Chapter 3 The Demand For Labor

Objectives Consumers maximize utility subject to a budget constraint Firms maximize profits subject to cost and production constraints

Two types of demand to consider: Consumer’s demand for goods and services derived from utility maximization Firm’s demand for inputs (labor, capital) derived from profit maximization

We will make the following assumptions: All firms wish to maximize profits. Firms employ only two homogeneous inputs - Capital (K) and Labor (L). The only cost of labor is the hourly wage (W) The only cost of capital is the hourly rental cost (C) Perfectly competitive labor and product markets

What rule do firms follow to maximize profits? Marginal Revenue = Marginal Cost MR = MC

Why? Suppose that MR > MC. What should the firm do? The firm should expand output because the unit is worth more to the firm (in terms of additional revenue) than it costs the firm to produce Suppose that MC > MR. What should the firm do? The firm should reduce output because the last unit cost the firm more to produce than it is worth (in terms of additional revenue)

Since a firm can only expand or contract output by changing its level of inputs, we can think of the profit-maximization decision in terms of employment of inputs:

If the revenue generated by hiring an additional unit of an input > additional expense of hiring that unit, the firm should add that unit (because it will increase profit) If the revenue generated by hiring an additional unit of an input < additional expense of hiring that unit, the firm should reduce employment of that input (because that unit will decrease profit) If the revenue generated by hiring an additional unit of an input = additional expense of hiring that unit, no further changes in that input should be made (profits are maximized)

Short-Run Demand for Labor

Let’s do an example: The Short-Run Demand for Labor When Both the Product Market and the Labor Market Are Perfectly Competitive

Definition of the Short-Run: Capital is fixed at K* Note that the length of the short-run will vary across different firms

What happens to output as we add more labor? Marginal Product of Labor MPL = DQ/DL

Suppose we are running an apple farm Two inputs: capital (fixed at K*) and labor Apples sell in a competitive market for $4/bushel We hire apple pickers in a competitive labor market for $8/hour (This implies that the Marginal Expense [MEL] of hiring a worker is equal to $8.) HOW MANY WORKERS DO WE HIRE?

Output for Apple Farm L (#pickers) Q (bushels/hour) 0 0 1 7 2 12 3 15 0 0 1 7 2 12 3 15 4 17 5 18

Measuring Output of Labor L Q 0 0 1 7 2 12 3 15 4 17 5 18 MPL ---- 7 5 3 2 1

Law of Diminishing Marginal Returns after some point, each additional unit of labor will result in smaller increases in output eventually, marginal product can become negative (implying that hiring an additional unit of input will result in a decrease in output) this is true for any input in the short-run (because at least one other input is fixed)

How much is that additional output worth? We need to include information on the price of apples.

Valuing Output of Labor L Q MPL P 0 0 ---- 4 1 7 7 4 2 12 5 4 3 15 3 4 4 17 2 4 5 18 1 4

We can use information on MPL and P to calculate the Marginal Revenue Product of Labor (MRPL) MRPL is the additional revenue a firm earns by hiring an additional unit of labor MRPL = MPL X MR (general case) MRPL = MPL X P (competitive output market)

Valuing Output of Labor L Q MPL P 0 0 ---- 4 1 7 7 4 2 12 5 4 3 15 3 4 4 17 2 4 5 18 1 4 MRPL ---- 28 20 12 8 4

So, how many workers would we hire if we have to pay them a wage of $8/hour? L Q 0 0 1 7 2 12 3 15 4 17 5 18 MPL P MRPL ---- 4 ---- 7 4 28 5 4 20 3 4 12 2 4 8 1 4 4

We would hire workers up to the point where the last worker adds nothing to profits. That is where the additional revenue from hiring that worker equals the addition to total costs (“expense”) of hiring him/her The firm hires workers to the point where MRPL = MEL MRPL = MEL

Since the labor market is competitive (in our example): MEL = w Since the product market is competitive (in our example): MRPL = P * MPL

MRPL = MEL is the same thing as MRPL = w which is the same thing as P X MPL = w Dividing both sides by P, we get: MPL = w/P

Thus, we can express the profit-maximization decision in terms of the nominal wage: MRPL = w Or in terms of the real wage: MPL = w/P

Let’s do another example:

Competitive firm producing ping-pong balls that sell for $0. 50 each Competitive firm producing ping-pong balls that sell for $0.50 each. Hourly output: K* L Q 10 0 0 10 1 14 10 2 46 10 3 84 10 4 116 10 5 130 10 6 140

Let’s calculate MPL: K* L Q 10 0 0 10 1 14 10 2 46 10 3 84 10 4 116 10 0 0 10 1 14 10 2 46 10 3 84 10 4 116 10 5 130 10 6 140 MPL ---- 14 32 38 10

Now, let’s calculate MRPL. We need to include information on price: K* L Q MPL 10 0 0 ---- 10 1 14 14 10 2 46 32 10 3 84 38 10 4 116 32 10 5 130 14 10 6 140 10 P MRPL 0.50 ---- 0.50 7 0.50 16 0.50 19 0.50 5

If the wage is $7/hour, how many workers do we hire? K* L Q MPL 10 0 0 ---- 10 1 14 14 10 2 46 32 10 3 84 38 10 4 116 32 10 5 130 14 10 6 140 10 P MRPL 0.50 ---- 0.50 7 0.50 16 0.50 19 0.50 5

Let’s graph MRPL:

The firm’s demand for labor curve is the downward sloping portion of the MRPL curve.

The market demand for labor is a horizontal summation of the firms’ demand for labor.

Monopoly What happens to the firm’s short-run labor demand when the firm is a monopoly in its output market?

A monopoly has the same goal as a competitive firm A monopoly has the same goal as a competitive firm. It wishes to maximize profit. However, P  MR (indeed, MR < P at all output rates except Q=1) This means that we must use the general formula to calculate MRPL. MRPL = MR X MPL

For a monopoly, MR always lies below P. D Q MR

The rule to find the profit-maximizing level of labor hired is the same for all firms (whether the product market perfectly competitive or not): Hire labor up to the point where MRPL = w For a monopolist: MR X MPL = w For a competitive firm: P X MPL = w

Since MR < P for a monopolist: MRPL for a monopolist will be lower than MRPL for a competitive firm this implies that the monopolist’s demand for labor would lie below (or to the left) of the competitive firm’s demand for labor

Since the labor demand curve for a monopolist lies below and to the left of the labor demand curve for a competitive firm, then at any given wage the monopolist will hire less labor than the competitive firm.

Therefore, just as output is lower for a monopolist, so is the level of employment.

Let’s do an example: Suppose we own the only pizzeria in town Thus, we face the market demand curve for pizza (which is downward-sloping) We do, however, hire labor in a competitive labor market Let’s see how we would decide how many workers to hire

Output per day as the amount of labor varies: L Q 0 0 1 45 2 75 3 95 4 102 5 105 6 106

Let’s calculate MPL: L Q 0 0 1 45 2 75 3 95 4 102 5 105 6 106 MPL ---- 0 0 1 45 2 75 3 95 4 102 5 105 6 106 MPL ---- 45 30 20 7 3 1

Now let’s add information and calculate MR: L Q MPL 0 0 ---- 1 45 45 2 75 30 3 95 20 4 102 7 5 105 3 6 106 1 P TR MR ---- ---- ---- 4.75 213.75 4.75 4.50 337.50 4.13 4.30 408.50 3.55 4.15 423.30 2.11 4.05 425.25 0.67 4.00 424.00 -1.25

Now let’s calculate MRPL: L Q MPL P TR MR 0 0 ---- ---- ---- ---- 1 45 45 4.75 213.75 4.75 2 75 30 4.50 337.50 4.13 3 95 20 4.30 408.50 3.55 4 102 7 4.15 423.30 2.11 5 105 3 4.05 425.25 0.67 6 106 1 4.00 424.00 -1.25 MRPL ---- 213.75 123.90 71.00 14.77 2.00 -1.25

Again, we should be able to determine how many workers we would hire at different values of the daily wage L Q MPL P TR MR 0 0 ---- ---- ---- ---- 1 45 45 4.75 213.75 4.75 2 75 30 4.50 337.50 4.13 3 95 20 4.30 408.50 3.55 4 102 7 4.15 423.30 2.11 5 105 3 4.05 425.25 0.67 6 106 1 4.00 424.00 -1.25 MRPL ---- 213.75 123.90 71.00 14.77 2.00 -1.25

So far, we have been assuming that the labor market is competitive So far, we have been assuming that the labor market is competitive. But, what if it is not? Remember that profit-maximization requires the firm to hire labor until MRPL = MEL We have used the rule: MRPL = w because we have assumed a perfectly competitive labor market (MEL = w).

MONOPSONY exists when only one firm is the buyer of labor in a particular market Some examples may include coal mining and nursing

If the firm is the only buyer of labor, it faces the entire labor supply curve. No longer can the firm hire all of the labor it chooses at the going market wage Since the market labor supply curve is upward-sloping, the firm must raise the wage to hire additional workers Thus, when hiring an additional worker, labor costs rise in 2 parts: (a) the additional worker’s wages and (b) the increase in wages paid to all workers

Let’s do an example: Suppose we are running a coal mine which is the major employer of the region

The table below shows how wages paid (per day) increase as the firm hires additional workers 100 40 101 41 102 42 103 43 104 44 105 45 106 46

Let’s calculate Total Expenditure on Labor (TEL = w X L) 100 40 101 41 102 42 103 43 104 44 105 45 106 46 TEL 4000 4141 4284 4429 4576 4725 4876

Now, let’s calculate MEL: L w TEL 100 40 4000 101 41 4141 102 42 4284 103 43 4429 104 44 4576 105 45 4725 106 46 4876 MEL ---- 141 143 145 147 149 151

Note that MEL > w at every level of labor (for L>1) This implies that when we graph MEL , it will lie above the labor supply curve Let’s draw a graph showing a monopsony:

To maximize profit, the firm sets MRPL = MEL to find the quantity of labor they should hire. The wage rate that the firm must pay can be found by following the quantity of labor hired up to the supply curve.

Thus a monopsony hires less labor than firms in a competitive labor market and pays a lower wage.

Monopsony and MinimumWage Laws

Suppose the government sets the minimum wage at $10/hr Suppose the government sets the minimum wage at $10/hr. How will the monopsony react?

Minimum Wage

Minimum Wage

Minimum Wage

Let’s try another example where the minimum wage is set at $8/hr:

Minimum Wage

Minimum Wage

Minimum Wage

The government was able to force the monopsony to act as if it were operating in a competitive labor market by setting the minimum wage equal to the competitive market wage!

Long-Run Demand for Labor

In the long-run, employers can vary both capital and labor. This implies that changes in wages will bring about both a scale effect and a substitution effect.

Suppose a firm is currently maximizing profit. This means that MR = MC. An increase in the wage raises MC without affecting MR ( MR < MC). THE FIRM IS LOSING MONEY ON THE LAST UNITS PRODUCED. It can increase its profits by cutting back on production . This implies SCALING DOWN and reducing both K and L.

A SUBSTITUTION EFFECT also occurs. To maximize profits, the firm must minimize costs to produce whatever level of output it produces. This occurs when the last dollar the firm spends employing capital yields the same increment to output as the last dollar spent on labor This is sometimes referred to as the equi-marginal principle

Remember that C is the rental rate of capital Remember that C is the rental rate of capital. The firm will hire levels of K and L so that: MPL/w = MPK/C

What happens when the wage rises What happens when the wage rises? How does the firm adjust so that it returns to this equality?

When the wage increases: In the short-run the firm will cut back on labor hired. In the long-run, the firms will cut back on output (scale effect). This means lowering the level of both K and L. As L falls, MPL rises. As K falls, MPK rises. (But, keep in mind that MPL and MPK will both also be affected by the drop in each other.)

Eventually, the firm will keep adjusting K and L until the equi-marginal principle is satisfied.

We have been assuming that there are only two inputs in the production process (K and L). What if there are more than two?

When more than two inputs are used in production then the inputs may be either gross complements or gross substitutes.

Price of backhoes   Demand for shovels  Inputs are gross substitutes when the increase in the price of one input increases the demand for the other input, for example: Price of backhoes   Demand for shovels 

Price of computers   Demand for computer operators  Inputs are gross complements when an increase in the price of one input results in a decrease in the demand for the other input, for example: Price of computers   Demand for computer operators 

Keep in mind that labor can be divided into two categories -- Skilled and Unskilled.

Policy Application: Incidence of a Payroll Tax We are going to once again assume that the labor market is perfectly competitive.

The incidence of the payroll tax is unaffected by whether the tax is placed on the employer or whether it is placed on the employee.

Example One: Payroll Tax Placed on Employers

Demand shifts down by $2

wp Demand shifts down by $2 wr

Example Two: Payroll Tax Placed on Employees

Supply decreases by $2

Supply decreases by $2 wp wr

It does not matter who the tax is placed on! Employers end up paying the same amount and employees end up receiving the same amount.

Tax on employers: Supply decreases by $2

Tax on Employees: Demand shifts down by $2

wp wr

More inelastic supply or more elastic demand implies the higher the incidence of a payroll tax on the worker. The opposite would be true if we were concerned with the incidence of the tax on the employer.

Let’s look at elasticity of demand first.

DI

S0 DI

S1 S0 $3 tax paid by employees DI

S1 S0 wr $3 tax paid by employees wr DI

Now, let’s look at elasticity of supply.

w SI SE L

w SI SE D L

w SI $3 tax paid by employers SE D L

w SI $3 tax paid by employers SE wr wr D L

Figure 3A.1 A Production Function

Figure 3A.2 The Declining Marginal Productivity of Labor

Figure 3A. 3 Cost Minimization in the Production of Q Figure 3A.3 Cost Minimization in the Production of Q* (Wage = $10 per Hour; Price of a Unit of Capital = $20)

Figure 3A. 4 Cost Minimization in the Production of Q Figure 3A.4 Cost Minimization in the Production of Q* (Wage = $20 per Hour; Price of a Unit of Capital = $20)

Figure 3A.5 The Substitution and Scale Effects of a Wage Increase