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DEMAND FOR LABOR
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LIR 809
Overview
Short-run Demand for Labor
Long-run Demand for Labor
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
LIR 809
DEMAND FOR LABOR DEPENDS ON 3
FACTORS
COMPOSITION OF OUTPUT
What do we Make?
TECHNOLOGY (or Production
Process)
How do we Make it?
 LEVEL OF OUTPUT
How Much do we Make?
LIR 809
Firms Have to take 3 Markets into Account
LIR 809
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
LIR 809
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
LIR 809
 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
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
LIR 809
 CHANGE IN
COMPOSITION OF
OUTPUT: PIG ROAST FOR
24
 Intermediate inputs:
 1 pig, firewood, 1
apple
 Capital: Shovel, spit
 Labor: 6 person hours
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 homogeneous
4. Hourly wage only cost of labor
5. Both labor market and product
market are competitive.
LIR 809
II. SHORT-RUN DEMAND FOR
LABOR
Major Distinction between long and
short run. In short run:
Firm can only vary labor to change
output
Technology is fixed
 Product price does not change
LIR 809
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
LIR 809
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
LIR 809
 Cost of hiring 1 additional unit of labor (=wage in
competitive economy)
DEMAND FOR LABOR: FIRMS
LOOKING FOR A ‘STOPPING RULE’
 MARGINAL PRODUCT CURVE
 Visual representation of the effect on output
of adding 1 more worker
 MPL 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
LIR 809
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 employment
If MRPL < MCL, decrease employment
If MRPL = MCL, do not change
employment
LIR 809
Marginal Product Curve
Marginal
Product
Labor
LIR 809
Relationship between
Marginal and Total Product
Marginal
Product
Total
Labor
LIR 809
DETERMINING HOW MANY
TO HIRE
Labor
0
1
2
3
4
5
6
LIR 809
Qty.
0
6
14
20
24
27
29
MP
0
6
8
6
4
3
2
MR
0
2
2
2
2
2
2
MRP
0
12
16
12
8
6
4
MC
0
6
6
6
6
6
6
Demand Curve
Demand curve
starts here
Marginal
Product
Labor
LIR 809
Demand Curve
Demand curve
starts here
Marginal
Product
Market wage
rate
Stop hiring
here
Labor
LIR 809
WHAT THIS SAYS ABOUT WAGES
 EFFICIENT POINT:
 MCL = MRPL
or
 MCL = MR * MPL
 In competitive economy, MCL = W and
MR = P, so:
 W = MPL * P or
 W/P = MPL
 Real wage must = marginal productivity
Digression: Nominal versus Real Wages
LIR 809
DEMAND FOR LABOR CURVE:
MOVEMENT ALONG VS. SHIFTING
 Movement along demand curve:
 If wage rate changes, employment changes
 Negative slope: if wages increase, demand drops &
vice versa.
 Shifting the demand curve
 If MRPL changes, demand curve will shift
 If demand for firm’s product increases, product
price will increase, increasing MRPL
LIR 809
LONG-RUN DEMAND FOR
LABOR BY FIRMS
I. Overview
II. Theory: Demand response
to wage changes
III.Elasticity: Measuring
demand response
LIR 809
I. Overview: LONG-RUN
DEMAND
 Firms still looking for decision rule
 How 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
LIR 809
Production Function
 Shows possible combinations of labor &
capital used to produce output
 Marginal Rate of Technical Substitution
 Slope of the Production function
 Shows relative productivities of 2 inputs:
Technological relationship
 MRTS = MPL/MPK
 Family of isoquants:
 Each level of output, different curve
 Greater output level, further curve is from
origin
 Firm wants to be on highest curve
LIR 809
Production Function
Capital
Q1
Q0
LIR 809
Labor
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
LIR 809
Cost Constraint
Capital
LIR 809
Labor
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
productivities
Want MCL/MCK = MPL/MPK (= W/C)
LIR 809
Most Efficient (Profit
Maximizing) Point
Capital
Most Efficient Combination of Capital & Labor
Q0
Labor
LIR 809
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) Effect
Reaction to change in total cost of
production
We only observe the net effect
LIR 809
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
LIR 809
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
LIR 809
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 output
 Net effect – what we observe
LIR 809
ELASTICITY
 Definition:
 % Change Quantity/% Change in Price
 Measure of Responsiveness
 Quantifiable (i.e., tells us magnitude)
 Empirically determined
 Two types:
 Own-Price
 Cross-Price
LIR 809
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.
LIR 809
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)
LIR 809
HICKS-MARSHALL LAWS
OF DERIVED DEMAND
Own-price elasticity of demand is high when:
1) Price Elasticity of product demand is high
 Logic: 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.
LIR 809
HICKS-MARSHALL LAWS OF
DERIVED DEMAND, cont.
2) Other factors of production can be easily
substituted for labor
 Logic: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
elastic
 Logic: If producer can attract large #
substitute inputs with slight price increase,
will shift inputs (Input market)
LIR 809
HICKS-MARSHALL LAWS OF
DERIVED DEMAND, cont.
4) When the cost of employing labor is
a large share of total costs of
production
Logic: An increase in cost for a small
group of inputs will have a smaller
effect on product price
LIR 809