# Economics 324: Labor Economics 1.Any questions? Labor Demand A firm’s demand for labor is a derived demand. Let’s start with a Production function, which.

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Economics 324: Labor Economics 1.Any questions?

Labor Demand A firm’s demand for labor is a derived demand. Let’s start with a Production function, which represents the technology a firm uses to produce their good/service. –Q = f(L,K) –Assumptions about Labor: 10 workers @ 8 hrs/day gives same output as 20 @ 4 hrs/day labor is labor … but there are different types (skill, experience) This is important since many public policy issues are targeted at specific types of labor (min wage, tax credits, etc.)

Marginal Product and Average Product Marginal Product of Labor (MP L ) is the change in output resulting from hiring one more worker/hour, ceteris paribus MP L = (  Q/  L ) > 0[  implies ceteris paribus] MP K = (  Q/  K ) > 0 Employment Output (Total Product) MP L AP L MRP L0 111 227 347 466 583 698 7111 8122 9131

Total, Marginal, and Average Average Product of Labor (AP L ) is the output per worker. AP L = Q/ L If the Average is rising, Marginal curve lies above Average curve, & Marginal is below the Average, if the average is falling. Profit Maximization –We assume the firm wants to maximize  (profits) –Profit = Total Revenue - Total Cost = PQ - (wL + rK) P = price of firm’s output Q = amount of firm’s output –P, w, r assumed constant for now  perfect competition –Decision variables for the firm are K and L --- “right” combination?

Short-run Employment Decision How many workers should the firm hire? A competitive firm can hire all the workers they want at going wage. Hire so that MRP L = MC L For a competitive firm, this is MRP L = W NB: This does not say “the firm should set W equal to MRP L ” A competitive firm takes their W as given or pre-determined. It does say “A competitive firm should hire until MRP L = W” Additional conditions for short-run employment decision 1. MRP L = W 2. The MRP L curve must be downward-sloping at the optimal # workers 3. W must be < ARP L (P*AP L ), otherwise the per-worker contribution to the firm is less than the wage,  < 0 and the firm will EXIT the market. In other words, we must also be on the downward portion of the ARP L curve (after the intersection of MRP L & ARP L ).

Labor Demand Profit Maximization & Derived Demands –We assume the firm wants to maximize  (profits) –Profit = Total Revenue - Total Cost = PQ - (wL + rK) P = price of firm’s output Q = amount of firm’s output Big Picture -- what does the profit maximization condition look like for various possibilities? Input Market Structure Output Mkt Structure:CompetitionMonopsony Competition P * MP L = wP * MP L = MC L Monopoly MR * MP L = w MR * MP L = MC L

Long-run Employment Decision Capital stock, K, is not fixed. Must choose both K and Labor. First, define an isoquant as the possible combinations of K and L which produce the same level of output. Properties of Isoquants: (1) isoquants are downward sloping (2) isoquants do not intersect (3) higher isoquants are associated with higher levels of Q (4) isoquants are [strictly] convex to the origin

Slope of an Isoquant Slope measures the rate at which a firm is willing to trade labor for capital and maintain the same level of output, Q Loss in output from X to Y =  L * MP L Gain in output from X to Y =  K * MP K Same isoquant   L * MP L +  K * MP K =0 A little algebra yields the slope:  K/  L = - MP L / MP K In words, the absolute value of the slope of an isoquant is the ratio of the marginal products, and we call this the Marginal Rate of Technical Substitution Slope is steep when lots of K, little L, but flatter when little K & lots of L K L Q = 500 Y X

Iso-Cost Lines & Optimal Inputs Total Cost = wL + rK K = (-w/r)L + (TC/r) Properties of Iso-Cost lines: (1) it shows the different combinations of K and L which are equally costly (2) higher lines imply higher costs (3) slope of isocost line equals the negative of the ratio of the input prices A firm minimizes the costs of producing Q units of output at point Z where the isocost line is tangent to the isoquant  MRTS = ratio of the input prices MP L /MP K = w/r K LaborTC/w TC/r Z B A Q = 100 widgets

Shocks to Input Prices Decrease in the price of labor (wage) A change in the price of an input generates scale and substitution effects. Substitution Effect (X to Y) lower wages  L relatively less expensive  shift toward L Scale Effect (Y to Z) lower wages  lower costs  expand production ‘til MR = MC again  now what’s cost-minimizing way to produce new Q  more Labor needed K LaborTC/w TC/r X Y Q=100 Q=200 Z

Long-run Employment Decision Capital stock, K, is not fixed. Must choose both K and Labor. Lagrangian derivation For Labor we have derived: MRP L = MC L Same for capital: MRP K = MC K w/MP L = r / MP K The firm adjusts L and K so that the marginal cost of producing an extra unit of output (widgets) using Labor is the same as the marginal cost of producing that extra widget using Capital. If they’re not equal, then you can produce the same output at lower cost! Alternatively, MP L / w = MP K / r

Firm’s Demand for Inputs Initially at point E Labor Capital (K) TC 1 /r TC 1 /r’ TC 2 /r’ TC 1 /wTC 2 /w Q1Q1 E E \$ per unit QQ1Q1 MC AC MC AC Shock:  P capital (  r) Slope of the dashed isocost line is flatter, but SAME Total Cost (TC 1 ) TC 2 is new least-cost way to produce Q 1 units of output Movement E to E is the Input Substitution Effect; Capital is now more expensive  use less K, more L This higher TC 2 changes MC, AC Costs can vary in two ways: (1) as output varies | input prices (movement along MC, AC curves) (2) as input prices vary (shifting MC,AC) expansion path  w,r´ expansion path  w,r Q2 MR  lower Q MR Q2Q2

Firms’ Demand for Inputs Initially at point E Labor Capital (K) TC 1 /r TC 1 /r’ TC 2 /r’ TC 1 /wTC 2 /w Q1Q1 E E \$ per unit QQ1Q1 MC AC MC AC Profit maximization yields: MRP L = w MRP K = r With 2 inputs,  L/  w = [  L/  w]  Q +  L/  w (from  Q) [  L/  w]  Q < 0  L/  w (from  Q) = (  L/  q) (  Q/  P) (  P/  MC) (  MC/  w) (+/-) (-) (1) (+/-) Thus,  L/  w (from  Q) < 0 expansion path’ expansion path Q2 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/14/4184069/slides/slide_14.jpg", "name": "Firms’ Demand for Inputs Initially at point E Labor Capital (K) TC 1 /r TC 1 /r’ TC 2 /r’ TC 1 /wTC 2 /w Q1Q1 E E \$ per unit QQ1Q1 MC AC MC AC Profit maximization yields: MRP L = w MRP K = r With 2 inputs,  L/  w = [  L/  w]  Q +  L/  w (from  Q) [  L/  w]  Q < 0  L/  w (from  Q) = (  L/  q) (  Q/  P) (  P/  MC) (  MC/  w) (+/-) (-) (1) (+/-) Thus,  L/  w (from  Q) < 0 expansion path’ expansion path Q2

Labor Demand Elasticities Context of Minimum wage debate –Labor Demand theory tells us to expect job losses if we increase the minimum wage –1995 book Myth and Measurement (Card & Krueger) concluded that “the predicted job losses associated with increases in the minimum wage simply could not be observed to occur, at least with any regularity.” –Debate over usefulness of Labor demand theory vs. accuracy of the studies cited in Myth and Measurement There’s general consensus that we’d see significant job losses for big changes in the min wage However, for small changes (such as those we have in the US), it is an empirical question.

Labor Demand Elasticities Labor demand elasticities will help us look at this debate. How much does employment respond to changes in wages? Definition, analysis, measurement, applications Own-wage elasticity of labor demand is defined as the percentage change in employment (E) caused by a 1 percent change in the wage rate (w)  ii = %  E i / %  w i It applies to any category of labor Since labor demand curve slopes downward,  ii < 0 We want to know it’s magnitude. Why do we use concept of elasticity rather than slope?

Own-Wage Elasticity of Demand  w  E Labor demand is: 1% > 1% elastic 1% < 1% inelastic 1% 1% unit-elastic Labor demand is: Total Income & w elastic move opposite ways inelastic move same direction unit-elastic Tot Inc unchanged Total Income here is defined as wage * employment level (w*E) elasticinelasticunit-elastic 0 --

Relative Demand Elasticities Flatter D-curve is more elastic Compare the change in Employment for the same change in Wage D 3 is perfectly inelastic D-curve  ii = 0 D 4 is perfectly elastic D-curve  ii = -  Employment Wage D1D1 D2D2 w w’ Employment Wage D3D3 w D4D4

Linear Demand Curves Technically, we shouldn’t say that a D-curve is only inelastic or elastic Why? Because D-curves generally have ranges in which they are elastic and ranges in which they’re inelastic We’re interested in the  ii around the wage in the labor market we’re analyzing Compare the % changes in w & E at A (high wage, low empl) to the % changes at Z (low wage, high empl) A linear demand curve, w = a-bE, is unit-elastic at its midpoint. (a,b are constants > 0) (good exercise) Employment Wage Elastic Demand A Z A’ Z’ Inelastic Demand

Minimum Wage Law Minimum wage is a prime example of a price floor. Introduced in 1938 by FLSA Goal was to ensure reasonable compensation for work effort and mitigate prevalence of poverty \$0.25/hour for employees of large, interstate firms –43% non-supervisory workers covered at first –Agriculture and retail sales exempt at first –Today? http://www.dol.gov/

Minimum Wage Law What is the effect on employment of  minimum wage? Theoretically –Reduces employment of low-skilled/low-wage –Helps those who happen to keep their job –If D for low-wage labor is elastic, Total Income would be made smaller if W raised Labor demand is: Total Income & wage elastic move in opposite directions inelastic move same direction unit-elastic Total Income unchanged

Effects of Minimum Wage Empirically 1.Teenage workers are primarily affected (low wages anyway) 10%  W  1-3%  teenage employment 2.Min wage is set nominally & adjusted infrequently Constantly changing incentives for employment Divide the nominal min wage by price level Regional differences in prices  W AK < W MS   E AK <  E MS 3. Min wage does not cover everyone Employees of small retail & service firms not covered Plus, compliance is not 100% –How does this affect the employment response to  W ? Overall loss of jobs is less than  jobs in covered sector

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