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Labour Market Economics, 5/e

Wages and Employment in a Single Labour Market

# Chapter Notes

The Competitive Labour Market

• assuming that firms can buy all the labour they wish at the going wage rate (firms are wage takers in the labour market), the market labour demand curve for perfectly competitive firms (firms that are price takers in the product market) is the horizontal summation of the labour demand curves of the individual firms
• as discussed in the previous two chapters, a perfectly competitive firm's labour demand curve is the Value of the Marginal Product of Labour (VMPL = P*MPL) schedule minus any (amortized) fixed costs
• if the firm is a monopolist, the market demand curve corresponds to the monopolist's Marginal Revenue Product of Labour (MRPL = MR*MPL) curve minus any (amortized) fixed costs
• the market labour supply curve is the horizontal summation of the individual labour supply curves (as derived in Chapter 2)
• the intersection of the market labour demand curve and the market labour supply curve determines the equilibrium wage rate and the equilibrium employment level
• given the LDo and LS curves in Figure 7-1, the competitive market equilibrium occurs at point Eo; the equilibrium wage rate Wo 'clears' the labour market  (7.0K) Figure 7-1
• assuming 'linear' curves, the labour demand and supply curves can be written as:
• LD = a + bW + gX , where b is a negative parameter and X represents exogenous (shift) variables such as product price, fixed costs and payroll taxes
• LS = c + fW + hZ, where Z represents exogenous (shift) variables such as consumer prices and income taxes
• since economists have traditionally plotted the wage rate on the vertical axis of a labour demand and supply diagram, these two equations have to be re-arranged with W on the left hand side of the equation to represent the traditional labour demand and supply curves drawn in Figure 7-1
• in Figure 7-1 the vertical intercept of the labour demand curve would be – a/b (recall that b is a negative parameter) and the vertical intercept of the labour supply curve would be – c/f
• reduced form equations for the equilibrium wage W and employment level L can be obtained by solving the structural equations for labour demand LD and labour supply LS
• equating labour demand LD and labour supply LS produces the following equation
a + bW + gX = c + fW + hZ,
which can be re-arranged to obtain the reduced form equation for W
W = [ a + gX – c – hZ ]/ [f – b ]
• substituting the W reduced form equation into L = LD = a + bW + gX,
L = a + gX + b [ a + gX – c – hZ ]/ [f – b ]
and re-arranging produces the following reduced form equation for L
L = [ af – bc +gfX – bhZ ] / [ f – b ]
• the W and L reduced form equations allow us to determine the effects on the equilibrium wage and employment level from a change in an exogenous factor (X or Z)
• for example, if X increases by one unit, the equilibrium wage W will increase by g/[f – b] and the equilibrium employment level L will increase by gf/[f – b]; again recall that b is a negative parameter and thus the divisor [f – b] is a positive number
• we now examine how equilibrium wages and employment levels in a competitive labour market are affected by the imposition of a payroll tax

The Labour Market Effects of Payroll Taxes

• a payroll tax is a tax levied on employers with the amount of tax payable based on the size of the payroll (the wage rate multiplied by the quantity of labour employed)
• the federal government levies two payroll taxes: employer-paid premiums for Unemployment Insurance (UI) and for the Canada Pension Plan (CPP), both of which are 'capped' (there is no premium paid for earnings above the cap)
• UI premiums: in 2002 employers paid 3.08% of payroll costs for annual labour earnings up to \$39,000 (the cap); in 2002 the maximum annual UI premium paid by the employer for one employee is \$1,201
• CPP premiums: in 2002 employers paid 4.7% of payroll costs for annual labour earnings from \$3,500 to \$39,100 (the cap); in 2002 the maximum annual CPP premium paid by the employer for one employee is \$1,673.20.
• for employees earning less than the cap (\$39,000), in 2002 employers pay a combined UI and CPP premium of 7.78% of the employee's earnings; the maximum annual premium paid to the federal government by the employer for one employee is \$2,874.20
• in addition to federal UI and CPP premiums (a euphemism for payroll taxes), employers also pay workers' compensation (WC) premiums to provincial governments
• in 1997 payroll taxes were 12% of labour income (see textbook page 199)
• the firm must pay part of the value of the marginal product of labour (VMPL) to governments in the form of UI, CPP, and WC premiums
• the demand for labour curve will be represented by the VMPL schedule minus the payroll tax (PT)
• a profit-maximizing firm will hire labour up to the point where W = VMPL – PT
• for example, if the VMPL for the nth worker is \$110 and payroll taxes are 10%, a profit-maximizing firm will hire the nth worker as long as the wage is not greater than \$100 (W = VMPL – PT)
• the imposition of a payroll tax shifts the labour demand curve downwards by the amount of the payroll tax
• Figure 7-1 illustrates the labour market effects of the imposition of a payroll tax
• with no payroll tax, the labour demand curve is represented by the LDo = VMPL line and the equilibrium position in the labour market is Eo; the equilibrium wage rate is Wo and the equilibrium quantity of labour is Lo
• imposing a payroll tax shifts the labour demand curve down to LD1 = VMPL – PT
• the vertical intercept of the labour demand curve shifts down by PT, the portion of the VMPL which must be paid to the government (payroll taxes)
• the new equilibrium position in the labour market is E1; the equilibrium wage rate decreases to W1 and the equilibrium quantity of labour decreases to L1
• the imposition of a payroll tax (paid by the employer) reduces the demand for labour, the equilibrium wage paid to labour and the equilibrium quantity of labour
• in the long run (when all factors are variable in the production process), the imposition of a payroll tax on labour will cause profit-maximizing firms to substitute other non-taxed factors of production (such as capital) for labour, further reducing the demand for labour
• the incidence of the payroll tax (who actually pays it) depends on the elasticities (slopes) of the labour demand and supply curves
• given a downward-sloping labour demand curve, employees will pay part of the payroll tax levied on firms in the form of lower wage rates (and less employment)
• if the labour supply curve were perfectly inelastic (vertical in Figure 7-1), then the equilibrium wage rate will fall by the full amount of the employer-paid payroll tax and there will be no effect on employment levels
• while the employer remits the payroll tax to the government, the tax is shifted back on to the employee who implicitly pays the payroll tax (wages decline by the full amount of the payroll tax if the labour supply curve is perfectly inelastic)
• from the reduced form equations above, a 1 unit increase in X from an increase in payroll taxes results in a g/[f – b] decrease in wages and a gf/[f – b] decrease in employment; the size of these wage and employment effects depends on b, the slope of the LD curve, and f, the slope of the LS curve
• as the textbook points out (page 201), "the growing body of empirical evidence seems to support the conclusion that in the long run ... the incidence of payroll taxes falls largely on workers, and that the disemployment effect is small."
• workers are the big losers when the government imposes payroll taxes on employers; while the employer remits the payroll tax to the government, the payroll tax comes out of the pockets of the employees
• besides any loss in employment, a payroll tax paid by employers reduces the wage rate received by employees and thus reduces employees' utility level (the employee's income budget-line in the income-leisure choice model rotates inwards given a fall in the wage rate)
• since UI and CPP premiums are also paid by employees (both employees and employers pay UI and CPP premiums), workers suffer a double hit in utility
• UI and CPP premiums lower 'net' take-home pay in two ways: there is a lower 'gross' wage (because the firm shifts employer-paid UI and CPP premiums back onto the employee in the form of lower wages) and the employee also pays UI and CPP premiums which further reduce 'net' pay (after tax deductions)

The Effects of a Minimum Wage in the Labour Market

• minimum wages are set by provincial governments
• as illustrated in the textbook (page 209), the ratio of minimum wages to average wages in the Canadian manufacturing sector declined from .50 in 1975 to .35 in 1985 and then rose back to approximately .40 in the late 1990s
• we analyze and discuss the effects of minimum wages under two different labour market assumptions: (i) a competitive labour market and (ii) monopsony in the labour market

A Competitive Labour Market

• the traditional economic argument against minimum wages assumes a competitive labour market
• each profit-maximizing firm is assumed to be able to hire all the labour it wishes at the competitive market wage rate
• in Figure 7-2 the market-clearing wage rate is Wo with Lo workers employed  (4.0K) Figure 7-2
• suppose that the government imposes a minimum wage of Wmin > Wo
• at the wage Wmin, profit-maximizing firms will only employ Lmin workers and (Lo – Lmin) workers will lose their jobs
• the number of workers who lose their jobs following the imposition of a minimum wage depends on the elasticity of the labour demand curve for minimum wage workers and the size of the (Wmin – Wo) differential (factors affecting the elasticity of the demand for labour curve were discussed in Chapter 5)
• for example, if the elasticity of labour demand curve is – 1/3 and there are 1,000,000 Canadian workers paid the minimum wage, an increase in the minimum wage of 3% (about \$.20) will result in 10,000 Canadian workers losing their 'minimum wage' jobs; the vast majority of 'minimum wage' workers (990,000 out of 1,000,000) keep their jobs and receive a 3% wage increase
• a modest increase in the minimum wage creates a few big losers (minimum wage workers who lose their jobs and their entire annual labour income) and many small winners (workers who keep their jobs and receive a modest increase in wages and annual income)
• most of the 'losers' tend to be young people with few skills and little work experience
• it should also be noted that raising the minimum wage does little to alleviate poverty because relatively few low-income households have minimum wage workers (most poor individuals do not work) and relatively few minimum wage workers live in low-income households
• many 'minimum wage' workers (particularly young singles) are part of a family and have access to family income well above poverty levels

Monopsony in the Labour Market

• a perfectly competitive firm is a price taker in the product market (it can sell all it wants to at the market price) and is a wage taker in the labour market (it can buy any quantity of labour at the market wage rate — the labour supply curve is horizontal)
• the perfectly competitive firm is typically a very small player in a very large product market and a very large labour market
• a monopolist faces a downward-sloping product demand curve and sets the price (by restricting output) to maximize profits
• a monopolist equates marginal revenues (MR) to marginal costs
• a monopsonist faces an upward-sloping labour supply curve and sets the wage rate (by restricting the amount of labour hired) to maximize profits
• a monopsonist equates the marginal cost of hiring another worker with the Value of the Marginal Product of Labour (VMPL = P*MPL); if the monopsonist is also a monopolist, the marginal cost of hiring is equated to the Marginal Revenue Product of Labour (MRPL = MR*MPL)
• a monopsonist firm is typically a large player in a small labour market (for example, a 'one company' town in an isolated region); it can exercise market power as a buyer of labour

The Monopsonist's Demand for Labour

• Figure 7-3 depicts the monopsonist's upward-sloping labour supply (LS) curve  (7.0K) Figure 7-3
• to attract and hire additional labour, the monopsonist must raise the wage (LS slopes up)
• if a monopsonist reduces the wage, some (but not all) workers will withdraw their labour services
• if a perfectly competitive firm reduces the wage below the market-clearing level, all workers will leave the firm
• given an upward-sloping labour supply (LS) curve, there is an upward-sloping marginal cost (MC) of labour curve
• to hire additional workers the monopsonist has to raise the wage rate; since all existing employees will also receive the new higher wage, the marginal cost of hiring an additional worker is greater than the wage paid to the additional worker
• for example, suppose that a firm has 10 employees being paid \$100 each; to hire an additional worker, the firm must raise the wage rate, say to \$105; the marginal cost of adding the 11th worker is \$155, i.e., \$105 for the new worker and an additional \$5 for each of the 10 workers already employed
• the slope of the MC curve is steeper than the slope of the LS curve
• a profit-maximizing monopsonist will keep hiring workers up to the point where the marginal cost (MC) of hiring an additional worker is equal to the value of the marginal product of labour (VMPL), or equal to the marginal revenue product of labour (MRPL) if the monopsonist is also a monopolist
• in Figure 7-3, profit maximization occurs at point A, the intersection of the marginal cost (MC) of labour curve and the VMPL curve
• the monopsonist will hire Lm workers, pay each worker Wm, and make a profit equal to the profit triangle AED (the sum of VMPL – MC for each worker)
• the last worker hired by the monopsonist has a VMPLm > the wage (Wm)
• at the profit-maximizing wage Wm, there are vacancies equal to the horizontal distance BF in Figure 7-3; the profit-maximizing monopsonist does not fill these vacancies because that would require an increase in wages for all existing employees
• compared to perfect competition in the labour market (point C in Figure 7-3), the monopsonist hires fewer workers (Lm < Lc) and pays each worker a lower wage (Wm < Wc)

Minimum Wages in a Monpsonist Labour Market

• Figure 7-4 illustrates the effects of a minimum wage in a monopsony labour market  (8.0K) Figure 7-4
• the profit-maximizing position for a monopsonist is again point A (where MC = VMPL)
• the monopsonist hires Lm workers, pays each worker Wm, and makes a profit equal to the profit triangle AED
• now suppose that the government sets the minimum wage at Wmin
• the minimum wage replaces that segment of the original labour supply curve to the left of point J in Figure 7-4; the minimum wage law prevents firms from hiring labour at a wage less than Wmin
• the new kinked LS curve is the horizontal line HJ (at the minimum wage) and the original LS curve for wage rates greater than the minimum wage
• given a new kinked LS curve, there will be a new kinked marginal cost (MC) of hiring labour curve
• along the new HJ horizontal section of the LS curve, the marginal cost of hiring an additional worker is the minimum wage
• the HJ horizontal section of the LS curve is also the monopsonist's marginal cost (MC) of labour curve (for labour quantities up to Lj)
• if the firm hires more than Lj workers, it will have to pay all it's existing workers a wage higher than the minimum wage; the marginal cost for hiring an additional worker past point J is considerably higher than the minimum wage
• past point J the marginal cost curve corresponds to the original marginal cost curve
• the new 'minimum wage' marginal cost (MC) of labour curve is discontinuous at point J and is represented by the kinked line HJKN
• the monopsonist will maximize profits at point X, where the new kinked MC curve intersects the VMPL curve
• given a minimum wage Wmin, the monopsonist will hire Lmin workers and make a profit equal to the new profit triangle HEX
• imposing a minimum wage on a monopsonist has the following labour market effects:
• an increase in employees hired, from Lm to Lmin
• an increase in the wage rate paid to employees, from Wm to Wmin
• a decrease in monopsonist profits (in Figure 7-4, the new profit triangle HEX is smaller than the original profit triangle ADE
• in effect, the imposition of a minimum wage redistributes some of the monopsonist's profits to workers in the form of higher wages and/or increased employment levels
• if the government wanted to achieve the maximum positive wage effect, it should set the minimum wage at point A; the monopsonist would hire no new employees but would pay all of its existing workers a much higher wage (point A compared to point B)
• if the government wanted to achieve the maximum employment effect, it should set the minimum wage at point C (which corresponds to the competitive labour market outcome)
• the monopsonist would hire (Lc – Lm) additional employees and pay all workers a higher wage (Wc versus Wm)
• the AC segment of the VMPL curve represents a 'trade-off' curve for a government imposing a minimum wage on a monopsonist
• moving from A towards C increases the positive employment effect of the minimum wage but decreases the wage gain for all existing workers
• in conclusion, the imposition of a minimum wage in a labour market where employers have monopsony power can result in an increase in employment
• in a perfectly competitive labour market the imposition of a minimum wage will result in a decrease in employment
• the radically different employment effects of a minimum wage under different assumptions about the competitive structure of the labour market raises an obvious question: are there monopsonists in the real world, or only in labour economics textbooks?
• most firms have some monopsony power in the short run; most firms can lower the wage rate without immediately losing all of their workers and a firm may have to raise the wage rate to attract more workers in a local labour market
• however, most firms do not have monopsony power in the long run; if the firm cuts its wage rate, eventually its employees will move to other employers (in the long run workers are mobile)
• the obvious exception to the 'no monopsony in the long run' argument is a 'one company' town in an isolated labour market (for example, a mining company or pulp/paper mill in Northern Ontario)
• there are few other employers in the immediate area, existing workers are reluctant to leave their hometown, and new workers are reluctant to move to an isolated area (there is limited labour mobility)
• however, in most cases workers in the 'one company' have unionized and bargained for wage rates higher than the government would set as the minimum wage (see Chapter 15); the imposition of a minimum wage less than the union wage would have no effect on labour demand
• are there any examples of labour markets where employers have monopsony power and employ low wage workers?
• perhaps the McJob market, low-wage jobs in fast-food outlets
• unskilled, low-wage workers tend to be immobile: there are costs to moving and little expected gain from a move (what difference does it make if you flip hamburgers here or there?)
• a fast-food outlet may have a well defined local labour market (within walking distance or a short bus ride)
• it may also be the case that high welfare benefits reduce the net gain from working and the firm may have to offer a higher wage to attract welfare recipients
• given a local labour market with limited labour mobility of low skilled workers, the labour supply curve for McJobs may slope up; the firm may have to increase the wage rate (or offer recruitment bonuses) to attract additional workers
• under such circumstances, a minimum wage could increase employment levels
• for a discussion of the U.S. literature on the employment effects of minimum wages, including the Card and Krueger study of minimum wages and 'fast-food' jobs (see textbook page 215), click-on:
http://www.uvm.edu/~vlrs/doc/min_wage.htm