Lecture: Factor & Labor Markets
Lecture script · about 15–20 minutes spoken · Week 13
Opening
Picture a help-wanted sign taped to a bakery window. Behind the glass, 4 bakers are already working. The owner is asking a question you may face one day from either side of the counter: is one more worker worth hiring? A nursing student weighing a night-shift bonus asks a version of it too. So does an apprentice electrician deciding whether more training will pay off. They are all reading the same market, the labor market.
Here's where we are. In Weeks 3 and 4 you built the supply-and-demand model and learned to name the curve, the direction, and the new price and quantity. In Week 7 you met the minimum wage as a price floor in the labor market. In Week 9 you opened the bakery and read its production schedule. And in Week 10 you watched a firm that takes its price as given decide how much to make.
In this lecture the firm stops selling and starts buying, and what it buys is work. I'll show you why a bakery wants workers at all, how to put a dollar value on each one, and the rule that tells the owner when to stop hiring. Then we'll see what moves a firm along its demand for labor and what shifts it. We'll bring supply and demand back to find a wage, ask why wages differ, and finish with three debates about pay. Next week, in Week 14, we turn to costs that land on people outside a market.
1. Factor markets and derived demand
Start with a plain question. Why does a bakery hire bakers? Not because the owner enjoys company. It hires them because they bake bread, and it sells bread because buyers want it.
The inputs a firm uses have a name. The factors of production are the inputs firms use to make goods and services: labor, land, and capital. 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. Notice that the roles flip. Workers are the sellers. Firms are the buyers.
And the bakery's demand for bakers has a special name. 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. If bread stopped selling, the bakers would lose hours, however good they were at the job.
Pause and try this. If buyers suddenly lost interest in bread, what would happen to the bakery's demand for bakers?
Follow the chain from the customer back to the kitchen.
Here's the answer. It would fall, because the demand for bakers is derived from the demand for bread.
2. Reading the bakery's marginal product
Let's go back into the kitchen from Week 9. It's a classroom model built for this course, not a real bakery. With 0 to 6 workers in a fixed kitchen, the bakery bakes 0, 10, 25, 45, 60, 70, and 75 loaves a day.
You met marginal product in Week 9: the extra output from adding one more worker while everything else stays fixed. Here it is 10, 15, 20, 15, 10, and 5 loaves. The first few workers split the jobs, so each adds more than the one before. Then the kitchen gets crowded. One oven, the same counter, more elbows. From the fourth worker on, each one adds less.
That's the law of diminishing marginal returns, and it sets in with the fourth worker. The later workers aren't lazy. They're sharing a fixed kitchen.
Pause and try this. Which worker adds the most loaves, and which is the first worker to add fewer than the one before?
Read the six numbers again in your head.
Here's the answer. The third worker adds the most, 20 loaves, and the fourth is the first to add fewer, 15, so diminishing returns begin there.
3. The value of the marginal product
Here's the problem with loaves. The owner doesn't pay wages in bread. She pays in dollars. So she needs to know what each worker's extra loaves are worth.
The idea is everyday arithmetic. If a worker adds 20 loaves and each loaf sells for 4 dollars, that worker adds 80 dollars of bread a day. The term for it is the 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. Economists shorten it to VMPL, and it equals the price times the marginal product.
At 4 dollars a loaf, the six workers add 40, 60, 80, 60, 40, and 20 dollars of bread a day. Each number is the loaves from the last section times 4. That's what each worker is worth to the bakery.
Pause and try this. At 4 dollars a loaf, what is the fourth worker's 15 loaves worth?
Multiply the loaves by the price.
Here's the answer. It's worth 60 dollars, because 15 loaves at 4 dollars each comes to 60.
4. The hiring rule
Now the owner can answer the question in the window. You learned the rule in Week 8: do one more unit while what it adds is at least what it costs. Here the unit is a worker.
The hiring rule says 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. It applies the rule on the part of the schedule where marginal product is falling.
Say the daily wage is 50 dollars. The fourth worker adds 60 dollars, more than her wage. The fifth would add only 40, less than his wage. So the bakery hires 4. You can check it. With 4 workers the bakery sells 240 dollars of bread and pays 200 in wages, which leaves 40. With 3 or with 5 workers it leaves only 30. The rule found the best number without trying every row.
Pause and try this. At a 50-dollar wage, why doesn't the bakery hire the fifth worker?
Compare what that worker adds with what that worker costs.
Here's the answer. The fifth worker adds 40 dollars of bread but costs 50, so hiring that worker would lower what the bakery keeps.
5. The rising-part trap
Now look at the first worker. At 4 dollars a loaf, her value is only 40 dollars, and the wage is 50. Read the rule too fast and you'd say stop, hire no one.
That would be a mistake. With 1 worker, the bakery takes in 40 dollars and pays 50, a loss of 10. But the second, third, and fourth workers add 60, 80, and 60 dollars, each more than 50. With 4 workers the bakery keeps 40 dollars. The first worker alone doesn't pay for herself, but she makes the next three possible.
Here's an analogy. Think of the first few steps of a staircase that bends upward before it starts to come down. You don't judge the staircase by its bottom step. That's why the rule is applied where marginal product is falling. In Week 10 the workshop chose output where marginal cost was rising. Same idea, turned around.
Pause and try this. Should a firm stop hiring the first time a worker's value falls below the wage, even if marginal product is still rising?
Think about which part of the schedule the rule uses.
Here's the answer. No, because the rule is applied on the falling part of the schedule, and later workers may add more than the wage.
6. A wage change: moving along labor demand
Suppose the going wage in town falls to 30 dollars a day. Nothing else changes. Same kitchen, same oven, same 4 dollars a loaf.
At 30 dollars, the fifth worker's 40 dollars is now worth it. The sixth worker's 20 still isn't. So the bakery hires 5 instead of 4.
Line up those choices and you have a demand curve. 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's the falling part of the value schedule, which here is 80, 60, 40, and 20 dollars. Picture workers along the bottom and dollars up the side, with the curve stepping down through those four values. A flat line at the wage cuts across it.
The wage is the price of labor. And from Week 3 you know that a change in a thing's own price moves you along its demand curve. So a wage change is a movement along labor demand, not a shift.
Pause and try this. When the wage falls from 50 to 30 dollars, does the bakery's labor demand curve shift, or does the bakery move along it?
Ask which price changed.
Here's the answer. The bakery moves along it, because the wage is the price of labor and its value schedule hasn't changed.
7. Shifting labor demand
Now change a different price. Bread gets more popular and rises to 6 dollars a loaf. Every loaf each worker bakes is worth more.
The values become 60, 90, 120, 90, 60, and 30 dollars. Go back to the 50-dollar wage. The fifth worker now adds 60, more than 50, while the sixth adds 30, less. So at the same wage the bakery hires 5 instead of 4. With 5 workers it sells 420 dollars of bread and pays 250 in wages, which leaves 170.
Here the curve itself moved. Labor demand shifts right with the price of bread. That's derived demand at work: buyers wanted more bread, so the bakery wanted more bakers. Productivity does the same thing. A bigger oven or a faster method raises each worker's marginal product, and labor demand shifts right too.
Pause and try this. Bread rises from 4 to 6 dollars a loaf. Name the curve that moves and the direction.
Remember which price moves you along the curve.
Here's the answer. The bakery's labor demand curve shifts right, because the price of bread is a determinant of labor demand, not the wage.
8. Labor supply and the market wage
So far the wage came from outside. Where does it come from? From the whole market for a kind of work, and that market has two sides.
Think about lifeguards in a city in summer. At a low wage, few people want long days watching a pool in the sun. At a higher wage, more sign up. That's 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.
Where labor demand meets labor supply you find the market wage, the wage at which the quantity of labor employers want to hire equals the quantity workers offer. These are your curves from Weeks 3 and 4 with new labels. If more people earn a lifeguard certificate, labor supply shifts right, the wage falls, and the number employed rises. If the city opens new pools, labor demand shifts right, and both the wage and employment rise.
Pause and try this. More people train as lifeguards. Which curve shifts, which way, and what happens to the wage?
Use the Weeks 3 and 4 routine.
Here's the answer. Labor supply shifts right, so the market wage falls and the number of lifeguards employed rises.
9. Why wages differ
If every kind of work has its own market, why are some wages so much higher? Part of the reason is that the curves sit in different places for different jobs.
An apprentice electrician spends years training before she can wire a building alone. That builds human capital: the knowledge and skills a worker builds through education, training, and experience, which raise what the worker can produce. More human capital raises a worker's marginal product, and fewer people can do the job, so it tends to pay more.
Now picture a hospital at three in the morning. Few people would pick the night shift at day-shift pay. So the hospital offers more. That's a 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.
Economists also measure and debate other forces, such as union bargaining and discrimination. The course names them factually and grades no number for either.
Pause and try this. A night-shift nurse earns more than a day-shift nurse with the same training. Is that human capital or a compensating differential?
Ask what the extra pay is making up for.
Here's the answer. It's a compensating differential, because the extra pay makes up for the hours, not for extra skill.
10. Three debates, positive and 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 evidence can check it. A normative statement says what ought to be, and it rests on values.
Take the minimum wage. The model's 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, in 1994, found no fall in fast-food jobs in New Jersey after its increase. Neumark and Wascher, in 2000, used payroll records and found a fall. Card and Krueger's reply, also in 2000, used government employment records and again found no fall. Whether an increase is worth its costs is a normative judgment.
Unions and gig work follow the same pattern. Supporters of unions say they raise members' pay; critics say a wage above the market wage means fewer jobs. Supporters of app-based work point to flexible hours; critics point to missing benefits and unsteady pay. Each side makes claims a study could test, and each also makes value judgments.
Pause and try this. Is "unions are worth any jobs they cost" a positive or a normative statement?
Listen for a word that weighs one good thing against another.
Here's the answer. It's normative, because "worth" rests on how you weigh members' pay against lost jobs.
11. The classic wrong turns
Most slips this week aren't deep. They're a missing price, the wrong price, or the rule read on the wrong stretch.
The first slip compares loaves with dollars, asking whether 15 loaves beats a 50-dollar wage. Multiply by the price first. The second slip stops at the first worker on the rising part. Skip ahead to where marginal product falls. The third slip calls a wage change a shift. A new wage moves you along labor demand; a new bread price or better productivity shifts it.
Pause and try this. A classmate says a rise in the wage shifts the bakery's labor demand to the left. What's the fix?
Ask which price changed.
Here's the answer. A wage rise is a movement along the bakery's labor demand curve to fewer workers, because the wage is the price of labor.
Closing
Let me pull it together in the order we went. Labor demand is derived from the demand for what workers make. The bakery's marginal product, times the price of bread, gives the value of each worker. The hiring rule says hire while that value is at least the wage, where marginal product is falling, so at 50 dollars the bakery hires 4. A lower wage moves it along its labor demand curve, and a higher bread price shifts that curve right. Labor supply and labor demand together set the market wage. Human capital and compensating differentials help explain why wages differ. And in every pay debate, keep what the evidence shows apart from what you think ought to happen.
Next in this module come the Readings & Resources page, the lecture tutorial, the practice set, and the quiz. Next week, in Week 14, we look at externalities, public goods, and market failure.
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