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Chapter 3
The Demand
for Labor
Copyright © 2009 Pearson Education, Inc.
Profit Maximization
Output Approach: Increase output if the
additional revenue > additional cost until
MR=MC
Input Approach: Hire inputs if the additional
revenue > additional cost until
MRP=MEI
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Important Definitions - Marginal Revenue Product
 Derived Demand
 Marginal Product (MP)
 Diminishing Marginal Returns
 Marginal Revenue (MR)
 Marginal Revenue Product (MRP)
 Marginal Expense of an Added Input
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Important Definitions - Marginal Revenue Product
MP = Change in Output/Change in Input
MR = Change in Revenue/Change in Output
MRP = Change in Revenue/Change in Input
MRP = MP x MR (general case)
MRP = MP x P (competitive product market)
MEI = Change in Total Cost/Change in Input
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Short-Run Demand for Labor
Assume:
1. Two inputs, capital and labor
2. Labor is variable and capital is Fixed
3. Both labor and final product markets
are competitive
4. MP of labor is diminishing
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Table 3.1: The Marginal Product of Labor
in a Hypothetical Car Dealership
(capital held Constant)
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Let:
MC = Marginal Cost
MR = Marginal Revenue
MEI = Marginal Expense of the Added Input
L = Labor Units
MP
W = Wage
P = Price of Final Product
MRP = Marginal Revenue Product
The profit maximization criteria in the output market is:
L
In competitive markets, MEI
W and MR
The input market profit maximization condition becomes:
Or
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W=P
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The Short-Run Labor Demand Curve
Based on the SR profit maximization
criteria for hiring inputs, the labor demand
curve for the firm can be represented by
the MP curve or the MRP curve
If the labor and product markets are competitive, hire until:
MRP = MP x P = W (nominal wage)
or
MP = W/P (real wage)
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Figure 3.1: Demand for Labor in the Short
Run (Real Wage)
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Table 3.2: Hypothetical Schedule of
Marginal Revenue Productivity of
Labor for Store Detectives
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Figure 3.2: Demand for Labor in the
Short Run (Money Wages)
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Long-Run Demand for Labor
Characteristics of Isoquants:
1. Although each isoquant represents a unique level of
output,each point on an individual isoquant
represents the same level of output
2. Isoquants have negative slopes
3. Isoquants are convex
4. The slope of an isoquant is called the Marginal Rate
of Technical Substitution
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Figure 3A.1: A Production Function
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The Isoexpenditure Curve
Let: TE = wL + cK
w = wage, L = labor input, c = capital expense, K = capital input
and TE = Total expenditures on inputs
Then: K = TE/c - w/c x L
and the equation for isoexpenditure curve B
is:
K = 1,500/20 - 10/20 x L
= 75 - .5L
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Figure 3A.3: Cost Minimization in
the Production of Q*
(Wage = $10 per Hour;
Price of a Unit of Capital = $20)
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Cost Is Minimized in the Long Run Where:
An isoexpenditure curve is tangent to an isoquant
MRTS = - MPL/MPk = - W/C
or
W/MPL = C/MPC, where
W = wage, MPL = marginal product of labor
C = capital expense, MPC = marginal product of capital
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Important Definitions - Multiple Inputs
 Substitutes in Production
 Complements in Production
 Gross Substitutes
 Gross Complements
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Figure 3.3: Effect of Increase in the Price of
One Input (k) on Demand for Another Input (j),
where Inputs Are Substitutes in Production
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When Product Markets Are Not Competitive,
The Profit Maximization Condition Becomes :
MRP = MP x MR = W
Because MR < P, the labor demand curve of
a price maker in the product market lies to the
left of the labor demand curve of a price taker
in the product market.
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Figure 3.4: The Market Demand Curve
and Effects of an Employer-Financed
Payroll Tax
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Figure 3.5: Payroll Tax with a
Vertical Supply Curve
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