![Page 1: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/1.jpg)
Economics 324: Labor Economics
1. Any questions?
![Page 2: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/2.jpg)
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.)
![Page 3: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/3.jpg)
Marginal Product and Average Product• Marginal Product of Labor (MPL) is the change in output
resulting from hiring one more worker/hour, ceteris paribus
• MPL = (Q/ L ) > 0 [ implies ceteris paribus]
• MPK = (Q/ K ) > 0
• Employment Output (Total Product) MPL APL MRPL
0 0
1 11
2 27
3 47
4 66
5 83
6 98
7 111
8 122
9 131
![Page 4: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/4.jpg)
Total, Marginal, and Average
• Average Product of Labor (APL) is the output per worker.
• APL = 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?
![Page 5: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/5.jpg)
Short-run Employment DecisionHow many workers should the firm hire?
A competitive firm can hire all the workers they want at going wage.Hire so that MRPL = MCL
For a competitive firm, this is MRPL = WNB: This does not say “the firm should set W equal to MRPL”
A competitive firm takes their W as given or pre-determined.It does say “A competitive firm should hire until MRPL = W”
Additional conditions for short-run employment decision1. MRPL = W2. The MRPL curve must be downward-sloping at the optimal # workers3. W must be < ARPL (P*APL), 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 ARPL curve (after the intersection of MRPL & ARPL).
![Page 6: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/6.jpg)
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: Competition Monopsony
Competition P * MPL = w P * MPL = MCL
Monopoly MR * MPL = w MR * MPL = MCL
![Page 7: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/7.jpg)
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
![Page 8: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/8.jpg)
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 * MPL
• Gain in output from X to Y = K * MPK
• Same isoquant L * MPL + K * MPK =0
• A little algebra yields the slope:
K/ L = - MPL/ MPK
• 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
LQ = 500
Y
X
![Page 9: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/9.jpg)
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
MPL/MPK = w/r
K
LaborTC/w
TC/r
ZB
A
Q = 100 widgets
![Page 10: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/10.jpg)
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
XY
Q=100Q=200
Z
![Page 11: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/11.jpg)
Long-run Employment Decision• Capital stock, K, is not fixed.
• Must choose both K and Labor.
• Lagrangian derivation
• For Labor we have derived: MRPL = MCL
• Same for capital: MRPK = MCK
w/MPL = r / MPK
• 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, MPL / w = MPK / r
![Page 12: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/12.jpg)
Firm’s Demand for Inputs• Initially at point E
Labor
Capital (K)
TC1/r
TC1/r’
TC2/r’
TC1/w TC2/w
Q1
E
E
$ per unit
QQ1
MC
AC
MCAC
• Shock: Pcapital ( r)
• Slope of the dashed isocost line is flatter, but SAME Total Cost (TC1)
• TC2 is new least-cost way to produce Q1 units of output
• Movement E to E is the Input Substitution Effect; Capital is now more expensive use less K, more L
• This higher TC2 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 pathw,r´
expansion path w,r
Q2<
E
• E to E is the Scale Effect
MC higher MC > MR lower Q
MR
Q2
![Page 13: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/13.jpg)
Firms’ Demand for Inputs• Initially at point E
Labor
Capital (K)
TC1/r
TC1/r’
TC2/r’
TC1/w TC2/w
Q1
E
E
$ per unit
QQ1
MC
AC
MCAC
• Profit maximization yields:
MRPL = w
MRPK = 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<
E
P
Q2
![Page 14: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/14.jpg)
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.
![Page 15: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/15.jpg)
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 = %Ei / %wi
• 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?
![Page 16: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/16.jpg)
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)
-1•
elastic inelasticunit-elastic
0-
![Page 17: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/17.jpg)
Relative Demand Elasticities
• Flatter D-curve is more elastic
• Compare the change in Employment for the same change in Wage
• D3 is perfectly inelastic D-curve
ii = 0
• D4 is perfectly elastic D-curve
ii = -
Employment
Wage
D1D2
ww’
Employment
Wage
D3
wD4
![Page 18: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/18.jpg)
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 DemandA
Z
A’
Z’
Inelastic Demand
![Page 19: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/19.jpg)
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/
![Page 20: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/20.jpg)
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
![Page 21: 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](https://reader036.vdocuments.net/reader036/viewer/2022062515/56649cbb5503460f94983974/html5/thumbnails/21.jpg)
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 levelRegional differences in prices WAK < WMS EAK <EMS
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