Labor Demand. 1. The Derivation of the Labor Demand Curve in the Short Run:

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1 CON 361: Labor conomics 1. The Derivation o the Curve in the Short Run: We ill no complete our discussion o the components o a labor market by considering a irm s choice o labor demand, beore e consider equilibrium. We ill no revisit the production unction rom your microeconomics course. Let the production unction ith labor hours () and capital () as actors o production be q = (, Where is increasing and concave in, and. Let s irst consider the scenario o a irm in a competitive goods, and actor market. The proit unction 1 is then π = pq r = p (, r The irst order condition tells us that the irm ill hire labor up to the point here the value o the marginal product o labor (VMP ) equates ith the age rate. p, = VMP = Note that VMP is a concave unction o. The same can be said o the choice o capital, but in the long run. Ho can e depict this choice diagrammatically? First let us describe hat is the value o average product o labor? (, VAP = p = p AP Ho ould the VAP look like? Since it is a unction o the production unction it should have an initially increasing portion, but because it is divided by the amount o labor hours used, and e have assumed that (, is increasing and concave in (hile is strictly increasing in, there ill come a point here the denominator is groing at a aster rate that the production unction), there ill come a point here VAP ill start decreasing. Further, since (, is still increasing, hen VMP starts decreasing, there ill be a point here VMP intersects VAP rom the top. No e are ready to dra VMP and VAP. 1 It should be noted that or intents and purpose o our discussion, e assume proit maximization o the irm, reality may dictate that a irm consider other actors that may not be relected in proit maximization. An example being concerns about damage to reputation, as ell as the short run versus the long run needs o a irm. For example, even i the short run maximization dictates that a irm should lay o orkers, the irm may choose not to lay o any orkers under short run economic donturns i the cost o rehiring, and retraining labor is higher then the immediate need o maximizing proits. What other reasons could there be? 1

2 CON 361: Labor conomics Output Number o Labor Hours Required The labor demand is the portion o the VMP that is belo the VAP. Why should that be the case? Why not in the upard portion o VMP? At that portion o VMP, an increase in the number labor hours required ould result in greater value attained given the age rate (i.e. the VMP must be greater or equal to the going age rate, assuming the labor market the irm is in is also competitive). That is the marginal gain in revenue is greater than the cost o hiring an additional hour o labor. Hence the stopping rule or the irm is hen the VMP equates ith the age rate, and it s on the portion here VMP is donard sloping or is decreasing. Why must the supply be the segment belo the VAP? Any age level above the maxima attained by the VAP ould mean the average cost is greater than the average beneit, i.e. the irm ould be making losses. Hence the labor demand is the ay it is, and describes the amount o labor hours/labor (depending hat you have on your horizontal axis) desired at a given age rate. Note that this is given a particular technology, i.e. this is the short run labor demand curve. Is there an alternative interpretation to the irm s stopping rule? First note that p, = p = = = MC (, MP Next note that s denominator is increasing but at a reducing rate, hile the MP numerator, the age rate is strictly increasing. Then MC is increasing, and stopping rule is at the point here marginal cost equates ith the price o the product sold. 2

3 CON 361: Labor conomics The market s labor demand in this industry ould then be the horizontal sum o these individual demand or labor curves. Is there another ay to think about this proit maximizing strategy besides through the use o isoquants and isocost curves. pq Where is less than. 2. The mployment Decision in the Long Run From the above irst order condition o the proit maximizing problem, e have p, = The same is true or capital, Then in long run equilibrium, r VMP p VMP = (, = r = r (, (, r (, = = (, = MRTS Ho ould you depict this equilibrium using isoquant and isocost curves? 3

4 CON 361: Labor conomics Is the labor demand more or less elastic in the long run? The decomposition o a change in age rate, and cost o capital is similar to that in your consumer theory, and our analysis o labor supply. Income eect is no replace by scale eect (As a result o a uniorm rate o reduction in cost, or as a result o technological change that aected the cost o production uniormly), hile substitution eect remains the same (and is dependent on the change in the relative cost o the actor inputs). 4

5 CON 361: Labor conomics 3. lasticity o Demand or Labor The elasticity o labor demand is just Percent change in employment SR δ SR = = Percent change in age SR What are some determinants o this elasticity? These are also knon as Marshall s Rules o Derived Demand a. Availability o Substitute Inputs: The greater the number o substitutes, the more elastic the demand. b. lasticity o Supply o Substitute Inputs: The more elastic the supply o substitute inputs, the more elastic labor demand is. c. lasticity o Demand or Output: I demand or output is inelastic, the demand or labor ould also be inelastic. The converse is true. d. Ratio o Labor Cost to Total Cost: The smaller the proportion to total cost, the more inelastic is labor demand. Application o the above to Union Behavior: A union s ar cry is generally or the increase in collective ages or unionized members through the poer o collective bargaining. Hoever, as e kno the greater the ages above the equilibrium level, the more labor ould go unemployed. A union ould then be most eective i the industry under consideration aces an inelastic demand or labor. It is then in the interest o a union to loer the irm s elasticity o demand or labor. Ho can this be achieved? It is then not surprising the unions typically resist technological advances that increase the possibilities o substituting beteen labor and capital. Point a and b above. Unions oten ant to limit the availability o goods that compete ith the output o unionized irms. A good example as the resistance to the entry o Japanese cars into the U.S. market. This relates to point c above. Unions are more successul hen their age bill makes up a small proportion o total cost, such as electricians, and carpenters. For a more detailed description, see Borjas page Changing Demand Conditions and Global Competition Since labor demand is a derived demand, derived rom the demand or a irm s product, changes in the product s demand ill aect the labor demand or the irm. Ho has global competition aected Canadian Labor demand? With the advent o global competition and trade, there is greater availability o substitute products. This competition drives prices don, reducing the derived labor demand. Can e prove such a conclusion based on our simple model o irm proit maximization? From the irst order conditions, e can dierentiate implicitly ith respect to p to obtain the olloing implicit relationship beteen labor demand, and price o product manuactured; 5

6 CON 361: Labor conomics (, + p (, (, (, = 0 p p This means that as competition drives don prices o Canadian goods, labor demand alls, since by concavity (, is less than zero. O course this argument negates the possibility that ages may be driven don to maintain Canadian irms competitive edge. That is e could have ages alling to meet the all in prices due to competition. Can you prove this conclusion rom our proit maximizing condition? = (, 0 p Another approach to understanding ho trade and competition may aect domestic demand or labor is the olloing: With competition, and reer trade, prices in both domestic and oreign markets must equate, else there ould be arbitrage possibilities (i.e. i the product is cheaper in one market than another, someone could just buy rom the cheaper market, and resell the items in the more expensive market or nonzero proits). Let the superscript or domestic irms be denoted by d, and or oreign. Then in equilibrium d MP MP = p = d No i both economies have the same marginal product o labor, ith the exception that the Canadian labor commands higher ages, open trade ould require ages to all to that attained in the oreign economy. This argument could also be extended to the case hen ages are the same, ith the exception that marginal product are dierent. Suppose the sole dierence is the Canadian labor is less productive. To maintain equality in the condition, e could either raise marginal productivity, or loer age rates. Your text has a good sample o here Canada stands in terms o labor cost to both Nely Industralized conomies, and developed estern economies in table 5.1 on page 160, hile table 5.2 on page 161 reveals Canada in terms o productivity. An interesting question to ask yoursel in all these comparisons is the olloing: Ho does Canada s industrial composition compare ith the other advanced economies? That is ithout ull knoledge o this composition, those numbers reveal little about ho capable an economy ill be able to meet the challenges o changing taste in consumption. Read exhibit 5.1 on page 165 about the Free Trade Agreement beteen US and Canada, and ho it aected Canada in the short-run and long run. p = 0 6

7 CON 361: Labor conomics 5. What is the Relationship beteen the Firms Production Function and the Demand or Labor? (This section is just good to kno, but not necessary to kno) Let start by assuming the typical production unction, but no ith only labor as the sole input, q = = α β The proit unction is then, ( pq r [ p( α β π = max = max ) r ], Assuming e ould like to ind the long run labor demand, that is is variable as ell. The irst order conditions or and are respectively, α 1 β αp =, α β 1 ( = r βp Combining these to irst order conditions e can ind the equilibrium condition. Thereore, αp = βp = r β = α r Hoever note that the irm irst chooses its optimal output given the competitive price. Let this choice o output be y. α β y = β y = α We can no substitute this condition into the demand unction or labor, α 1 y αp = α αpy = ln = lnα + ln p + ln y ln Which is just your long run labor demand unction in natural logarithm. Note the relationship beteen price o output, age rate, and total output. Do the signs concur ith your expectations? β α 1 1 α 1 1 β 7

8 CON 361: Labor conomics 6. What i e have Imperect Competition in the Product Market? Suppose the irm ho is doing the hiring operates as a monopoly in the goods market. Again let us ix the output o this monopoly irm at y hich it has chosen as its proit maximizing level. Recall then its proit unction is as ollos, maxπ = max p,, m ( ) r Thus it is not a price taker, unlike the competitive good irm. Its demand unction o labor is thus, p, + p = ( ) q MR q MP = MRP = Note the dierence in the implicit demand unction or labor. Instead o equating the value o marginal product o labor to ages, e no equate it to the marginal revenue product o labor. This is because the monopoly is a price setter, as opposed to a price taker. In and o itsel hat does this mean or the labor market? I the irm s labor skills are not speciic, that is i the labor market is competitive, hether the irm is a monopoly or otherise makes no dierence, since its demand is aggregated into the market labor demand. Hoever, the olloing section deals ith the possibility that the irm may in act be a monopoly labor demander in the labor market, monopsony. 7. What i the irm has Monopoly Poer in the Labor Market, i.e. is a Monopsony. I a irm is a monopsonist in the labor market, it is eectively the only demander o labor, and hence dictates the going ages. Ho ould the proit maximizing problem or a monopsonist look like? First note that instead o being a age taker, it no sets the ages. maxπ = max p, c m r here c is the increasing and convex cost unction ith respect to labor. The demand unction no or labor is p, = c = c pmp That is the amount o labor hired is attained hen the value o marginal product o labor equates ith marginal cost, i.e. age is not a horizontal line at a speciic age rate or the irm, but a upard sloping curve. Diagrammatically, 8

9 CON 361: Labor conomics MC Supply m VMP m 2 Let consider the simplest case here the monopolist s cost unction is c = α here the labor supply unction is = α. Then marginal cost is just c = 2α. Then the labor supply curve is belo the marginal cost the irm aces, hich in turn determines the amount o labor it hires. Further, since there is no necessity or the irm to pay a age higher than hat is desired on the labor supply curve, a monopsonist hires less labor and at a loer age rate than a competitive labor market. 8. stimating hen e have ndogeneity Problem? The method o Instrumental Variables. What is endogeneity? It is bias in our estimated coeicient o interest, hich in our estimation o say, the demand o labor, or the supply o labor may be the elasticity o demand, and supply respectively. Consider a simple regression or labor supply, ln i = α + a ln pi + bln yi c ln i + ε i Think about hat our data might be telling us. The observations o labor supply involves typically equilibrium points at dierent times. These equilibrium points may in act involve shits in both demand, and supply labor as in the igure belo. Then at least rom the diagram, e ould be biased to ind elasticity o supply that may in act be negatively sloped, hen e ere expecting a positively sloped labor supply! The bias is created because there are other variables aecting labor supply, such as demand conditions, hich is captured in the error term. 9

10 CON 361: Labor conomics Wage Supply 1 Supply 2 Regression Line Demand 1 Demand 2 Number o Workers What can e do then? The Method o Instrumental Variables One strategy is to ind a situation here some underlying actor is shiting the demand ithout shiting the supply. In econometrics, a variable that causes a shit in one curve ithout another, a instrument, or instrumental variable, and the technique used to perorm such a regression as Method o Instrumental Variables (IV). Diagrammatically, Wage Supply 1 Regression Line Demand 1 Demand 2 Number o Workers That is the technique is able to isolate the labor supply curve. (What do e need to estimate demand?) Hoever, this is conditional us being able to ind a good instrument, and it is usually highly debatable hether an instrument is good, or hether one is better than the other. 10

11 CON 361: Labor conomics As an example, consider the estimation o omen s labor supply during the periods hen omen ere increasingly empoered through the legalization o abortion, or the availability o contraceptive technology. The typical argument o these technologies aecting omen is through alloing them to complete their desired human capital investment, hence increasing their skills, and the demand or emale orkers. Hoever, these technologies also aected omen through permitting to entering the labor orce hence increasing labor supply. Ho then can e estimate the true elasticity o labor supply or omen during these periods, and separate beteen hat as the previous value o elasticity, and hat as caused by the advent o these technologies? Can you think o an instrument? For an example on the estimation o labor demand, read Borjas, section 4.12, pages