Week 13 · Chapter

Chapter 13 — Factor & Labor Markets

Principles of Microeconomics Free sample edition

The module's primary reading · ~40–50 minutes · Objective 7 (analyze monopolistic competition and oligopoly, including a two-player game, the prisoner's dilemma, and Nash equilibrium, and analyze labor markets as derived demand with the value-of-the-marginal-product hiring rule), building on Objective 5 (describe a firm's short-run production and costs — total, marginal, and average product; diminishing marginal returns; and fixed, variable, total, average, and marginal cost — and distinguish accounting profit from economic profit) and Objective 2 (explain how demand and supply determine a market's equilibrium price and quantity, and predict how a shift in demand or supply changes them) · Read it first this week; the lecture, the slide deck, the tutorial, the quiz, and the Model Workshop all build on it.

In plain language

This week the firm stops selling and starts hiring. You will see why a business wants workers only because of what they make, which economists call a derived demand (a demand for an input that comes from the demand for the product). You will put a dollar value on each worker's extra output, the value of the marginal product of labor (the price of the product times the extra output one more worker makes), and use it to decide how many people a bakery should hire. Then you will bring back supply and demand to see how a market sets a wage, and why some jobs pay more than others. Last, you will meet three live debates about pay and learn to keep what the model predicts apart from what people think ought to happen.

Why you already care about this

Picture a help-wanted sign taped to a bakery window. The bakery bakes 60 loaves a day with 4 workers. Bread sells for 4 dollars a loaf. The daily wage is 50 dollars. Should the owner hire a fifth baker? Every one of those numbers matters, and by the end of this chapter you can answer the question in two lines.

You have probably asked a bigger version of the same question. Why does one job pay more than another? Why do night shifts sometimes pay extra? Why might more training raise what you earn? Until now this course has treated the firm as a seller of chairs, ferry tickets, or coffee. This week the firm becomes a buyer, and what it buys is your time.

By the end of this chapter you will be able to:

explain why the demand for labor is a derived demand;
compute the value of the marginal product of labor from a production schedule and a price;
apply the hiring rule to decide how many workers a firm hires at a given wage;
tell a movement along a labor demand curve from a shift of it, and name what shifts labor demand and labor supply;
explain the main sources of wage differences and label claims in a pay debate as positive or normative.

Carry this sentence with you: hire on what the bread sells for, not on loaf counts.

Where we are

Already covered: Weeks 3 and 4 built the supply-and-demand model and taught you to name the curve, the direction, and the new price and quantity. Week 7 met the minimum wage as a price floor in the labor market. Week 8 taught the margin. Week 9 built the bakery's production schedule and the law of diminishing marginal returns. Week 10 showed a price taker choosing output with P = MC.
This week: factor markets and derived demand; the value of the marginal product of labor; the hiring rule; movements along and shifts of labor demand; labor supply and the market wage; wage differentials; and three debates about pay.
How they connect: the bakery's marginal product from Week 9, multiplied by the price of bread, becomes its demand for workers, and the Weeks 3 and 4 model then sets the wage.
Where we're going next: this week begins a new unit on factor markets. Week 14 then turns to market failure, where some costs land on people outside the market.

Week 9 is the chapter this one leans on most. Recall its bakery: with 0 to 6 workers in a fixed kitchen, it bakes 0, 10, 25, 45, 60, 70, and 75 loaves a day. Recall too that marginal product is the extra output from one more worker, and that it eventually falls because the kitchen and oven stay the same size. Week 8's rule matters too: do one more unit while what it adds is at least what it costs.

1. Meet factor markets and derived demand

A bakery owner does not hire bakers because she enjoys having people around. She hires them because they bake bread, and she sells bread because buyers want it. If no one bought bread, no one would hire a baker.

That simple chain has a name. The things firms use to make goods are inputs, and economists sort them into three groups.

The factors of production are the inputs firms use to make goods and services: labor (people's work), land (natural resources), and capital (tools, machines, and buildings).
A factor market is a market in which firms buy the factors of production, such as the labor market, where employers buy workers' time and the wage is the price.
A derived demand is a demand for an input that comes from the demand for the output it helps make; a bakery wants bakers because buyers want bread.

In the markets of Weeks 3 to 12, households bought and firms sold. In a factor market the roles flip. Workers are the sellers, offering their time. Firms are the buyers. The wage is the price of an hour or a day of work. Everything you learned about demand and supply still applies; only the names of the buyers and sellers change.

Derived demand explains a pattern you may have noticed. When a product becomes popular, firms that make it start hiring. When buyers lose interest, those same firms cut hours. Workers do not suddenly become better or worse at their jobs. The demand for what they make moved, and the demand for their work moved with it.

Misconception check. Students often think a firm's demand for workers depends only on how hard the workers try. Effort matters, but the firm's demand starts with its customers. The cure: ask first what happened to the demand for the product. A bakery whose bread stops selling hires fewer bakers, however skilled they are.

2. Read the bakery again: marginal product

Go back into the bakery's kitchen. The first baker works alone. The second lets them split the jobs, one mixing and one shaping. The third tends the oven. After that the kitchen gets crowded, and each new baker has less room and less oven time.

This is Dataset K from Week 9, a classroom model built for this course, not real data. Write L for the number of workers and Q for loaves of bread per day. Week 9 defined marginal product as the extra output from adding one more unit of a variable input, such as one more worker. Write MP for the marginal product of labor, in loaves per day.

Worked example — the bakery's marginal product. Subtract each day's output from the next.

The first worker. 10 − 0 = 10 loaves.
The second worker. 25 − 10 = 15 loaves.
The third worker. 45 − 25 = 20 loaves.
The fourth worker. 60 − 45 = 15 loaves.
The fifth worker. 70 − 60 = 10 loaves.
The sixth worker. 75 − 70 = 5 loaves.

In words: the marginal product of each worker is 10, 15, 20, 15, 10, and 5 loaves. It rises while the first workers split the jobs. Diminishing marginal returns set in with the fourth worker, who adds 15 loaves instead of 20. That falling stretch will matter a great deal in Section 5.

Misconception check. Students often read the falling marginal product as a sign that later workers are lazy. Every worker here is equally good. The cure: marginal product falls because the kitchen is fixed, so each new worker shares the same oven with more people.

3. Turn loaves into dollars: the value of the marginal product

A bakery owner does not pay wages in loaves. She pays in dollars. To compare a worker with a wage, she needs to know what the worker's extra loaves are worth.

Here is the idea in everyday words. If a worker adds 20 loaves a day and each loaf sells for 4 dollars, that worker adds 80 dollars of bread a day. That is the most the owner could pay the worker and still break even on hiring that worker.

The value of the marginal product of labor is the dollar value of the extra output one more worker produces, found by multiplying the price of the output by the marginal product of labor (VMPL = P × MP).

Write P for the price of the output, in dollars per loaf, and VMPL for the value of the marginal product of labor, in dollars per day. The bakery sells bread at the market price, like the price taker of Week 10, so every extra loaf brings in the same 4 dollars.

Worked example — VMPL at 4 dollars a loaf. Multiply each worker's marginal product by the price.

The first worker. 4 × 10 = 40 dollars.
The second worker. 4 × 15 = 60 dollars.
The third worker. 4 × 20 = 80 dollars.
The fourth worker. 4 × 15 = 60 dollars.
The fifth worker. 4 × 10 = 40 dollars.
The sixth worker. 4 × 5 = 20 dollars.

In words: at 4 dollars a loaf, the six workers add 40, 60, 80, 60, 40, and 20 dollars of bread a day. That is what each worker is worth to the bakery. The third worker's 80 dollars versus the sixth worker's 20 is a 4-fold gap, the same as 20 loaves versus 5, because the price multiplies every row by the same 4.

In practice (your tools). In Google Sheets, type the workers 0 to 6 in cells A2 to A8 and the loaves 0 to 75 in cells B2 to B8. In cell C3 type =B3-B2 for marginal product and drag it down to C8. Put the price of bread, 4, in cell F1. In cell D3 type =$F$1*C3 for VMPL and drag it down to D8. Column D now reads 40, 60, 80, 60, 40, and 20.

Misconception check. Students often compare the wage with the marginal product itself, asking whether 15 loaves is more than 50 dollars. Loaves and dollars cannot be compared. The cure: multiply by the price first, so both sides are in dollars, and then compare.

4. Apply the hiring rule

Now the owner can answer the question from the bakery window. Week 8 said to do one more unit while what it adds is at least what it costs. Here the unit is a worker. What a worker adds is VMPL, and what a worker costs is the wage.

The hiring rule is that a firm that takes the wage as given keeps hiring workers while the value of the marginal product of labor is at least the wage, applied on the part of the schedule where marginal product is falling.

Write W for the wage, in dollars per worker per day. In symbols, the rule is VMPL ≥ W. The bakery takes the wage as given because it is one small employer among many in its town.

Worked example — hiring at a 50-dollar wage. Compare each worker's VMPL with the wage of 50 dollars, on the falling part of the schedule.

The fourth worker. VMPL is 60 dollars, at least 50, so the fourth worker adds more than she costs.
The fifth worker. VMPL is 40 dollars, less than 50, so the fifth worker would add 40 dollars of bread and cost 50.
The choice. The bakery hires L = 4 workers.

Check the choice by computing bread revenue minus the wage bill at the numbers of workers around it.

At 3 workers. Revenue is 4 × 45 = 180 dollars, and 180 − 150 = 30 dollars.
At 4 workers. Revenue is 4 × 60 = 240 dollars, and 240 − 200 = 40 dollars.
At 5 workers. Revenue is 4 × 70 = 280 dollars, and 280 − 250 = 30 dollars.

In words: at a 50-dollar wage the bakery hires 4 workers, because 4 workers leaves the most, 40 dollars, after paying wages. The fourth worker brings in 60 dollars of bread for a 50-dollar wage; the fifth would bring in only 40. So the owner should not hire that fifth baker.

An honesty note on the model: this check counts only bread revenue and wages. A real bakery also pays for flour and power, which this model leaves aside to keep the hiring logic visible. The rule still works, because those other costs do not change the comparison between one worker's VMPL and that worker's wage in this model.

Misconception check. Students often think a firm hires until marginal product equals the wage. That compares loaves with dollars. The cure: the rule is VMPL ≥ W, the value of the marginal product against the wage, both in dollars a day.

5. Avoid the rising-part trap

Look at the first worker again. At 4 dollars a loaf her VMPL is only 40 dollars, and the wage is 50. Read the rule too quickly and you might stop right there and hire no one.

Worked example — why the bakery does not stop at zero. Compare hiring 1 worker with hiring 4.

With 1 worker. Revenue is 40 dollars and the wage bill is 50, so revenue minus wages is 40 − 50 = −10 dollars.
With 4 workers. Revenue minus wages is 40 dollars, from Section 4.
What changed. The second, third, and fourth workers add 60, 80, and 60 dollars, each more than the 50-dollar wage.

In words: the first worker alone does not pay for herself, but she makes the next three workers possible, and together they leave the bakery 40 dollars ahead. That is why the rule is applied on the falling part of the schedule. On the rising part, where marginal product is still climbing, a low first value does not mean stop.

This is the same "rising part" idea you met in Week 10, turned around. There, the firm chose output where marginal cost was rising. Here, it chooses workers where marginal product is falling. Both say the same thing: look where the next unit is getting less worthwhile, not where it is still getting better.

Misconception check. Students often apply the hiring rule on the rising part of the marginal-product schedule and conclude the bakery should hire no one at 50 dollars. The cure: skip ahead to where marginal product is falling, then find the last worker whose VMPL is at least the wage.

6. Move along labor demand: a change in the wage

Suppose the town's going wage for bakers falls to 30 dollars a day, perhaps because more people move to town looking for work. The bakery's kitchen, its oven, and the price of bread have not changed. Only the wage has.

Worked example — hiring at a 30-dollar wage. Compare each worker's VMPL with 30 dollars, on the falling part.

The fifth worker. VMPL is 40 dollars, at least 30, so the fifth worker is now worth hiring.
The sixth worker. VMPL is 20 dollars, less than 30, so the sixth is not.
The choice. The bakery hires L = 5 workers, and revenue minus wages is 280 − 150 = 130 dollars.

In words: when the wage falls from 50 to 30 dollars, the bakery hires 5 workers instead of 4. A cheaper worker makes the fifth baker worth it, but not the sixth.

Line up those choices and you have a demand curve for labor.

A labor demand curve is the curve showing how many workers a firm or market wants to hire at each wage; for a firm that takes the wage as given it is the falling part of the value-of-the-marginal-product schedule, so a wage change moves along it.

For the bakery at 4 dollars a loaf, that falling part is 80, 60, 40, and 20 dollars for the third to sixth workers. Picture a graph with workers along the horizontal axis and dollars a day up the vertical axis. The labor demand curve steps down through those four values. A flat line at the wage cuts across it. At 50 dollars the line crosses between the fourth and fifth steps; at 30 dollars it crosses between the fifth and sixth.

A change in the wage is a movement along that curve, not a shift. The wage is the price of labor, and Week 3 taught you that a change in a good's own price moves you along its demand curve.

Misconception check. Students often draw a wage rise as a shift of labor demand to the left. The bakery does hire fewer workers when the wage rises, but its VMPL schedule has not moved. The cure: a change in the wage is a change in the quantity of labor demanded, a movement along the curve.

7. Shift labor demand: the price of bread and productivity

Now change something other than the wage. Suppose bread becomes more popular and its price rises to 6 dollars a loaf. Every loaf each worker bakes is now worth more.

Worked example — VMPL at 6 dollars a loaf. Multiply each marginal product by the new price.

Workers one to three. 6 × 10 = 60, 6 × 15 = 90, and 6 × 20 = 120 dollars.
Workers four to six. 6 × 15 = 90, 6 × 10 = 60, and 6 × 5 = 30 dollars.
Hiring at the same 50-dollar wage. The fifth worker's VMPL of 60 is at least 50 and the sixth worker's 30 is less than 50, so L = 5 workers.
The check. Revenue minus wages is 6 × 70 − 5 × 50 = 420 − 250 = 170 dollars.

In words: at the same 50-dollar wage the bakery hires 5 instead of 4, because the higher price of bread raised every worker's VMPL. Labor demand shifts right with the price of bread. This is derived demand in action: buyers wanted more bread, and the bakery wanted more bakers.

The price of the product is one thing that shifts labor demand. Productivity is the other. If the bakery buys a bigger oven or its workers learn a faster method, each worker's marginal product rises. At the same price of bread, VMPL rises too, and labor demand shifts right. A fall in the price of bread, or anything that lowers marginal product, shifts it left.

Name the curve, the direction, and the result every time. Here: the bakery's labor demand curve shifts right, and at a 50-dollar wage it hires 5 workers instead of 4.

Misconception check. Students often think a higher price of bread is a movement along the labor demand curve, since a price changed. The cure: the price that moves you along labor demand is the wage. The price of bread is a different price, a determinant of labor demand, so a change in it shifts the whole curve.

8. Bring back supply and demand: labor supply and the market wage

So far the wage arrived from outside, the way the market price of chairs arrived in Week 10. Now ask where the wage comes from. It comes from the whole market for a kind of work, and that market has two sides.

Picture the summer market for lifeguards in one city. At a low hourly wage, few people want to spend long days in the sun watching a pool. At a higher wage, more people sign up, and those already working offer more hours.

Labor supply is the relationship between the wage and the hours or number of workers people offer; it slopes up, and it shifts when the number of workers, pay in other jobs, tastes for work, or training changes.
The market wage is the wage at which the quantity of labor employers want to hire equals the quantity workers offer, found where labor demand meets labor supply.

These are the curves of Weeks 3 and 4, with new labels. The wage sits on the vertical axis. The quantity of labor sits on the horizontal axis. Labor demand, the sum of every employer's VMPL steps, slopes down. Labor supply slopes up. Where they cross you find the market wage and the number employed.

Worked example — two shifts in words. This is the Weeks 3 and 4 routine: name the curve, the direction, and the new wage and employment. No numbers are pinned for this market, so you reason with the directions alone.

More people earn a lifeguard certificate. More workers can do the job at every wage, so labor supply shifts right. The market wage falls and the number of lifeguards employed rises.
The city opens two new public pools. Employers want more lifeguards at every wage, so labor demand shifts right. The market wage rises and the number employed rises.

In words: a shift of labor supply to the right lowers the wage and raises employment, and a shift of labor demand to the right raises both. That is the same comparative-statics pattern you learned for any good, read in the labor market.

A caveat on the model: the lifeguard market is a classroom sketch, not a description of any real city. It shows the direction of each change. It does not tell you how large the change would be, which depends on how steep the real curves are.

Misconception check. Students often think a rise in the wage shifts labor supply to the right, since more people want to work. The cure: a change in the wage moves you along labor supply. Labor supply shifts only when something other than the wage changes, such as the number of trained workers or pay in other jobs.

9. Explain why wages differ

If every market had its own wage set by supply and demand, why are some wages so much higher than others? Part of the reason is that the curves sit in different places for different jobs. Economists have names for the forces that put them there.

A wage differential is a difference in pay between jobs or between workers, explained by forces such as human capital, compensating differentials, union bargaining, and discrimination, which economists measure and debate.
Human capital is the knowledge and skills a worker builds through education, training, and experience, which raise what the worker can produce.
A compensating differential is extra pay a job offers to make up for a feature workers dislike, such as risk, unpleasant tasks, or night and weekend hours.

Take human capital first. An apprentice electrician spends years in training before she can wire a building on her own. That training raises her marginal product, so it raises her VMPL and the demand for her work. Fewer people can do the job, so labor supply is smaller too. Both forces point the same way: jobs that need more human capital tend to pay more.

Now a compensating differential. A hospital needs nurses at three in the morning as well as at noon. Few people would choose the night shift at the same pay as the day shift, so labor supply for nights is smaller. The hospital offers extra pay to fill it. The extra pay is not a reward for working harder. It makes up for the hours.

Economists also measure and debate other forces. Union bargaining can raise the wages of a union's members, and economists disagree about how large that effect is and what it does to the number of jobs. Economists also measure gaps in pay between groups of workers and debate how much of a gap comes from differences in jobs, hours, and training, and how much from discrimination. The course names these forces factually and grades no number for any of them.

Pause and reflect — choose one. Pick either prompt; they count the same.

(a) Think of a job you have done or would like to do. In two sentences, name one skill it needs that took training to build, and say whether you think that training raises the pay.
(b) Think of a job with a feature many people dislike, such as early hours, heavy lifting, or travel. In two sentences, say whether you would expect it to pay more than a similar job without that feature, and why.

Misconception check. Students often think a higher wage always means the worker is more skilled. Sometimes it does, through human capital. The cure: a higher wage can also be a compensating differential, paying for the hours or the risk rather than the skill, so ask which force is at work.

10. Weigh three debates: positive versus normative

Pay is personal, so arguments about it get heated. The tool that keeps them clear is the one from Week 1. A positive statement says what is, and it can be checked against evidence. A normative statement says what ought to be, and it rests on values. Here are three debates, each with both sides at full strength.

The minimum wage. Week 7 treated it as a price floor in the labor market. The model's positive prediction is plain: a binding minimum raises the wage of workers who keep their jobs and lowers the quantity of labor employed. The debate is about size. Card and Krueger (1994) compared fast-food jobs in New Jersey, after its 1992 increase, with neighboring Pennsylvania and found no fall. Neumark and Wascher (2000) reworked the question with payroll records and found a fall. Card and Krueger's reply (2000), using Bureau of Labor Statistics records, again found no fall. One reason some economists expect small effects is that an employer with few local rivals may set wages below workers' VMPL, a case beyond this course. Whether a given increase is worth its costs is a normative judgment.

Unions. Supporters argue that unions raise their members' pay and give workers a stronger voice in setting hours and safety rules. Critics argue that a wage set above the market wage leads employers to hire fewer workers, the same prediction as any binding floor. Both are positive claims about effects, and economists measure them and disagree about their size. Whether the gains to members outweigh any lost jobs is a normative question.

Gig work. Many people now drive, deliver, or do tasks through apps, choosing their own hours. One side argues that this flexibility is a real benefit workers value, the way a compensating differential works in reverse: some workers accept less steady pay in exchange for control over their time. The other side argues that gig workers often go without the benefits and steady hours that employees receive. Each side makes claims a study could test, about pay, hours, and how workers choose. How to weigh flexibility against security is a normative choice.

Worked example — labeling claims in a pay debate. Sort four sentences.

"A binding minimum wage lowers the quantity of labor employed in the simple competitive model." Positive: it is the model's prediction.
"Card and Krueger (1994) found no fall in fast-food jobs in New Jersey." Positive: it reports what a study found, and others can check it.
"Unions are worth any jobs they cost." Normative: "worth" rests on how you weigh members' pay against lost jobs.
"Gig workers should have the same benefits as employees." Normative: "should" is a value judgment.

In words: the first two sentences can be checked against a model or a study, and the last two cannot be settled by evidence alone. The course grades whether you can tell them apart, never which side you take.

Pause and reflect — choose one. Pick either prompt; they count the same.

(a) Pick one of the three debates. In two sentences, write the strongest positive claim on each side, without saying which side you agree with.
(b) Pick one of the three debates. In two sentences, write one normative statement a supporter might make and one a critic might make, and label each.

Misconception check. Students often think that because economists disagree about the minimum wage, they disagree about what a binding floor does in the model. They do not. The cure: the disagreement is about how large the effect is in real markets, which is a positive question about evidence; whether the trade-off is worth it is a separate, normative question.

11. Check the classic wrong turns

Most mistakes this week are not deep confusions. They are a missing price, the wrong price, or the rule read on the wrong stretch of the schedule. A short routine catches them.

Step one: put workers in dollars. Multiply marginal product by the price of the output to get VMPL.
Step two: find the falling part. Look where marginal product is falling, not where it is still rising.
Step three: apply the rule. Hire the last worker whose VMPL is at least the wage.
Step four: what changed? A new wage moves along labor demand; a new output price or productivity shifts it.
Step five: which side of the market? Training and the number of workers move labor supply; product prices and productivity move labor demand.

Worked example — checking a classmate's work. A classmate writes: "At a 50-dollar wage the bakery compares 15 loaves with 50 dollars. The first worker adds only 40 dollars, so it hires no one. And if the wage rose, labor demand would shift left."

The loaves claim. Loaves must be turned into dollars first: the fourth worker's 15 loaves at 4 dollars are worth 4 × 15 = 60 dollars.
The zero-workers claim. The rule is read on the falling part, where the fourth worker's VMPL of 60 is at least 50 and the fifth worker's 40 is less, so the bakery hires 4.
The shift claim. A rise in the wage is a movement along the bakery's labor demand curve, not a shift.

In words: the corrected statement is "at a 50-dollar wage the bakery hires 4 workers, where the falling VMPL schedule passes the wage, and a higher wage would move it along its labor demand curve to fewer workers."

Misconception check. Students often treat any change that lowers hiring as a shift of labor demand. The cure: ask which price changed. If it was the wage, the firm moved along its labor demand curve. If it was the price of the product, or productivity changed, the curve itself shifted.

Key terms

Factors of production — The inputs firms use to make goods and services: labor (people's work), land (natural resources), and capital (tools, machines, and buildings). (first used: 1. Meet factor markets and derived demand)
Factor market — A market in which firms buy the factors of production, such as the labor market, where employers buy workers' time and the wage is the price. (first used: 1. Meet factor markets and derived demand)
Derived demand — A demand for an input that comes from the demand for the output it helps make; a bakery wants bakers because buyers want bread. (first used: 1. Meet factor markets and derived demand)
Value of the marginal product of labor — The dollar value of the extra output one more worker produces, found by multiplying the price of the output by the marginal product of labor (VMPL = P × MP). (first used: 3. Turn loaves into dollars: the value of the marginal product)
Hiring rule — A firm that takes the wage as given keeps hiring workers while the value of the marginal product of labor is at least the wage, applied on the part of the schedule where marginal product is falling. (first used: 4. Apply the hiring rule)
Labor demand curve — The curve showing how many workers a firm or market wants to hire at each wage; for a firm that takes the wage as given it is the falling part of the value-of-the-marginal-product schedule, so a wage change moves along it. (first used: 6. Move along labor demand: a change in the wage)
Labor supply — The relationship between the wage and the hours or number of workers people offer; it slopes up, and it shifts when the number of workers, pay in other jobs, tastes for work, or training changes. (first used: 8. Bring back supply and demand: labor supply and the market wage)
Market wage — The wage at which the quantity of labor employers want to hire equals the quantity workers offer, found where labor demand meets labor supply. (first used: 8. Bring back supply and demand: labor supply and the market wage)
Wage differential — A difference in pay between jobs or between workers, explained by forces such as human capital, compensating differentials, union bargaining, and discrimination, which economists measure and debate. (first used: 9. Explain why wages differ)
Human capital — The knowledge and skills a worker builds through education, training, and experience, which raise what the worker can produce. (first used: 9. Explain why wages differ)
Compensating differential — Extra pay a job offers to make up for a feature workers dislike, such as risk, unpleasant tasks, or night and weekend hours. (first used: 9. Explain why wages differ)

Summary

Labor demand is derived from the demand for the product workers make.
VMPL is the output price times the marginal product of labor.
Hire while VMPL is at least the wage, where marginal product is falling.
A change in the wage moves a firm along its labor demand curve.
A change in the output price or in productivity shifts labor demand.
Labor supply slopes up; the market wage sits where labor demand meets labor supply.
Human capital and compensating differentials help explain why wages differ.
In pay debates, keep positive claims apart from normative ones.

Check your understanding

Work these before looking at the answers — they are ungraded, and the answers (with reasoning) are at the bottom of the page.

A neighborhood car wash (an illustrative case) charges 8 dollars a wash and takes that price as given. With 0 to 5 workers it washes 0, 12, 27, 39, 48, and 54 cars a day. Compute each worker's marginal product and VMPL.
Using the car wash's numbers, decide how many workers it hires at a daily wage of 80 dollars, and then at a daily wage of 60 dollars. Say whether the change is a movement along labor demand or a shift of it.
The price of a wash rises to 10 dollars, and the wage stays at 80 dollars. Compute the new VMPL for each worker, decide how many workers the car wash hires, and name what happened to its labor demand curve.
In one town, a new training program certifies many more home health aides. Name the curve that shifts and its direction, and say what happens to the market wage and to employment. Then label this sentence positive or normative: "The town should pay for the training program."

Answers (worked reasoning — read after attempting)

Marginal product subtracts each day's washes from the next: 12 − 0 = 12, 27 − 12 = 15, 39 − 27 = 12, 48 − 39 = 9, and 54 − 48 = 6 cars. VMPL multiplies each by 8 dollars: 8 × 12 = 96, 8 × 15 = 120, 8 × 12 = 96, 8 × 9 = 72, and 8 × 6 = 48 dollars. Marginal product rises to the second worker and falls from the third on.
At 80 dollars, read the falling part: the third worker's VMPL of 96 is at least 80 and the fourth worker's 72 is less, so the car wash hires 3 workers. At 60 dollars, the fourth worker's 72 is at least 60 and the fifth worker's 48 is less, so it hires 4. Only the wage changed, so this is a movement along the car wash's labor demand curve.
At 10 dollars a wash, VMPL is 10 × 12 = 120, 10 × 15 = 150, 10 × 12 = 120, 10 × 9 = 90, and 10 × 6 = 60 dollars. At an 80-dollar wage the fourth worker's 90 is at least 80 and the fifth worker's 60 is less, so the car wash hires 4 instead of 3. The price of the product rose, so labor demand shifted right. Calling this a movement along the curve would be the classic slip.
More certified aides means more workers can do the job at every wage, so labor supply shifts right. The market wage falls and the number of aides employed rises. "The town should pay for the training program" is normative, because "should" rests on a value judgment about how to spend the town's money.

Next up in this module: the Readings & Resources page, the lecture tutorial, the practice set, and the quiz — and next week the externality model shows what happens when a market's costs fall on people outside it.

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