Chapter 3
The Demand for Labor
Short Run Labor Demand
• Short run
– short enough period of time that capital is fixed
• Marginal Product of Labor (MPL )
– increase in output (Q) from adding one unit of labor (L), holding
other inputs constant.
• Law of Diminishing Marginal Returns
– Holding other inputs constant, as the amount of a single input
increases, its marginal product will eventually decrease.
• Marginal Revenue (MR)
– increase in total revenue (TR) from producing one more unit of
output.
Short Run Labor Demand
• MR for a firm
– identical to price if firm sells its product in a perfectly
competitive industry.
– MR=P(1-1/e) where e=elasticity of product demand if
firm faces a downward sloping product demand
curve. [e expressed as positive number.]
– If firm sells product in a perfectly competitive industry,
e is infinite and MR=P.
– As a firm increases the sales of its product, MR
generally falls. The steeper the product demand
curve is, the steeper the MR curve.
Short Run Labor Demand
Relationship between product demand and MR
Perfectly competitive product market
Monopolistic product market
D
D=MR
MR
Short Run Labor Demand
• Marginal Revenue Product of Labor (MRPL)
– increase in total revenue from adding one more unit
of labor, ceteris paribus.
– MPL* MR
• MRPL will fall as L increases for 2 reasons:
– MPL decreases as L increases due to Law of
diminishing marginal returns
– MR falls as L (and output) increases unless the firm
is in a competitive product market.
Short Run Labor Demand
• Marginal Expense of Labor (MEL )
 increase in total cost (TC) from adding one
more unit of labor
 DTC / DL
• If a firm is in a competitive labor market,
 MEL=W
• If firm is in a monoposonistic labor market
 MEL>W.
Short Run Labor Demand
Competitive labor market
Market
Firm
W=ME L
W*
units of labor
units of labor
Short Run Labor Demand
Monopsonistic Labor Market
ME
L
Labor supply
units of labor
Short Run Labor Demand
• Profit maximization: L where MRPL = MEL
ME
L
MRP
L*
L
UNITS OF LABOR
Short Run Labor Demand
Assume competitive product and labor markets
• Analyze the effect of an increase in product
demand on
– employment in market, at firm.
– firm profits (change in area between MRPL and MEL)
– labor’s rents (area between W& LS)
• Analyze the effect of an increase in labor supply
on
– employment in market, at firm.
– firm profits
Short Run Labor Demand
• Use short run supply/demand model to
discuss winners/losers from:
– More open immigration laws
– NAFTA/CAFTA
– Increase in minimum wage
Long Run Labor Demand
• In the LR, all inputs can be varied.
• Assume two inputs: L and K.
• In the LR, the profit maximizing condition
 MRPL = MEL
 MRPK = MEK
• If the firms purchase their labor and capital in
competitive markets,
 MEL = W
 MEK = C.
where W=wage rate
C =cost per period of a unit of K.
Long Run Labor Demand
• If the firms sell their products in competitive
product markets,
MRPL=P*MPL
MRPK=P*MPK
• Using these facts, the profit maximizing
conditions can be rewritten as:
P*MPL = W
P*MPK = C
• Which can be rewritten as:
W/MPL = C/MPK = P
Long Run Labor Demand
• Long run effect of an increase in price of capital
on labor.
– substitution effect: for every given level of output, use
more labor and less capital.
– scale effect: an increase in price of capital reduces
product supply, reduces equilibrium quantity
produced, and reduces amount of labor employed.
• L & K are
– gross substitutes if subst effect > scale effect
– gross complements if subst effect < scale effect
Long Run Labor Demand
• When there are more than two inputs, any pair can be classified
as gross substitutes or complements depending on whether
the scale or substitution effect dominates.
Long Run Labor Demand
Other Applications of Labor Demand Models.
• Minimum wages and monopsony.
• Effect of a payroll tax.
– does it matter whether tax is levied on employer or employee?
– how does the elasticity of labor supply affect incidence of tax?
– how does the elasticity of labor demand affect incidence of tax?
• Effects of employment subsidies.
– given to employers.
– given to employees.
• Financing medical payments for black lung disease.
– tax on coal workers' wages (surface versus land)
– tax on coal (unions versus management)