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Firm’s Demand in SR. Only labor input is variable while capital amount is fixed. Marginal revenue product (MRP) Additional revenue earned if employ one more unit of input

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firm s demand in sr
Firm’s Demand in SR
  • Only labor input is variable while capital amount is fixed.
  • Marginal revenue product (MRP)
    • Additional revenue earned if employ one more unit of input
    • When factor price is fixed, MRP is obtained by marginal product of labor times marginal revenue of the output. (you need to be careful on this)
firm s demand in sr1
Firm’s Demand in SR

Wage rate and MRP

  • Marginal product of labor is defined as the contribution to output by adding an additional unit of labor.
  • So the amount of labor needed to produce one more unit of output is:
  • And the cost of this amount is (this, by definition, refers to marginal cost of x):
firm s demand in sr2
Firm’s Demand in SR

Wage rate and MRP

  • Now we know that when the firm maximizes profit, they set marginal revenue equal to the marginal cost:
  • So:
firm s demand in sr3
Firm’s Demand in SR

Two major points drawn from the algebra:

  • It confirms that a profit-maximizing firm operates where the wage rate of labor is equal to its marginal product of labor.
  • The firm’s demand curve for labor coincides with the MRPL curve.
some comparative statics
Some comparative statics
  • Wage goes up.
  • Output price goes up.
  • An increase in plant size
some comparative statics1
Some comparative statics
  • Wage goes up.
  • Output price goes up.
  • An increase in plant size
some comparative statics2
Some comparative statics
  • Wage goes up.
  • Output price goes up.
  • An increase in plant size
critiques of marginal productivity theory
Critiques of MarginalProductivity Theory

A common criticism is that the theory bears little relation to the way that employers make hiring decisions.

Another criticism is that the assumptions of the theory are not very realistic.

However, employers act as if they know the implications of marginal productivity theory (hence, they try to make profits and remain in business).

recap production and costs in the long run
Recap Production and Costs in the Long Run
  • Firm can adjust employment of capital and labor
    • Achieve the least cost method of producing a given quantity of output
isoquants
Isoquants
  • Geometry of LR production
    • Requires labeling vertical axis with K, stands for capital
    • Requires labeling horizontal axis with L, which stands for labor
    • Requires fixed period of time
  • Least costly method
    • Avoid technologically inefficient points which are outside the boundary
  • General observations about isoquants
    • Slope downward
    • Fill the labor-capital plane
    • Never cross
    • Convex to origin
marginal rate of technical substitution
Marginal Rate of Technical Substitution
  • Absolute value of slope of isoquant
    • MPL divided by MPK
  • Amount of capital necessary to replace one unit of labor while maintaining a constant level of output
    • If much labor and little capital employed to produce a unit of output, MRTSLK is small
  • Provides geometric proof that isoquant is convex
marginal rate of technical substitution1
Marginal Rate of Technical Substitution
  • The discussion above assumed a one-unit change in labor. More generally, if labor changed by some amount of ∆L, we will have:

and we would have:

choosing a production process
Choosing a Production Process
  • Minimizing cost necessary for maximizing profit
  • Isocost curve
    • Tracks set of all baskets of inputs employed
    • Assume cost fixed
    • Slope: -PL/PK
  • Firm chooses point where isocost and isoquant curves tangent
    • Means MRTS = PL/PK
  • Tangencies lie along firm’s expansion path
firm s demand in the lr
Firm’s Demand in the LR
  • All factors variable
  • Assume fixed technology (the production function), rental rate (PK), and market price (PX).
  • Note that making the assumption that PKis fixed incurs no loss of generosity, as only the relative price matters.
construction of lr labor demand
Construction of LR Labor Demand

Factor demand vs output demand:

  • The major difference is that a firm, unlike the case of output demand, has no budget constraint. Instead it has an infinite family of isocost lines, and it could choose to operate on any one of them.
  • So we call factor demand “derived” from output demand. In short, we have to consider the optimal decision on the output market.
construction of lr labor demand1
Construction of LR Labor Demand
  • To be more precise, we need to determine how much to produce before we determine exactly how much factors to hire. Eg:
  • We, again, need to resort to the principle of MR=MC.
construction lr labor demand
Construction LR Labor Demand

Substitution and scale effects associated with a factor price change

  • SubE: When the price of an input changes, that part of the effect on employment that results from the firm’s substitution toward other inputs.
  • ScaE: When the price of an input changes, that part of the effect on employment that results from changes in the firm’s output
substitution and scale effects
Substitution and Scale Effects
  • Direction of substitution effect
    • Reduces firm’s employment of labor
substitution and scale effects1
Substitution and Scale Effects
  • Direction of scale effect
    • LRTC rise and shallower
      • LRMC rises
    • Regressive factor
  • Combine effects
    • Labor demand curve always slopes downward
    • Scale effect never dominates substitution effect
    • The proof is here.
sr and lr relationship
SR and LR Relationship
  • In LR
    • MRP shifts due to adjustments in capital employment
  • Infinite number of steps
industry s demand
Industry’s Demand
  • Sum of individual firm’s demand curve for factor of production
  • Monopsony
    • Upward-sloping supply curve
    • Marginal labor cost (MLC)
    • Employment and wage rate
industry s demand1
Industry’s Demand
  • Existence of monopsony
    • Even a firm that is unique in its industry has no monopsony power, provided that firms in other industries compete with it for the use of the factors.
    • Monopsony is rare, especially in the long run.
application
Application
  • Affirmative action and production costs:
    • A firm is “color blind” if race does not enter the hiring decision.
    • Discrimination shifts the hiring decision away from the cost minimization tangency point on the isoquant.
affirmative action
Affirmative Action

Black Labor

Q

P

q*

White Labor

The discriminatory firm chooses the input mix at point P, ignoring the cost-minimizing rule that the isoquant be tangent to the isocost. An affirmative action program can force the firm to move to point Q, resulting in more efficient production and lower costs.

slide42

Black Labor

Q

P

q*

White Labor

Affirmative Action

A color-blind firm is at point P, hiring relatively more whites because of the shape of the isoquants. An affirmative action program will increase this firm’s costs if it must further increase its amount of black labor.

do monopoly firms hire more or less
Do monopoly firms hire more or less?

To answer this question formally, we need to examine the optimal principle for a firm to hire workers:

so

This implies that a monopoly’s labor demand lies below the one for an otherwise identical competitive firm.

Intuitively, as a monopoly firm produces less than a competitive market would do, the firm hires less labor.

do monopoly firms pay more or less
Do monopoly firms pay more or less?
  • The wage rates that monopolies pay, however, are not necessarily different from competitive levels even though employment levels are.
  • An employer with a product-market monopoly may still be a very small part of the market for a particular kind of employee and thus be a price taker in the labor market.
  • However, the ability to pay high wages makes a manager’s life more pleasant by making it possible to hire people who might be more attractive or personable or have other characteristics managers find desirable (Efficiency wage theory)
comparative statics pay roll tax
Comparative statics: pay-roll tax
  • Suppose the government decides to levy a pay-roll tax on the employer, to what extent does the employer bears the tax burden?
comparative statics pay roll tax1
Comparative statics: pay-roll tax
  • Tax burden will be shared by the supplier and the demander.
  • The tax incident is independent of the way the payroll tax is levied.
  • What matters here is the elasticity of demand and supply.
tax on phd s income
Tax on PhD’s income
  • GuoTaiming argued for tax on PhD’s low income (or occupations)
tax on phd s income1
Tax on PhD’s income
  • There is no way to implement it successfully.
  • It’s not students who waste resources, it’s the subsidy for higher education.
slide51

Mandatory tip?

  • AGAIN, There is no way to implement it successfully due to non-compliance.
  • Different components of wage compensation are substitutes.
definition of own wage elasticity of demand
Definition of own-wage elasticity of demand
  • The own-wage elasticity of demandis defined by the percent change in its employment (E) induced by a 1 percent increase in its wage rate (W):
  • Using percent change, instead of level change, to avoid the effect of measurement unit.
  • We usually pay attention only to the magnitude, as the sign is assumed to be negative.
definition of own wage elasticity of demand1
Definition of own-wage elasticity of demand
  • Note that it is a measure for a point, not for the entire curve. But colloquially, a flatter demand curve exhibits a higher elasticity than a sleeper one.
  • For a straight line, the higher region is more elastic than the lower region. (why?)
hicks marshall laws of derived demand
Hicks–Marshall laws of derived demand
  • When the price elasticity of demand for the product being produced is high.
  • When other factors of production can be easily substituted for the category of labor.
  • When the supply of other factors of production is highly elastic (that is, usage of other factors of production can be increased without substantially increasing their prices).
  • When the cost of employing the category of labor is a large share of the total costs of production.

To view the proof, here is an example.

applications of ld elasticity
Applications of LD elasticity

Elasticity and union:

  • Most unions value both wage and employment opportunities for their members.
  • So the more elastic the demand for labor, the smaller the wage gain that a union will succeed in winning for its members.
  • Because, the more elastic the demand curve, the greater the percentage employment decline associated with any given percentage increase in wages.
applications of ld elasticity1
Applications of LD elasticity

So we can infer the following:

  • Unions would win larger wage gains for their members in markets with inelastic labor demand curves.
  • Unions would strive to take actions that reduce the wage elasticity of demand for their members’ services.
  • Unions might first seek to organize workers in markets in which labor demand curves are inelastic (because the potential gains to unionization are higher in these markets).
applications of ld elasticity2
Applications of LD elasticity

The truck industry is split into two distinct segments:

  • One type of general freight carrier exclusively handles full truckloads (TLs), taking them directly from a shipper to a destination – LD is more elastic (why?)
  • The other type of carrier handles less than-truckload (LTL) shipments, which involve multiple shipments on each truck and an intricate coordination of pickups and deliveries – LD is less elastic.
complements or substitutes
Complements or substitutes?
  • When there are more than one input, we need to consider whether the two inputs are complements or substitutes.
  • If two inputs are substitutes in production, then increases in the price of the other input may shift the entire demand curve for a given category of labor either to the right or to the left, depending on the relative strength of the substitution and scale effects.
  • That is, the cross-elasticity is positive.
  • Are skilled and unskilled workers complements or substitutes?
slide62

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

complements or substitutes1
Complements or substitutes?
  • Q: In the case of are sub or com?
definition of cross wage elasticity of demand
Definition of cross-wage elasticity of demand
  • The cross-wage elasticity of demandis defined by the percent change in its employment (E) induced by a 1 percent increase in the price of another factor:
  • the two factors are gross substitutes
  • the two factors are gross complements
definition of cross wage elasticity of demand1
Definition of cross-wage elasticity of demand

whether two inputs are gross substitutes or gross complements depends on the relative sizes of the scale and substitution effects. Assume that adults and teenagers are substitutes in production, a decrease in the teenage wage:

  • There is a substitution effect: for a given level of output, employers will now have an incentive to substitute teens for adults in the production process and reduce adult employment.
  • There is a scale effect: a lower teenage wage reduces costs and provides employers with an incentive to increase employment of all inputs, including adults.
important findings about the cross elasticity
Important findings about the cross elasticity
  • Skilled labor and unskilled labor are substitutes in production.
  • We are not certain whether either skilled or unskilled labor is a substitute for or a complement with capital in the production process. What does appear to be true is that skilled (or well-educated) labor is more likely to be complementary with capital than is unskilled labor—and that if they are both substitutes for capital, the degree of substitutability is smaller for skilled labor.
important findings about the cross elasticity1
Important findings about the cross elasticity

Thus, we have 2 important implications:

  • The finding that skilled labor is more likely than unskilled labor to be a gross complement with capital is important to our understanding of recent trends in the earnings of skilled and unskilled workers (see chapter 15), because the prices of computers and other high-tech capital goods have fallen dramatically in the past decade or so.
  • Other things equal, own-wage labor demand elasticity will be larger in magnitude for unskilled than for skilled workers. (why?)
example minimum wage
Example: minimum wage

To estimate the effects of MW, we need to consider at least the following concerns:

1. Real vs nominal wage

example minimum wage1

Dollars

Dollars

(If workers migrate to covered sector)

SU

SC

SU

w

SU

(If workers migrate to uncovered sector)

w*

w*

DU

DC

Employment

Employment

E

EC

EU

EU

EU

(b) Uncovered Sector

Example: minimum wage

To estimate the effects of MW, we need to consider at least the following concerns:

2. Uncovered sector – an issue about partial vs general equilibrium

example minimum wage2
Example: minimum wage

To estimate the effects of MW, we need to consider at least the following concerns:

3. Noncompliance

  • It is possible that some firms do not comply with the regulation
  • This is especially possible for countries such as Taiwan, where wage compensation structure is complex and overtime work is often unpaid.
facts about minimum wage
Facts about minimum wage
  • Card and Kreuger’s 1992 paper is one of few outliers. Neumarkhas reviewed more than 100 academic studies on the impact of government wage-setting and concluded that the vast majority “find a negative employment effect on low-skilled workers.”
  • The effect of MW on confronting poverty is also limited.
  • Alternative policies, such as EITC, should be considered.
evidence of the effects of raising the minimum wage
Evidence of the effects of raising the minimum wage
  • David Card and Alan Krueger, American Economic Review, 2000
  • In 1992, New Jersey raised the min. wage from $4.25 to $5.05 largest min. wage in the United States at that time.
  • Card and Krueger telephoned managers at fast-food restaurants in New Jersey and Pennsylvania a few months before and after the change.
evidence of the effects of raising the minimum wage1
Evidence of the effects of raising the minimum wage
  • They asked about wages paid to employees, how many employed in each restaurant (part time and full time)
  • Chose fast-food industry because most workers in the industry paid min. wage
  • Question: Did the min. wage increase in N.J. lead to a decrease in employment in the fast-food industry?
what card and krueger conclude
What Card and Krueger conclude
  • No noticeable effect from raising the minimum wage 19% in New Jersey, compared to no change in Pennsylvania
  • Evidence that labour demand for minimum wage workers in perfectly competitive model very inelastic,
  • Or Evidence that firms have some monopsony power (price discriminating monopsonist might behave this way)
what others conclude
What others conclude
  • Controversial result
  • David Neumark and others have viciously attacked this finding
  • Baker, Benjamin, and Stanger find some evidence that min. wage increases reduced long-term employment in Canada
  • Find out more on my web page
labour demand example
Labour Demand Example
  • Hamermesh and Trejo(2000)
  • “The Demand for Hours of Labor: Direct Evidence from California,”
  • Review of Economics and Statistics
background
Background
  • At least since the 1970s, California required most women to be paid 1.5*wage for working beyond 8 hours a day
  • In 1980, California extended this overtime rule to men
  • Note, in 1998, California got rid of this policy
why this policy is cool to look at
Why this policy is cool to look at
  • To measure the elasticity of labour demand, we need to observe changes in wages that a firm must pay to workers, all else constant
  • Very hard to find changes in wages that are not driven by changes in labour supply (e.g. preferences for work), in contrast todemand shifts (e.g. technology shocks, recessions)
what does our theory predict will happen by introducing overtime laws
What does our theory predict will happen by introducing overtime laws?
  • Overtime raises the marginal cost to employers of assigning overtime. Firms should respond by lowering the incidence of long workdays and shortening the workdays of workers who continue to put in more than 8 hours a day
  • Some firms may impose 8-hour workdays
  • Our simple model suggests substituting away from hours of overtime for hours of regular day work (by hiring more workers)
a twist to trying to analyze this
A twist to trying to analyze this:
  • Even without California 8-hour overtime policies, federal government imposes must pay 1.5 * wage if working for than 40 hours a week, both for men and women
  • So for workers already working more than 40 hours a week, won’t see change from policy
  • We might observe substantial reduction in overtime work, or little effect.
slide85

Empirical Methodology:

% workers with workdays longer than 8 hours

Difference

Men, California

1973

1985

Any factors that leads to change in overtime changes will be attributed to reform change.

slide86

Empirical Methodology:

% workers with workdays longer than 8 hours

Diff. Before Change

Men, California

Diff. After Change

Men, New Mexico

1973

1985

Estimate Effect from Difference in Differences

slide87

Empirical Methodology:

% workers with workdays longer than 8 hours

Diff. Before Change

Women, California

Diff. After Change

Women, New Mexico

1973

1985

Should not observe same comparison for women:

their conclusions
Their conclusions
  • As theory predicted, percentage of workers working more than 8 hours a day declined after overtime policy introduced
  • Implied price elasticity of demand for daily overtime hours is about -.5
asymmetric variable adjustment costs
Asymmetric Variable Adjustment Costs

Changing employment quickly is costly, and these costs increase at an increasing rate. If government policies prevent firms from firing workers, the costs of trimming the workforce will rise even faster than the costs of expanding the firm.

estimating labor demand
Estimating Labor Demand

One can identify the slope of the labor demand curve, which can be used to calculate the elasticity of labor demand, when the supply curve shifts.

Problem: Must make sure the labor demand curve is not also changing.

problems with estimating labor demand
Problems with Estimating Labor Demand

S0

Dollars

S1

Z

P

w0

R

w2

Z

Q

w1

D1

D0

E1

E0

E2

Employment