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Chapter 3 Labor Demand. The labor is worthy of his hire. —The Gospel of St.Luke. 3.1 The Short-run Labor Demand. What does the term “short-run” mean? Firm can only change the employment of labor to maximize profit. That is, the stock of capital is assumed to be fixed.

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chapter 3 labor demand

Chapter 3 Labor Demand

The labor is worthy of his hire.

—The Gospel of St.Luke

3 1 the short run labor demand
3.1 The Short-run Labor Demand
  • What does the term “short-run” mean?

Firm can only change the employment of labor to maximize profit. That is, the stock of capital is assumed to be fixed.

  • Why do firms hire workers?

–The objective of hiring workers is to produce product that firm can sell.

–That is, demand for labor is a derived demand, which is derived from consumer’s demand for final product.

3 1 the short run labor demand1
3.1 The Short-run Labor Demand
  • How does a firm make decisions on its production (e.g., whether and how to produce, increase or decrease output level) ?

–The guide rule is simple: maximizing profit.

  • How to realize profit maximization?

–Profits are maximized at the point where added revenue of one extra unit of input equals added cost of one extra unit of input.

  • For simplicity, still assume two inputs, Kand L.
3 1 the short run labor demand2
3.1 The Short-run Labor Demand
  • Assumptions:

–Both product and labor market are competitive.

  • –Firm’s production

Production technology:Q=f(K,L), Kdenotes capital input and Ldenotes labor input

Examples: Q=L+K; Q=LK; Q=L1/2K1/2

  • –Firms seek profit maximization.
3 1 the short run labor demand3
3.1 The Short-run Labor Demand
  • Some analytical concepts

–Marginal Product (MP) of labor

  • Change of the output resulting from an additional unit of labor employment, holding capital input constant.
  • MPL=ΔQ/ΔL=Δf(L,K)/ΔL

–Similarly, marginal product of capital

  • MPK=ΔQ/ΔK=Δf(L,K)/ΔK
3 1 the short run labor demand4
3.1 The Short-run Labor Demand
  • –Marginal Revenue (MR)

Additional revenue generated by an extra unit of output.

MR depends on the characteristics of the product market.

e.g., MR=Pin the competitive product market.

  • –Marginal Revenue Product (MRP)

Simply combines marginal product and marginal revenue, i.e., MRP=MP*MR

3 1 the short run labor demand5
3.1 The Short-run Labor Demand
  • Average product (AP) of labor

–Defined as average output produced by one unit of labor input.

–APL=Q/L=f(K,L)/L

  • Average product of capital

–Defined as average output produced by one unit of capital input.

–APK=Q/K=f(K,L)/K

3 1 the short run labor demand7
3.1 The Short-run Labor Demand
  • Marginal Expense (ME) or Marginal Cost (MC)

–Added cost resulting from employing an additional unit of input.

  • A crucial assumption: The Law of Diminishing Marginal Returns

–Marginal product of labor will eventually decline as employment increases given a fixed capital.

–Why? Specialization, cooperation, externality, …

–Example of 4S.

3 1 the short run labor demand10
3.1 The Short-run Labor Demand
  • Profits are maximized at the point where marginal revenue product of labor equals marginal cost of labor.

MRPL=MPL*MR=MCL

  • In the competitive markets,

MPL*P=W <=> MPL=W/P

  • With the equation above, labor demand can be derived in terms of realmoney (nominal) wage.
3 1 the short run labor demand11
3.1 The Short-run Labor Demand
  • Labor demand against realwages

–MPL=W/P

–According to the law of diminishing marginal returns, we expect a negative relationship between employment and MP.

–Or a negative slope for the MPL curve.

3 1 the short run labor demand12
3.1 The Short-run Labor Demand
  • Labor demand against moneywage

–MRPL=W

–Again with the law of diminishing marginal returns, we have a labor demand curve sloping downward.

–Example of detective hiring. (also, e.g., police size)

–*The MRPLcurve and the labor demand curve coincide here.

3 1 the short run labor demand13
3.1 The Short-run Labor Demand
  • One remark

–The term “marginal” is not a function of individual’s characteristics.

–The size of “margin” depends on the number of employees that are already hired.

–The size of “margin” also depends on the size of other input.

3 2 the short run market demand curve
3.2 The Short-run Market Demand curve
  • Above we show the labor demand curve for a representative firm, which indicates the level of firm’s employment at each given wage rate.
  • The market demand curve is simply an aggregation of each firm’s employment at each wage rate.
  • Two objections

–Employers do not know the accurate output of individual workers, no mention of MRP.

–Additional labor produces nothing in some cases.

3 3 the long run demand for labor
3.3 The Long-run Demand for Labor
  • In the “long-run”, the size of other inputs can vary. For example, machines, materials, energy, and technology.
  • We first look at the situation that firm can only adjust the size of capital used.
  • For two variable inputs, profit maximization will be realized when two marginal conditions are satisfied.
3 3 the long run demand for labor1
3.3 The Long-run Demand for Labor
  • In formula,

MPL*P=MCL=W

MPK*P=MCK=C

C denotes the cost of capital (e.g., interest)

  • Rearrange the two equations,

P=W/MPL

P=C/MPK

3 3 the long run demand for labor2
3.3 The Long-run Demand for Labor
  • With the same P, profit maximization rule therefore requires that,

W/MPL=C/MPK

–The left-hand side W/MPLdenotes the added cost of producing one additional unit of output using labor.

–The right-hand side C/MPKdenotes the added cost of producing one additional unit of output using capital.

3 3 the long run demand for labor3
3.3 The Long-run Demand for Labor
  • What does the equation mean for a representative firm seeking profit maximization?
  • The firm must adjust the sizes of labor and capital so that the marginal cost of producing one additional output using labor is equal to the marginal cost of producing one additional output using capital.
3 3 the long run demand for labor4
3.3 The Long-run Demand for Labor
  • So, how is the long-run labor demand of a representative firm if wage increases (or decreases)?

–Equation W/MPL=C/MPKis disturbed.

–In the short-run, the marginal cost of production using labor exceedsthe marginal cost using capital.

•First the firm will cut the size of employment as before, which leads to raise MPL.

•Less labor also results in falling MPK, which will lead to reduction of its capital input.

3 3 the long run demand for labor5
3.3 The Long-run Demand for Labor
  • In the long-run, the firm can substitute capital for labor since capital is more cheaper than labor. The substitution also leads to

–Increase of MPLdue to higher capital per worker

–Decrease of MPK due to the Law of Diminishing Marginal Return

3 3 the long run demand for labor6
3.3 The Long-run Demand for Labor
  • In the end, a rise of wage rate will cause a decline of employment level.

–Falling output level (scale effect)

–More capital input (substitution effect)

–However, whether the sizes of capital increase is ambiguous.

–See Figure in next slide

  • The long-run story therefore provides further support to the proposition of the downward-sloping labor demand curve.
3 3 the long run demand for labor8
3.3 The Long-run Demand for Labor
  • The case of more than two types of inputs

–Labor demand is now a function of wage rate and the prices of all other inputs.

–Inputs are substitutes,

•Scale effect

•Substitution effect

–Inputs are complements

•Only scale effect

3 4 monopoly in the markets
3.4 Monopoly in the markets
  • Up to now, we are assuming that the representative firm is not only a price taker but also a wage taker.
  • We now turn to the situations in the noncompetitive markets.

–Monopolistic product market

–Monopolistic labor market

3 5 monopolistic labor market
3.5 Monopolistic Labor Market
  • What if a mandated wage is imposed?

–Change the market supply curve

–Change the firm’s MEcurve

–Change both the average cost and marginalcost of labor

–If Wmlie between Wm’ and W0, both wage and employment rise.

–If Wmis higher than Wm’, then ?

3 5 monopolistic labor market1
3.5 Monopolistic Labor Market
  • In the long-run, if the mandated wage is not too high, or reduce the MEof labor,

–Substitution effect more labor, less capital

–Scale effect:less output lower employment level

–Uncertain gross effect

summary
Summary
  • In the short run, a profit-maximizing firm hires workers up to the point where the wage equals the value of marginal product of labor.
  • In the long run, a profit-maximizing hires each input up to the point where the price of the input equals the value of marginal product of the input. This condition implies that the optimal input mix is one in which the ratio of marginal products of labor and capital equals the ratio of input prices.
summary1
Summary
  • In the long run, a decrease in the wage generates both substitution and scale effects. Both of these effects spur the firm to hire more workers.
  • Both the short-run and long-run demand curves for labor are downward sloping, but the long-run demand curve is more elastic than the short-run curve.
  • The short-run labor demand elasticity may be on the order of -0.4to –0.5.The long-run elasticity is on the order of -1.
summary2
Summary
  • Capital and skilled workers are complements in the sense that an increase in the price of capital reduces the demand for skilled workers. Capital and unskilled workers are substitutes in the sense that an increase in the price of capital increases the demand for unskilled workers.
  • The imposition of a minimum wage on a competitive labor market creates unemployment because some workers are displaced from their jobs and because new workers enter the labor market hoping to find one of the high-paying (but scarce) jobs.
summary3
Summary
  • The elasticity of teenage employment with respect to the minimum wage is on the order of -0.1 to -0.3.
  • The presence of variable adjustment costs implies that firms adjust their employment slowly when the wage changes. If fixed adjustment costs are important, employment changes in the firm are large and sudden, if they occur at all.
  • An instrument is a variable that shifts either the supply or demand curve. The variation caused by this shock can be used to estimate the labor demand or labor supply elasticity.
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