Demand for Labor

Profit Maximization and the Marginal Productivity Theory

• The assumption is that firms attempt to maximize profit by hiring inputs to produce output. Three possibilities for employing any given input, like labor:– If the revenue from employing another unit is greater

than the cost of employing it. Hire more of the input.– If the revenue from employing another unit is less than

the cost of employing it. Hire less of the input.– If the revenue from employing another unit is equal to

the cost of employing it. Stop. The profit-maximizing level of the input has been reached.

Revenue from Labor

• Marginal Product of Labor - Change in output from hiring another unit of labor, ceteris paribus (holding capital constant0 .– MPL = (ΔQ/ΔL) |K constant

• Marginal Revenue Product of Labor - Change in total revenue from hiring another unit of labor.– MRPL= ΔTR/ΔL– MRPL = MR x MPL

– MRPL = (ΔTR/ΔQ) x (ΔQ/ΔL)

• Example:– MR = $5/1Q or $5 and MPL=10Q/1L or 10– MRPL = ($5/1Q) x (10Q/1L) = $50/1L or $50– Hiring one worker results in 10 units of output and if each additional output

sells for $5, the revenue produced by one worker is $50.

• In competitive output markets, marginal revenue is equal to price so MR = P and– MRPL = MVPL = P x MPL

Cost of Hiring Labor

• Marginal expense of an input = change in total cost of hiring another unit of the input– MEL = ΔTC/ΔL

• In competitive labor markets, – MEL = Wage rate or W

• In monopsonistic or oligopsonistic labor markets,– MEL > W– This occurs because to hire another unit of labor the employer

must pay a higher wage to all workers– Say the current wage for 10 workers is $10, to hire another worker

the wage rises to $11, the MEL equals $11 for the extra worker plus $10 ($1 increase in wages for 10 workers) or $21.

Labor Demand in Competitive Output and Labor Markets

• Competitive output markets imply: – MRPL = P x MPL

• Competitive labor markets imply:– MEL = W

• Profit Maximization implies:– MRPL = MEL , or– P x MPL = W, or– MPL = W/P

Diminishing Marginal Product of Labor

• The law of diminishing marginal returns – as the increasing amounts of a variable input are applied to a fixed factor(s) the marginal product of the variable input will diminish.

• Intuitive proof: if the LDMR did not apply, you could grow the world’s food supply in a small flower pot.

The Demand Curve for Labor with Real Wages vs. Nominal Wages

• Real Wages – real wages are nothing more than valuing cost in terms of how mush output must be paid to the worker.

• For example, if an MP3 player sells for $100, and the wages of a worker is $20/hour. The real wage of the worker is .2 MP3 players/hour.

• Remember profit maximization:– Hire an additional worker if they produce revenue more

than they cost– Layoff an additional worker if they produce revenue less

than they cost

• If the worker’s,– MPL > .2 MP3 player, hire– MPL < .2 MP3 player, layoff– MPL = .2 MP3 player, optimal

• When real wages are placed on the vertical axis, the demand curve is just the MP curve, which is downward-sloping demand curve because of the LDMR.

• The demand curve quickly points out the rule above and firms will maximize profits by hiring until the MPL= W/P.

• Economic profit and economic rent. – Profit on labor is the difference between what firms were willing to pay and the

real wage rate– Economic rent is the difference between what labor was willing to supply labor

for and the real wage rate.

Demand for Labor and Nominal Wages

• Profit Maximization occurs when the firm hires labor up to the point where the– MRPL = W

• In competitive output markets,– P x MPL = W– The LDMR ensures that the MRPL curve is downward-sloping.– In this case, the firm looks at the revenue produced by an additional labor

and compares it to the nominal wage = cost of hiring an additional labor.

• The difference in using nominal wages is that changes in product price or demand will shift the MRPL curve. Using real wages, a change in the product price will cause a movement along the demand curve.

Labor Demand and Changes in other Inputs

• Changes in capital are usually associated with a time period long enough for the firm to make investment or plant-size decisions.

• Remember, the difference between the short- and long-run.– Short-run: at least one input is fixed, usually capital (plant-size fixed).– Long-run: all inputs are variable (plant-size is variable).

• Modified profit maximizing rule:– Remember cost minimization is a necessary condition for profit

maximization but is not a sufficient condition– With two inputs, the firm must simultaneously satisfy the following two

conditions:• MRPL = W• MRPK = C

• To show that profit maximization implies cost minimization, we recognize that in competitive markets MRP = P x MP;– P x MPL = W or P = W/ MPL

– P x MPK = C or P = C/ MPK, this leads to– W/ MPL = C/ MPK

• To get an intuitive idea why this is cost minimizing– W/ MPL = W/(ΔQ/ΔL) or (W x ΔL)/ΔQ or ΔTCL/ΔQ or finally MCQ|using more L

– C/ MPK = C/(ΔQ/ΔK) or (C x ΔK)/ΔQ or ΔTCK/ΔQ or finally MCQ|using more K

• Numerical example: If W = $5/hr and C=$100/hr (rental or imputed rent) and MPL = 10Q/1L and MPK=100Q/1K, what should the firm do? Use a more labor intensive or a more capital intensive approach?

• MCQ|using more L= ($5 x 1L)/10Q = $.50/1Q• MCQ|using more K= ($100 x 1K)/100Q = $1.00/1Q

↓

• If the W rises, the equality MCQ|using more L= MCQ|using more K is disturbed and the firm will change its hiring decisions and the following will result– MCQ|using more L will rise causing firms to cut back on labor in the short-run– L↓ → MPL↑ →MCQ|using more L↓ – L↓ → MPK↓ →MCQ|using more K↑– These movements help to restore MCQ|using more L= MCQ|using more K – The quantity demand of labor will fall for two reasons:

• Scale effect – MC of output ↑ so Q↓ and K and L both↓• Substitution effect – K is substituted for L because K becomes relatively cheaper (see

above)

– The change in wages will have an ambiguous effect on the firm’s desired stock of capital. The firm will produce output with a more capital intensive production method [(K/L) ↑] if the substitution effect outweighs the scale effect and more labor intensive [(K/L) ↓] if the scale effect outweighs the substitution effect

Various Inputs

• So far we have discussed K and L, but we could add natural resources and entreprenuership as well as break each input class into different qualities or characteristics (e.g. skilled versus unskilled workers)

• Inputs are gross substitutes when one input can be used in place of another input. The are perfect substitutes when they are interchangeable.

• Inputs are gross complements when increases (decreases) in one input is accompanied by an increase (decrease) in the other input. They are perfect complements if they need to be used in fixed proportions.

• Example: US unskilled workers, foreign unskilled workers, and computers:– WUS↑→ substitution effect: LUS↓ →LFUS↑ scale effect: LUS↓ and

LFUS↓

– Two possibilities: sub>scale→ LUS↓ →LFUS↑ gross substitutes

sub<scale LUS↓ and LFUS↓ gross complements

– Computers and workers are gross complements, reductions or increases in L will cause changes in the demand for computers. Also, changes in the price of computers will affect the DL

Imperfect Competition in Output and Labor Markets

• Monopoly in output markets and monopsony in input markets. Firms may have market power or the ability to affect market prices and/or wages.

• Monopoly in output markets:– Π max. rule is to hire L until MRPL = MRQ x MPL=W– MRQ<P the monopolist will produce less output and hire fewer workers that a

competitive market.– Theoretically, if monopolist has no market power in the labor market, they must

pay the going wages.In practice, however, it has been argued that:• Regulated monopolist are not subject to competitive market forces and therefore may

pay higher wages. The incentive to offer higher wages is similar to the argument for efficiency wages (less turnover, greater employee satisfaction)

• Unregulated monopolists may not wish to report high profits and thus the opportunity costs of offering reservation wages is lower.

• The empirical evidence is inconclusive.

• Monopsony in the labor market:– Π max. rule is to hire L until MRPL = MRQ x MPL=MEL

– In monopsony, the firm faces the entire market supply curve for labor and must raise the wage to obtain an additional worker. If all workers must be paid the same wage rate, the MEL>W

– Example: At the wage of $10, 10 workers are employed, to hire another worker requires raising the wage to $11. The MEL of labor is the wage of $11 for the additional worker plus the $1 increase in wages for the existing 10 workers, which comes to $21.

– Monopsony and competition in the major leagues. Leroy “Satchel” Paige and free-agency

– Monopsonist does not have a labor demand curve because they are wage makers (monopolist don’t have a supply curve because they are price makers).

– However, decreases in labor supply will raise wages, but reduce employment. The decline in employment will likely be greater in the long-run than in the short-run if the substitution effect outweighs the scale effect. Remember, in the case of two inputs MEL/ MPL = C/ MPK

• Mandated wages, such as a minimum wage, changes incentives for monopsonists. – In the short-run, if the wage is set between above the wage monopsonist

would have pay and below the amount that they would be willing to pay, the minimum wage will lower the MEL and will increase employment and average wages.

– In the long-run, there are two opposing effects:• Substitution effect: The reduction in the MEL can cause firms to substitute labor

for capital.• Scale Effect: The increase in wages (average wages) reduces profitability. If the

firm is a perfect competitor, this will cause exit from the industry and reduce the demand for labor.

• In summary, in monopsony the effect of mandated wages can be ambiguous, but decreases in the supply of labor reduce employment. In competitive markets, both will reduce employment.

Who Pays the Payroll Tax?• Taxes drive wedges between the price the buyer pays and

the seller receives. A payroll tax drives a wedge between the wages a firm pays and the wages that workers receive.

• Payroll taxes include social security retirement, disability, and medicare taxes; unemployment insurance, and Washington State L and I.

• The payroll tax maybe levied against the employee and/or the employer (e.g. social security is paid to the government by both the employer and the employee).

• The question we are asking is who really pays the tax or the tax incidence.

• Knowing that a tax will lower the wage to employees and increase the effective wage paid by the employee, both the employer and the employee will modify their behaviors. The employee will reduce the QL

S and the employer will reduce their QLD.

• The distortion in behaviors will cause both to share in the burden of the tax and the welfare loss.

• Imposing the payroll taxes on the employer shifts the demand curve for labor downwards and to the left.

Graphical Demonstration of tax burden

• Imposing the payroll taxes on the employee shifts the supply curve for labor up and to the left.

• The difference between the old and new curves is the tax and represents the difference between what employers pay and employees receive.

• It is important to note that the tax burden borne by the employee and employer is independent of who the tax is levied upon.

• The more inelastic the supply (demand) curve the more the employee (employer) bears the burden of the tax. Studies indicate in the long-run, most of the payroll tax is shifted onto employees.