070*72*TSW = 3,821,040*TSW If we know how a player s performance affects team stats we will have MRP Professor Schuetze - Econ Results Can do this by substituting 1. hitter s slugging average * % team at bats for team slugging avg 2. Pitcher s strikeout/walk ratio * % of teams innings pitched for team strikeouts to walks Results: Test if w/mrp is lower for free agents in compared to 84 using gross MRP 1984 w/mrp = 0.961, = for a difference of get p-values of between 5 and 11 (prob really no difference) Therefore, in general supportive of collusion among owners! Professor Schuetze - Econ