Chapter 4: Demand for Labor in Short Run

• Demand for labor: level of employment (L) desired by business firms.

• Topics: – Factors that determine a firm’s optimal

level of employment;

– How this optimal level responds to changes in wages, cost of capital, firm’s sales, and technology changes.

• Short run (SR): time period when capital (K) is fixed.

• Long Run: all inputs variable.

Pattern of Employment Over Time

• See Figure 4.1.• Level of employment reflects

demand for labor.• Three important features:• 1) Huge # jobs:

– 1950: 60 million; – 2001: 156 million.

• 2) composition of jobs: Agriculture; – big growth service and government

(now 80% of jobs).

• 3) cyclical variation in # jobs.– 10 recessions between 1950 and 2002.

Marginal Productivity Theory of Demand

• Simplifying assumptions:• 1) firm’s goal is to maximize

$ profits• 2) Two factors of production

(K and L).• 3) Both input and output

markets are perfectly competitive, or PC (wages and prices treated as fixed).

• 4) Wages are only cost of labor and labor is homogeneous.

Firm’s Hiring Decision in the Short Run (SR)

• Now K fixed; only L variable.

• Rule: Hire another worker as long as the worker adds at least $1 to profits.

• Or: hire another worker as long as the cost of that worker (his wage) is less than or equal to the value of that worker’s extra output.

New Terms

• Production Function: shows how inputs can be combined to produce output, given a specific state of technology.

• Q = F(K, L) – Q = output – K = capital – L = labor

• SR: Firm can only Q by L.• TP = total product = Q• TPL = TP at each amount of L (with

K fixed).

More Terms

• Marginal product of labor:

• MPL = Q/L.

• Average product of labor:

• APL = Q/L.

• Total revenue = TR = P * Q.• Marginal revenue = MR = TR/Q;

where MR = P. See each unit of Q sold at same market price.

• Marginal revenue product of labor: MRPL = MPL * MR.

• Marginal cost of labor: MCL = wage.

Firm’s Equilibrium Level of Employment

• Rule: keep hiring one more worker until worker’s marginal benefit (value of extra output) equals that worker’s marginal cost (wage).

• General Rule:

• W = MR * MPL = MRPL

• With PC assumption: P = MR.

• So: W = P * MPL or W/P = MPL

• See Table 4.1 and Figure 4.2.

To Note About Figure 4.2

• MPL = slope of tangent line at specific amount of L.

• APL = slope of line from origin to the point on the TP associated with specific amount of L.

• Relate shape of TPL to MPL: as long as TPL getting steeper, MPL is going up. (Relate point A to point L1)

• Note that MPL hits APL from above, at max point of APL

• Law of Diminishing Returns: With K fixed: at some point, MPL declines ( L will Q at decreasing rate).

Back to Table 4.1

• Impose the optimal hiring rule:• 5th worker:

– MRPL = 60 but W = only 40 yes hire 5th worker.

• 6th worker: – MRPL = 40 and W = 40 yes hire 6th

worker.

• 7th worker: – MRPL = 8 but W = 40 NO hire the 7th

worker.

• So it is optimal to hire 6 workers.

Firm’s SR Demand Curve for Labor

• Shows relationship between wage rate and firm’s desired employment level holding all other relevant factors (including other inputs) fixed (like K).

• Firm’s SR demand curve for labor IS the downward portion of the MRPL curve.

• Ignore upward sloped portion because at any price or wage, firm will hire as much labor as possible.

Demand for Labor Curve

• Two points to Stress:

• 1) A change in the wage causes movement along a given DL curve.

• 2) A change in a ceteris paribus factor (e.g., capital price or utilization, product demand) will cause a shift in the entire DL curve.

Effect of Product Demand on DL

• Key: product demand is D curve in output market; remember S and D curves for output, with intersection yielding P*.

• With product demand, this is shift to right of D curve, causing P* to go up.

• Back to firm:– MRPL = MR * MPL where

P=MR. – So P MRPL (shift to right)

Imperfect Competition in Product Market

• Key: with perfect competition, price always equals MR (and both same for any Q). Like saying that firm faces horizontal D curve and can sell at it wants to at P*.

• If product market is not competitive: firm faces downward sloping product demand curve, so if Q, P.

• So, MR P and more steep.• So this DL curve:

– 1) lies to left of original DL.

– 2) it is steeper.

Example

• Key: With imperfect competition: firm faces downward sloped product demand curve, so to Q, must P.

• Q = 10 when P = $10• So TR = P*Q = 10 * 10 = $100• Now Q = 12 and P = $9, so• TR = 12 * 9 = $108.• MR = TR/Q = 8/2 = 4.• MR = 4 but P = 9.

Derivation of Market DL Curve

• Start by defining market (e.g., by geographical area or by industry).

• Two factors: – 1) Total market DL curve is sum

of each individual firm’s DL curve.

– 2) If all firms experience a W so their DL, this makes market S curve for output shift right, pushing down market P; so MRPL for each firm must be redrawn.

Effect of Wage

• 1) If wage change only affects one firm, causing movement along given DL curve.

• 2) If wage change affects every firm in the industry, then it will also affect market price and so each firm will have entirely new DL curve (because this curve is the MRPL curve, which equals P * MPL under p.c.).

Criticisms of Standard DL Theory

• Starting Point: The theory does yield fairly good predictions of firm’s optimal level of employment and how optimal level will in response to economic events.

• Five Criticisms of DL Theory– 1. Limits to human cognition:

requires too much knowledge and rejected by firm case studies.

– 2. Non-maximizing behavior (ownership vs management)

Continue with Criticisms

– 3) Fixed K/L proportions– 4) Increasing returns to L

(perhaps MPL varies across business cycle).

– 5) Interdependence between wage and worker productivity.

– Overall: real world data support basic features of standard model.

Exercise

• Textbook pg. 216, #1: Use the marginal productivity theory of LD to predict the impact on the firm’s employment level of the following events (explain; graph).– A) in wage rate.– B) demand for firm’s product.– C) lower tariff on imported goods– D) conversion of firm from

perfectly competitive firm to non-competitive firm.

Elasticity of DL

• Elasticity of DL measures responsiveness of labor demand to changes in the wage rate.

• ED = %L / %W 0• Note:

%L = L/L %W = W/W

• ED = (L/L) / (W/W) • = (L/W) * W/L• ED = (1/ slope of DL) * W/L

Five Cases of ED

• 1) ED = 0: W causes no L

– Perfectly inelastic – vertical demand curve

• 2) ED 1: %W %L

– DL not very responsive to wage.

– Inelastic

– Steep DL curve

• 3) ED = 1: %W = %L

– Unit Elastic

More Cases of ED

• 4) ED 1– DL very responsive to wage es– %L %W – Elastic – Relatively flat DL curve

• 5) ED = - • Firm willing to hire any # workers at

prevailing market wage but none at any higher wage. – Perfectly elastic – Horizontal (flat) DL curve

• See Figure 4.6.

Elasticity Along a Single DL Curve

• One relatively flat DL curve is relatively more elastic than a steeper curve, but for all straight line DL curves, there is an elastic portion and an inelastic portion.

• Recall 2nd part of ED is W/L.

• As move down DL curve to right, W while L, so W/L and so ED is too. – Starts elastic and becomes inelastic.

• See Figure 4.7.

Relationship Between ED and Total Expenditures

on Labor• Total expenditures on labor is called

the firm’s wage bill.• Wage bill = W * L.• Question: When have W, how will

wage bill ?• Answer: Compare %W to %L

(W always L; issue is by how much?)

• 1) Inelastic: %W %L– So W leads to wage bill.

• 2) Elastic: %W %L– So W leads to wage bill.

Example

• Example 1:• Wage from $8 to $7 • % Wage change = -12.5%• Employment from 20 to 30• % Employment change = 50%• ED = 50 /-12.5 = - 4

– Very elastic or responsive

• Example 2• Wage 50% and L 12.5%• ED = 12.5 / 50 = 0.25

– Inelastic (not very responsive)

What Determines ED?

• Ease of substitutability:– 1) Between K and L– 2) Between this good and other

goods.

• Evidence from data:– 1) data show DL curve slopes

down.– 2) DL curve relatively inelastic.– 3) ED is greater for unskilled and

blue-collar workers than skilled and white-collar workers (due to greater subst K/L for former).

Relationship Between DL and Product Demand

• * DL is a derived demand.

• 1) DL over business cycle hrs or # workers?

• 2) DL and consumer expenditure patterns (relates to es in preferences and es in income)

• 3) Impact of imports on domestic employment (key: substitutes versus complement goods).– NAFTA: North American Free Trade

Agreement: winners versus losers.

Squeeze on Middle Class Jobs

• Trend in 1980s and 1990s: net job loss in mid-level jobs.– Banking: middle management– Manufacturing: high wage union

jobs.

Wage Subsidy Programs

• Designed to encourage employers to hire the hard-core (longterm) unemployed.

• The subsidy will cost to firm of hiring this type of worker (makes them relatively less expensive).

• Standard program design:– 1. Categorical eligibility– 2. Only covers new hires– 3. Covers workers with w wt

– 4. Subsidy is some % of difference between actual w and wt;

– Subsidy = r(wt – wa)– 5. Subsidy usually temporary.

Effects of Subsidy Program

• Good effects: – 1) employment of target group; – 2) gives largest subsidy to hardest to

employ (since their wages are lowest);– 3) as hard-to-employ take jobs and

gain experience, their wages rise so subsidy cost falls.

• Bad effects: – 1) employer might replace some

current workers with new (covered) workers;

– 2) employer might keep subsidized worker for the temporary period then layoff and hire NEW covered worker.

– 3) subsidy eligibility can be a stigma.

Union Wage Concessions

• Issue: Why unions might accept wage cuts? To preserve employment!

• Labor demand theory suggests: union wage concessions most likely to occur in industries that face a relatively elastic DL and are experiencing falling output so shifts leftward in DL.

• Data support this theoretical implication.

Exercise: ED

• Start: W = $10 and L = 80.

• Now: W = $20 and L = 60.

• 1. Calculate ED.

• 2. Calculate original and new total wage bill.

• 3. Relate the change in total wage bill to the calculated ED