Download A Simple Model of Labor Demand

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Lecture 4: The Demand for Labor
The demand for labor is a derived demand. Employer’s demand for
labor is a function of the characteristics of demand in the product market.
It is also a function of the characteristics of the production process.
 Two important features of the demand for labor:
1. It can be shown theoretically and empirically that labor demand curves
slope downward.
2. The quantity of labor demanded has varying degrees of responsiveness
to changes in the wage.
 When the demand for labor is analyzed, two sets of distinctions are
made:
1. Demand by firm v.s. the demand curves for an entire market.
Note: Firm and market labor demand curves have different properties
although both slope downward.
2. The time period for which the demand curve is drawn.
Short Run: A period over which a firm’s capital stock is fixed.
Long Run: A period over which a firm is free to vary all factors of
production.
A Simple Model of Labor Demand
Assumptions:
(1) Employers seek to maximize profit.
(2) Firms employ two homogeneous factors of production,
employee-hours (E) and capital (K), in their production of goods and
services. Their production function can be written as:
Q = f(E, K)
(3) Hourly wage cost is the only cost of labor.
Note: We ignore hiring, training cost and fringe-benefit costs for the time
being.
(4) Both a firm’s labor market and its product market are competitive.
1. Short-Run Demand for Labor by Firms
Defn. Marginal Product of Labor: The change in output resulting from
hiring an additional worker, holding constant the quantities of all other
input.
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Defn. Law of Diminishing Returns: Eventually each additional increment
of labor produces progressively smaller increments of output.
Defn. Value of the Marginal Product (VMP): The dollar values of the
additional output produced by an additional worker.
VMP = P * MPE
 The profits are maximized by the competitive firm when the value of
marginal product of labor is just equal to its marginal cost.
 Profit-Maximizing condition: Labor should be hired until its marginal
product equals the real wage. i.e., MPE = W/P
The firm’s demand for labor in the short run is equivalent to the
downward-sloping segment of its marginal product of labor schedule.
Note: The downward-sloping nature of the short-run labor demand curve
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is based on an assumption that MPE declines as employment is
increased.
 Elasticity of Labor Demand
We measure the responsiveness of labor demand to changes in the
wage rate by using an elasticity. The short-run elasticity of labor demand,
SR, is defined as the percentage change in short-run employment
resulting from a 1 percent change in the wage:
SR = (%△ESR)/ (%△w)
Since the labor demand curves slope downward, an increase in the
wage rate will cause employment to decrease; the (own-wage) elasticity
of demand is a negative number.
Note:
|SR| >1: a 1% increase in wage will lead to an employment
decline of greater than 1% → elastic demand curve
|SR| < 1: a 1% increase in wage will lead to a proportionately
smaller decline in employment → inelastic demand curve
Elastic demand: aggregate earnings↓ when w↑
Inelastic demand: aggregate earnings↑ when w↑
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2. Market Demand Curve
A market demand curve is just the summation of the labor demanded
by all firms in a particular labor market at each level of the real wage.
Note: When aggregating labor demand to the market level, product price
can no longer be taken as given, and the aggregation is no longer a simple
summation. However, the market demand curves drawn against money
wages, like those drawn as functions of real wages, slope downward.
3. Long-Run Demand for Labor by Firms
In the long run, employers are free to vary their capital stock as well as
the number of workers they employ.
 Profit Maximization’s Dual Problem – Cost Minization
Defn. Isoquant: An isoquant describes the possible combination of labor
and capital which produce the same level of output.
Defn. The Marginal Rate of Technical Substitution: The slope of an
isoquant is the negative of the ratio of marginal products. The absolute
value of the slope of an isoquant is called the marginal rate of technical
substitution.
Defn. Isocost: The isocost line gives the menu of different combinations
of labor and capital which are equally costly.
A profit-maximizing firm that is producing q0 units of ouptut wants
to produce these units at the lowest possible cost.
→The firm chooses the combination of labor and capital where the
isocost is tangent to the isoquant. i.e.,
MPE/MPK = w/r
→ Cost-minimization requires that the marginal rate of technical
substitution equal the ratio of prices.
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Note: To be minimizing cost, the cost of producing an extra unit of output
by adding only labor must equal the cost of producing that extra unit by
employment only additional capital. i.e.,
MPE / w = MPK /r
 The Effect of Change in w
Increase in w:
(1) Substitution Effect
As w increase, labor cost rises, and more capital and less labor are
used in the production process.
(2) Scale effect
The new-profit-maximizing level of production will be less. How
much less cannot be determined unless we know something about the
product demand curve.
Both the substitution effect and the scale effect work in the same
direction. So these effects lead us to assert that the long-run demand
curve for labor slopes downward.
Note: In general, if a firm is seeking to minimize costs, in the long run it
should employ all inputs up until the point that the marginal cost of
producing a unit of output is the same regardless of which input is used.
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Defn. The Elasticity of Substitution: The elasticity of substitution gives
the percentage change in the capital/labor ratio resulting from a 1 percent
change in the relative price of labor.
The size of the substitution effect directly depends on the magnitude of
the elasticity of substitution.
4. Marshall’s Rules of Derived Demand (The Hicks-Marshall Law of
Derived Demand)
The factors that influence own-wage elasticity can be summarized
by the four “Hicks-Marshall Laws of Derived Demand.” These laws
assert that, other things equal, the own-wage elasticity of demand for a
category of labor is high under the following conditions:
(1) When the price elasticity of demand for the product being produced
high;
(2) When other factors of production can be easily substituted for the
category of labor;
(3) When the supply of other factors of production is highly elastic;
(4) When the cost of employing the category of labor is a large share of
the total cost of production.
Note: (1), (2) and (3) can be shown to always hold. There are conditions,
however, under which the final law does not hold.
(1) Demand for the Final Product
The greater the price elasticity of demand for the final product, the
larger will be the decline in output associated with a given increase in
price and the greater the decrease in output, the greater the loss in
employment (other things equal). Thus the greater the elasticity of
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demand for the product, the greater the elasticity of demand for labor
will be.
(2) Substitutability of Other Factors
Other things equal, the easier it is to substitute other factors in
production, the higher the wage elasticity of demand will be.
Note: a. Sometimes collectively bargained or legislated restrictions
make the demand for labor less elastic by reducing substitutability
(not technically).
b. Substitution possibility that are not feasible in the short run may
well become feasible over longer periods of time, when employers are
free to vary their capital stock. → The demand for labor is more
elastic in the longer run than in the short run.
(3) The supply of Other Factors
As the wage rate increased and employers attempted to substitute
other factors of production for labor, the prices of these inputs were bid
up substantially. Such a price increase would dampen firm’s appetites for
capital and thus limit the substitution of capital for labor.
Note: Prices of other inputs are less likely to be bid up in the long run
than in the short run. → Demand for labor will be more elastic in the
long run.
(4) The Share of Labor in Total Costs
The greater the category’s share in total costs, the higher the wage
elasticity of demand will tend to be. If the share of labor cost is large, cost
increase due to wage increase is larger. The employer would have to
increase their product prices by more, output and hence employment
would fall more.
Note: This law, relating a smaller labor share with a less-elastic demand
curve, holds only when it is easier for customers to substitute among final
products than it is for employers to substitute capital for labor.
5. The Cross-Wage Elasticity of Demand
The elasticity of demand for input j with respect to the price of input
k is the percentage change in the demand for input j induced by 1 percent
change in the price of input k. i.e.,
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jk = %△E j%△Wk
jk = %△Ek%△Wj
If the cross elasticities are positive (with an increase in the price of
one increasing the demand for the other) the two are said to be gross
substitutes. If the cross elasticities are negative (and increase in the price
of one reduces the demand for the other), the two are said to be gross
complements.
Note: Whether two inputs are gross substitutes or gross complements
depends on both the production function and the demand conditions.
→ Knowing that two groups are substitutes in production is not
sufficient to tell us whether they are gross substitutes or gross
complements.