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 (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

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?

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).

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

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 * 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

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

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

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

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

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

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 = %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?

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-

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

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

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 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