LIR 809

DEMAND FOR LABOR Overview Short-run Demand for

Labor Long-run Demand for

Labor

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OVERVIEW:

Question of interest:How do firms decide how many

people to hire and what to pay them?

Demand for labor is Derived Primary role of firm is to produce

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DEMAND FOR LABOR DEPENDS ON 3 FACTORS

COMPOSITION OF OUTPUTWhat do we Make?

TECHNOLOGY (or Production Process)How do we Make it?

LEVEL OF OUTPUTHow Much do we Make?

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Firms Have to take 3 Markets into Account

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PRODUCTION FUNCTION(Formal version of how, what, how much)

Q = F(x1,x2,...L,K) or

Q = G(x1,x2,...L1,.L2, K1,.K2)Where: Q is quantity of output

• x1,x2 are intermediate inputs or raw materials

• L is labor• K is capital

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EXAMPLE: PRODUCING A SUMMER DINNER PARTY

BASE CASE: SALAD FOR 4 Intermediate inputs:

1 head of lettuce, 2 tomatoes, 1 onion, stuff for 1/2 cu. mayonnaise

Capital: Cutting Board,

knife, bowl, wire whisk

Labor: 1 Person hour

NEW LEVEL OF OUTPUT: SALAD FOR 24 Intermediate inputs:

6 heads of lettuce, 12 tomatoes, 2 onions, stuff for 1 1/2 cu. mayonnaise

Capital: Cutting Board,

knife, bowl, wire whisk

Labor: 4 person hours

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EXAMPLE, CONT.

CHANGE IN TECHNOLOGY: SALAD FOR 24 Intermediate

inputs: 6 heads of lettuce,

12 tomatoes, 2 onions, stuff to make 1 1/2 cu. mayonnaise

Capital: 1 Cuisinart Labor: 1 person

hour

CHANGE IN COMPOSITION OF OUTPUT: PIG ROAST FOR 24 Intermediate

inputs: 1 pig, firewood, 1

apple Capital: Shovel,

spit Labor: 6 person

hours

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ASSUMPTIONS OF SIMPLE MODEL OF LABOR DEMAND

1. Employers want to maximize Profits

2. Two factors of production: Capital & Labor: Q = f(L,K)

3. Labor is homogeneous4. Hourly wage only cost of labor5. Both labor market and product

market are competitive.

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II. SHORT-RUN DEMAND FOR LABOR

Major Distinction between long and short run. In short run:Firm can only vary labor to

change outputTechnology is fixed Product price does not change

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THE FIRM’S PROBLEM:HOW MANY WORKERS TO HIRE?

Firm’s Problem: Needs labor to produce output & needs decision rule to determine how much labor to use

Answer based on Marginal Productivity Theory of Labor:Answer: Hire additional workers as

long as each one adds to firm’s profits

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SOME DEFINITIONS

MARGINAL PRODUCT OF LABOR (MPL) Additional output produced with one additional unit of

labor MARGINAL REVENUE (MR)

Additional revenue generated by selling one additional unit (= product price in competitive economy)

MARGINAL REVENUE PRODUCT OF LABOR (MRPL) Extra revenue generated by selling one additional unit

that can be attributed to labor MRPL = (MPL) * MR

MARGINAL COST OF LABOR Cost of hiring 1 additional unit of labor (=wage in

competitive economy)

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DEMAND FOR LABOR: FIRMS LOOKING FOR A ‘STOPPING RULE’

MARGINAL PRODUCT CURVEVisual representation of the effect on

output of adding 1 more workerMPL is positive as long as output

increases with additional labor WHY OUTPUT BEGINS TO DECLINE: LAW

OF DIMINISHING RETURNS Increases in output begin to decline

with increases in 1 input with other inputs constant

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DECISION RULE FOR EMPLOYMENT LEVEL

Recall: Firms maximize profits Firms hired up to point where

MRP from hiring last worker = marginal cost of that worker

If MRPL > MCL, increase employmentIf MRPL < MCL, decrease employmentIf MRPL = MCL, do not change

employment

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Marginal Product Curve

Labor

Marginal

Product

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Relationship between Marginal and Total

Product

Labor

Product

Marginal

Total

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DETERMINING HOW MANY TO HIRE

64222966623275682424461226203616281426122661000000MCMRPMRMPQty.Labo

r

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Demand Curve

Labor

Marginal

Product

Demand curve starts here

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Demand Curve

Labor

Marginal

Product

Demand curve starts here

Market wage rate

Stop hiring here

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WHAT THIS SAYS ABOUT WAGES

EFFICIENT POINT:MCL = MRPL orMCL = MR * MPL

In competitive economy, MCL = W and MR = P, so:W = MPL * P orW/P = MPL

Real wage must = marginal productivity

Digression: Nominal versus Real Wages

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DEMAND FOR LABOR CURVE: MOVEMENT ALONG VS. SHIFTING

Movement along demand curve: If wage rate changes, employment

changesNegative slope: if wages increase, demand

drops & vice versa. Shifting the demand curve

If MRPL changes, demand curve will shiftIf demand for firm’s product increases,

product price will increase, increasing MRPL

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LONG-RUN DEMAND FOR LABOR BY FIRMS

I. OverviewII. Theory: Demand

response to wage changes

III. Elasticity: Measuring demand response

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I. Overview: LONG-RUN DEMAND

Firms still looking for decision ruleHow much labor AND how much capital?

Firms: profit maximizers In long-run, firms can vary capital

and labor Production function:

Combination of capital and labor firm can use to produce some level of output

2 inputs: Capital and Labor

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Production Function Shows possible combinations of labor &

capital used to produce output Marginal Rate of Technical Substitution

Slope of the Production functionShows relative productivities of 2 inputs:

Technological relationshipMRTS = MPL/MPK

Family of isoquants:Each level of output, different curveGreater output level, further curve is from

originFirm wants to be on highest curve

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Production Function

Labor

Capital

Q0

Q1

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Constraints on Production Marginal costs = W for labor, C for

capital Isoexpenditure line (or cost constraint)

shows trade-off between these two costs given firm’s resources

Shows how many units of capital firm can buy if gives up one unit of labor, and

Shows how many units of labor firm can buy if gives up one unit of capital

Slope shows relative prices of K & L

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Cost Constraint

Labor

Capital

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FIRM’S PROBLEM To find the best, most efficient

combination of capital and labor Use modified version of old

decision rule (MR=MC):Now want relative costs =

relative productivitiesWant MCL/MCK = MPL/MPK (= W/C)

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Most Efficient (Profit Maximizing) Point

Labor

Capital

Q0

Most Efficient Combination of Capital & Labor

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II. Theory: EFFECT OF PRICE CHANGE ON DEMAND FOR

LABOR

Two Simultaneous Effects:Substitution Effect

Reaction to fact that relative prices have changed

Scale (output) EffectReaction to change in total cost of

production We only observe the net effect

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SUBSTITUTION EFFECT

Response to change in Relative Price of Capital and Labor

When price of 1 input goes up, firm will substitute away from the relatively more expensive input.

Example: Price of equipment decreases, firm will try to use more inexpensive equipment and less labor

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SCALE (OUTPUT) EFFECT Response to change in Total Cost of

production Price in one input increases -->

--> Increase in total production cost--> Increase in product price--> Decreases demand for product--> Decreases output--> Decreases demand for labor &

capital

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NET EFFECT OF RELATIONSHIP BETWEEN TWO INPUTS

Increase Wages and:1) Demand for Capital will increase

(substitution effect)2) Output will be reduced decreasing

demand for both capital & labor In Practical terms:

Substitution effect result of change in technology

Scale effect result of change in outputNet effect – what we observe

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ELASTICITY Definition:

% Change Quantity/% Change in Price Measure of Responsiveness Quantifiable (i.e., tells us magnitude) Empirically determined Two types:

Own-PriceCross-Price

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Own-Price Elasticity Definition:

% Change Quantity/% Change in Own Price Is negative though expressed as

absolute value The larger the absolute value, the

more employment will decline with a wage increase

Measure of Economic Power: The more inelastic the demand for labor, the more powerful the workforce.

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CROSS-PRICE ELASTICITIES

Definition:% Change in Quantity i/% Change Price j

Two Directions:Gross Substitutes: If cross-elasticity is +Gross Complements; If cross-elasticity is -

Determinants:Production Technology (Substitution effect)Demand Conditions (Output effect)

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HICKS-MARSHALL LAWS OF DERIVED DEMAND

Own-price elasticity of demand is high when:

1) Price Elasticity of product demand is highLogic: If consumer demand for a

product responds to price changes (i.e., product demand is elastic), firms will not be able to pass higher labor costs to consumers without a fall in product demand.

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HICKS-MARSHALL LAWS OF DERIVED DEMAND, cont.

2) Other factors of production can be easily substituted for laborLogic:If producers can easily substitute

another type of input (i.e., high elasticity of substitution between inputs), they will (technology)

3) When supply of other factors is highly elasticLogic: If producer can attract large #

substitute inputs with slight price increase, will shift inputs (Input market)

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HICKS-MARSHALL LAWS OF DERIVED DEMAND, cont.

4) When the cost of employing labor is a large share of total costs of productionLogic: An increase in cost for a

small group of inputs will have a smaller effect on product price