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12
Unit 2 · The Logic of Competition

Factor Markets: Inputs, Capital, and Land

Where the future gets built

Chapter 12 ~ 30 min read

Two cities are growing. In one, more people want to live there, and the city builds: apartments above shops, townhomes near transit, taller buildings where the jobs are. In the other, more people want to live there, and the city says no: zoning fights, parking mandates, height limits, neighborhood vetoes, endless hearings. Both cities are getting the same signal from the market, but only one of them lets its land respond to it.

The second city isn't run by villains. The people who pack its hearings are mostly homeowners worried about traffic, parking, crowded schools, and streets they love changing shape. Their position has a name: NIMBYism, short for "not in my backyard." Hardly anyone at the hearing is against housing in general. They are against this building, on this block. Each objection may be reasonable on its own, but when objections like these add up across a whole city, almost nothing new gets built.

The people who pay for that are not in the room. They are the nurse who would have rented in the new building, the young family priced out to a long commute, the worker who never takes the better job across the country because there is nowhere she can afford to live. It's also worth noticing what the first city built. Instead of only adding houses at the edge of town, it put more homes on the same land, close to where people wanted to be.

Land isn't the only input that gets its value from somewhere else. A commercial pizza oven is worth a lot to a busy pizzeria. If the neighborhood empties out and customers stop coming, the oven is worth much less, even though it bakes just as well as before. What made it valuable was the demand for pizza.

Land, ovens, trucks, and buildings are inputs: the things firms buy so they can make the things we buy. A vacant lot can become housing, a warehouse can become a studio, and savings can become machines. The economy is not a museum of current uses; it is a system for discovering better ones. So what decides what a firm will pay for an input? And why do rents climb and climb in one city and stay within reach in the other?

The big picture
Inputs are priced the way everything is priced: at the margin. A firm will pay for a worker, a machine, or an acre up to what one more unit adds to its revenue, and that value comes from customers wanting what the input helps make. Capital adds one more price, the interest rate, because tools take time to pay off. And when the supply of an input can't grow, as with land in a good location, rising demand turns into rising rent. By the end you should be able to read a production table (marginal product, average product, and where diminishing returns set in), compute marginal revenue product, apply the hiring rule to any input, decide whether an investment beats the interest rate, and explain why rising demand for fixed land raises rent instead of acres.
Essential vocabulary — tap each card to reveal
Factor market
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A market for inputs (labor, capital, and land) in which firms are the buyers and households or resource owners are the sellers.
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Derived demand
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Demand for an input that comes from demand for the output it helps make. People want pizza, so pizzerias want ovens and cooks.
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Marginal revenue product (MRP)
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The extra revenue from one more unit of an input. For labor: MRP = MP × MR, which is MP × P for a firm in a competitive product market.
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Marginal resource cost (MRC)
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The extra cost of hiring one more unit of an input. For a firm that takes the market wage, MRC equals the wage.
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Interest rate
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The price of using money for a period of time, stated as a percentage per year. It is the cost of the funds tied up in capital.
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Economic rent
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Any payment to an input above what it would take to keep it in its current use. Land is the classic case, because its supply doesn't depend on its price.
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Also know — tap any term
rental rate The price of using an input for a period of time: rent on land, a lease payment on a machine. capital Produced goods used to make other goods: ovens, trucks, software, buildings. Not money. financial capital The money used to buy or rent physical capital: loans, savings, investors' funds. marginal product (MP) The extra output from one more unit of an input, holding the others fixed. production function The link between the inputs a firm uses and the most output it can make with them. A total product table is one written out. average product (AP) Output per worker: total product ÷ the number of workers. wage taker A firm too small to affect the market wage. It can hire as many workers as it wants at that wage. rate of return An investment's net gain (the revenue it brings in after operating costs, minus its cost) as a percentage of its cost. investment In economics, buying new capital: tools, machines, buildings. Not buying stocks. zoning Local rules about what may be built where: apartments or houses only, shops or homes only, tall or short. NIMBYism Short for "not in my backyard": local opposition to new building nearby. rent-seeking Spending effort to capture economic rent through political favors (license caps, tariffs, rules that keep rivals out) instead of by producing more.
Major concept 1 · The market behind the counter

Factor Markets and Derived Demand

Every market so far has been a market for things you buy: meals, apartments, phones. Behind each one sits a second set of markets, where firms do the buying. In a factor market, the roles flip: firms demand inputs, and households and other resource owners supply them. A bakery sells bread in the product market, but it hires bakers, leases ovens, rents a storefront, and borrows money in factor markets. Economists sort inputs into three families: labor (human effort and skill), capital (produced tools like ovens, trucks, and software), and land (locations and natural resources).

The price of an input is often a rental rate: the price of using it for a while. The wage is the rental rate on an hour of work; the lease payment is the rental rate on an oven; rent is the rental rate on a storefront. Even a firm that owns its oven pays a rental rate in the economist's sense, because the oven could have been leased to someone else or sold. That is the opportunity cost from Chapter 9, applied to inputs.

The most important idea in this chapter is that firms don't want inputs for their own sake. A pizzeria wants an oven because its customers want pizza. Demand for an input is derived demand: it comes from demand for the thing the input helps make. Demand for delivery drivers comes from demand for delivered meals; demand for downtown land comes from people wanting to live, work, and shop downtown; demand for nurses comes from patients. When customers want more of the output, firms want more of the inputs that make it. When customers stop wanting the output, demand for the workers who make it falls, no matter how hard those workers work.

Market for meals Meals Price of a meal ($) D₁ D₂ S P₁ Q₁ P₂ Q₂ Market for cooks Cooks hired Wage ($) D₁ D₂ S W₁ L₁ W₂ L₂
Fig 12.1 Derived demand. When demand for restaurant meals rises (left), restaurants want more cooks at every wage, so the demand for cooks shifts right (right). Both the wage and the number of cooks hired rise.
What to notice: the two graphs look alike, but the right-hand market is for an input. Its price is the wage, and its buyers are firms.
Quick check A coffee shop leases an espresso machine for $900 a month. Which market is this, and what is the $900? ▸
A factor market for capital. The $900 is the rental rate: the price of using the machine for a month.
Quick check Demand for electric vehicles rises. What happens to demand for battery engineers, and why? ▸
It rises. Demand for engineers is derived from demand for the cars they help build, so more demand for EVs means firms want more of the labor that makes them.
Retrieval practice In one or two sentences, contrast a product market with a factor market, and give an example of derived demand. ▸

In a product market, firms sell and households buy. In a factor market, firms buy inputs (labor, capital, land) from households and other resource owners. Example: more demand for meals raises demand for cooks, because the cooks' value comes from the meals they make.

Major concept 2 · What one more worker adds

Marginal Product and Marginal Revenue Product

How much will a firm pay for one more worker? As with every decision in this course, the answer is found at the margin. Rather than asking what its whole workforce is worth, the firm asks what the next worker would add.

That question has two parts. First, how much extra output does the next worker produce? That is the marginal product (MP). Second, how much extra revenue does the firm get from selling that output? Multiplying the two gives the worker's marginal revenue product (MRP):

MP = change in total product ÷ change in labor
MRP = MP × MR

For a firm in a perfectly competitive product market, MR = P, so MRP = MP × P. A smoothie shop sells each smoothie for $5. If the next worker adds 18 smoothies a day, that worker's MRP is 18 × $5 = $90 a day. (A firm with market power has to cut its price to sell more, so its MR is below the price and its MRP is smaller. That case comes in Unit 4.)

The smoothie shop: MP and MRP at a price of $5
Workers Total product MP P = MR MRP
0 0 — $5 —
1 20 20 $5 $100
2 38 18 $5 $90
3 52 14 $5 $70
4 62 10 $5 $50
5 68 6 $5 $30
6 70 2 $5 $10

Total product keeps rising as workers are added, but each new worker adds less than the one before. This is the diminishing marginal product from Chapter 9, now seen from the hiring side. The counter is the same size, there is one blender, and the sixth worker mostly waits for it. Since MRP is MP times a fixed price, MRP falls along with MP. That falling MRP is why a firm's demand for labor slopes downward.

Spiral · Chapter 9 · the full shape of a production table

Chapter 9 used diminishing marginal product to explain why costs eventually rise. This box shows the same idea in a table. A firm's production function is the link between its inputs and the most output they can make, and a total product table is a production function written out. The smoothie table starts where MP is already falling, but in many workplaces the first few hires raise each other's output: one takes orders while another bakes, and each gets faster by specializing. Here is a bakery with one oven.

A bakery with one oven
WorkersTotal product (loaves)MPAP
00——
1101010
2241412
3361212
444811
550610
65449
752−27.4

Diminishing returns set in after the second worker. MP rises from 10 to 14, then falls from the third worker on. "Sets in" means the first point where the next worker adds less than the one before.

MP can be negative. The seventh baker mostly gets in the way, and output falls from 54 to 52: MP = −2. Total product is still positive; only the change is negative. No firm would pay to hire that worker.

Average product is output per worker: AP = total product ÷ workers. With 5 bakers, AP = 50 ÷ 5 = 10 loaves. MP pulls AP the way one new grade pulls your average: when the next worker's MP is above AP, AP rises; when it is below, AP falls.

MP is the mirror image of marginal cost. If a baker costs $60 a day, each loaf the second baker adds costs $60 ÷ 14 ≈ $4.29, and each loaf the sixth baker adds costs $60 ÷ 4 = $15. When MP rises, MC falls; when MP falls, MC rises. MC = wage ÷ MP, which is the U-shape of marginal cost from Chapter 9, seen from the hiring side.

Worked example Find MP and MRP for the third worker

Hiring the third worker raises total product from 38 to 52 smoothies a day. Each smoothie sells for $5.

  1. MP = 52 − 38 = 14 smoothies.
  2. MRP = MP × P = 14 × $5 = $70.
The third worker adds $70 of revenue a day. Exam habit: find the change in total product first, then multiply by price. Multiplying total product by price gives total revenue, not MRP.
Quick check The price of a smoothie rises from $5 to $6. What is the third worker's MRP now? ▸
MP is still 14, so MRP = 14 × $6 = $84. A higher output price raises the value of every worker's marginal product, which is why output prices shift labor demand.
Retrieval practice Using the table, calculate the MP and MRP of the fifth worker, and explain why MRP falls as the shop hires more. ▸

Total product rises from 62 to 68, so MP = 6 and MRP = 6 × $5 = $30. MRP falls because marginal product falls: with a fixed counter and one blender, each added worker adds less output.

Major concept 3 · Hire until it stops paying

The Hiring Rule: MRP = MRC

Chapter 10 gave firms a rule for output: produce until MR = MC. Hiring follows the same logic. A worker is worth hiring if she adds at least as much revenue as she costs. The cost side is the marginal resource cost (MRC): the extra cost of hiring one more worker.

Hire if MRP > MRC. Stop before MRP < MRC. The profit-maximizing firm hires up to the point where MRP = MRC, or as close as it can get without hiring a worker who costs more than she adds.

Most firms are a small part of a large labor market. A smoothie shop can hire one more worker or ten without changing the going wage in its town. It is a wage taker, and for a wage taker, every extra worker costs exactly the market wage. So MRC = wage, and the rule becomes: hire until MRP equals the wage.

Worked example How many workers at a $50 wage?

Use the MRP column from the smoothie table: $100, $90, $70, $50, $30, $10. The market wage is $50 a day.

  1. Workers 1, 2, and 3 each add more than $50 (MRP of $100, $90, $70). Hire them.
  2. Worker 4 adds exactly $50, equal to the wage. Hire her, since she covers her cost.
  3. Worker 5 adds $30, less than the $50 she would cost. Stop.
Hire 4 workers. The fifth would lose the shop $20 a day.
Workers hired Dollars per day $0 $20 $40 $60 $80 $100 1 2 3 4 5 6 $100 $90 $70 $50 $30 $10 wage = MRC = $50 MRP = demand for labor hire 4
Fig 12.2 The hiring rule on a graph. Each dot is one worker's MRP from the smoothie table. The wage is a horizontal line because the shop is a wage taker. Workers whose MRP is at or above the line get hired; the shop stops at 4.
What to notice: the MRP curve is the firm's demand curve for labor. At any wage, the firm hires the number of workers where MRP meets that wage. Lower the wage to $30 and it hires 5.

The rule isn't just for labor. Every input gets the same test: hire, lease, or buy one more unit if its MRP is at least its price. Suppose a second oven would let a pizzeria sell 40 more pizzas a week at $12 each. The oven's MRP is 40 × $12 = $480 a week. If it can be leased for $300 a week, lease it. If the lease costs $550, don't. The same comparison decides whether a farmer rents another field or a store leases a bigger space. The next two concepts apply it to the two inputs that behave differently from labor: capital, which takes time to pay off, and land, which can't be made.

Spiral · Chapter 10 · one decision, two views

The hiring rule and Chapter 10's output rule are the same decision seen from two sides. The fourth smoothie worker costs $50 a day and adds 10 smoothies, so each of her smoothies costs $50 ÷ 10 = $5 to make. That is the marginal cost of a smoothie, and it equals the $5 price. Hiring until MRP = wage (P × MP = wage) is the same as producing until P = wage ÷ MP = MC. A firm that hires the right number of workers is automatically producing the right amount of output.

Quick check In the smoothie table, the wage rises from $50 to $80. How many workers does the shop hire? ▸
2 workers. Workers 1 and 2 have MRP of $100 and $90, above $80. Worker 3's MRP of $70 is below the wage.
Quick check Why is MRC equal to the wage for a smoothie shop, but not necessarily for a town's only hospital? ▸
The smoothie shop is a wage taker: it can hire more at the going wage. A hospital that is the only big employer of nurses in town may have to raise the wage to attract more nurses, so each extra nurse costs more than her own wage. That case, called monopsony, is in Chapter 13.
Retrieval practice State the hiring rule, and explain why a firm's MRP curve is its demand curve for labor. ▸

Hire until MRP = MRC; for a wage taker, until MRP = the wage. At any given wage, the firm hires workers until the last one's MRP equals that wage, so each point on the MRP curve gives the number of workers demanded at a wage. That is exactly what a demand curve is.

Major concept 4 · The price of time

Capital, Interest, and Investment

Capital is the input you have to wait for. An oven, a delivery van, or a warehouse has to be built before it can produce anything, and building it means using resources today that could have gone to something people would enjoy today. Someone has to save, giving up spending now, so that the economy can make tools that pay off later.

That waiting has a price: the interest rate, which is the price of using money for a period of time. It is the rental rate on funds. A firm that borrows $100,000 at 12% pays $12,000 a year for the use of it. A firm that uses its own $100,000 pays too, just less visibly: that money could have been lent out at 12%, so using it has an implicit cost of $12,000 a year. This is the opportunity cost of the firm's own funds, from Chapters 9 and 10. Accountants don't record it, but economists count it.

So a firm applies the same marginal test it uses for workers. An investment is worth making if what it adds beats what the money costs. Economists usually state both sides as percentages. The rate of return is the project's net gain as a percentage of what it costs to buy. The net gain is the revenue the project brings in after its operating costs, minus the cost of the project itself: a $100,000 project that brings in $120,000 nets $20,000, a 20% return. If that return is at least the interest rate, invest. If not, the money does better somewhere else.

One year, six possible projects (each costs $100,000 and is used up after a year)
Project Cost Revenue it adds, after operating costs Rate of return
A $100,000 $120,000 20%
B $100,000 $116,000 16%
C $100,000 $113,000 13%
D $100,000 $110,000 10%
E $100,000 $107,000 7%
F $100,000 $104,000 4%
Worked example Should the firm fund project C?

Project C costs $100,000 and adds $113,000 of revenue, after operating costs, before it wears out. The interest rate is 12%.

  1. Net gain from the project: $113,000 − $100,000 = $13,000, a 13% return.
  2. Cost of the funds: 12% of $100,000 = $12,000.
  3. The return ($13,000) beats the cost of the money ($12,000).
Fund it, barely. At the same 12% the firm funds A, B, and C, and skips D, E, and F. If the interest rate rose to 15%, C would no longer pay, and the firm would fund only A and B.
Projects, best return first Rate of return (%) 0% 4% 8% 12% 16% 20% 24% A B C D E F 20% 16% 13% 10% 7% 4% interest rate = 12% demand for capital fund 3
Fig 12.3 Ranking projects by return gives the firm's demand for capital. It funds every project whose return is at least the interest rate: here A, B, and C.
What to notice: this is the hiring rule again. MRP has become the rate of return, and the wage has become the interest rate. A higher interest rate means fewer projects pass the test, so less investment.
Common misconception"Capital means money." ▸

In everyday speech, a business "raising capital" is raising money. In economics, capital means produced tools: the oven, the forklift, the delivery van, the spreadsheet software. The money used to buy them is financial capital.

The distinction matters because only one of them makes pizza. A firm can have plenty of money and no ovens, and its output is zero. The interest rate is the price of financial capital; the rate of return measures what the physical capital adds.

Capital also does something for every other input. A worker with a backhoe moves more dirt in an hour than a worker with a shovel; a nurse with better diagnostic equipment helps more patients; an accountant with good software closes the books in a day instead of a week. Better tools raise workers' marginal product, and so their MRP. That is a large part of why an hour of work pays so much more in some countries than in others: workers there have far more capital and better technology to work with. Over the long run, saving and investment are how wages rise.

Rules of business success · Rule #6: give your people better tools

The surest way to afford higher pay is to raise what each hour produces. Invest in tools, training, and processes that make your people more productive. A firm that competes for workers by making them more valuable keeps the good ones.

Quick check The interest rate falls from 12% to 9%. Using the table, how many projects does the firm fund now? ▸
Four: A (20%), B (16%), C (13%), and D (10%) all beat 9%. E (7%) and F (4%) still don't. A lower interest rate raises the quantity of capital demanded.
Quick check A firm pays cash for a $50,000 machine instead of borrowing. Is the money free? ▸
No. The $50,000 could have earned interest somewhere else. At 8%, using it costs $4,000 a year in income the firm gives up, which is an opportunity cost even though no one sends a bill.
Quick check Demand for the firm's output falls, so every project would bring in less revenue. What happens to the demand for capital? ▸
It falls. Every project's return drops, so fewer clear the interest rate. Demand for capital is derived demand, just like demand for labor.
Retrieval practice State the investment rule, and explain why a higher interest rate reduces investment. ▸

Invest in a project if its rate of return is at least the interest rate. A higher interest rate raises the cost of the funds, so fewer projects clear the bar. The firm funds fewer of them, and the quantity of capital demanded falls.

Major concept 5 · They aren't making any more of it

Land, Economic Rent, and the Right to Build

An acre of Wyoming ranchland sells for a couple of thousand dollars. An acre in midtown Manhattan can sell for tens of millions. The soil is about the same; the difference is the location. You can build more ovens, trucks, and software, and you can train more nurses, but you cannot build another block of midtown Manhattan or another mile of California coastline. Land is different from most inputs because the supply of a particular location is fixed. Its supply curve is vertical: the same number of acres exist whether rent is high or low.

Chapter 4 showed what happens when a city caps rents: the shortage gets frozen in place. This chapter covers the other half of that story, which is why rents rise in the first place. When demand for a fixed location rises, the quantity can't respond, so all of the pressure goes into the price.

Quantity of land (acres) Rent per acre ($) D₁ D₂ S (fixed) R₁ R₂ Q̄ rent rises
Fig 12.4 Fixed land supply. Demand for a location rises from D₁ to D₂. The supply curve is vertical, so the quantity of land can't grow, and the whole increase in demand shows up as higher rent, from R₁ to R₂.
On the exam: with a vertical supply curve, a demand shift changes only the price. Don't draw the quantity increasing.

Economists call that extra payment economic rent, and it is one of the oldest ideas in economics. Adam Smith sorted income into three kinds: wages, earned by working; profit, earned by running a business and bearing its risks; and rent, earned by owning something scarce and letting others use it. Economists still use the word that way, and it covers far more than the check a tenant sends a landlord.

Economic rent is any payment to an input above what it would take to keep it in its current use. Take a downtown parking lot. Suppose the owner would keep renting out the spaces for as little as $500 a month, because that is what the land would earn in its next-best use. Downtown drivers compete for the spaces and pay $10,000 a month. The $9,500 above that $500 is economic rent. The owner receives it because the location is scarce and people want access to it, not because she works harder or spends more.

The idea isn't limited to land. You can train more basketball players, but you can't make another LeBron James, with his rare mix of size, skill, and fame. If he would keep playing for $100,000 a year, everything he is paid above that is economic rent. In short, economic rent is payment above opportunity cost, and it shows up wherever supply can't respond: a location, a rare talent, the Mona Lisa. When the supply curve is vertical (perfectly inelastic), every rise in demand becomes rent.

That makes rent ethically trickier than wages or profit. Most people see wages and profit as earned: you work, or you take a risk, and the payoff matches. Rent often comes from controlling something scarce instead, though that doesn't automatically make it unfair. The lot's owner may have paid a fair price for it, and the high rent is the signal that tells everyone how valuable that land is. But it does raise fair questions: who controls the scarce thing, how they came to control it, and whether the scarcity is natural or created.

Spiral · Chapter 11 · profit is a flare; rent stays lit

Chapter 11 showed that economic profit draws entry until it is gone. Rent isn't competed away like that, because entrants can't copy the scarce thing. Suppose a coffee shop on the busiest corner in town earns $3,000 a month more than identical shops a block away. Rivals can't open on that same corner, because there is only one. So when the lease comes up, the landlord can raise the rent by nearly $3,000 and the shop will still stay. The corner's advantage ends up as rent to whoever owns the corner, and the coffee shop is back to zero economic profit.

Sometimes people create scarcity on purpose. Rent-seeking is spending effort and money to capture rent through political favors instead of by producing more: lobbying for a cap on licenses, a tariff, or a rule written to keep rivals out. The firm that wins the favor gains, but nothing new gets made, and everything spent winning it is a cost to everyone else. This is the same protected barrier Chapter 11 called the chain across the river, viewed from the side of the people who lobby for it.

There is one catch in the Manhattan example. The land is fixed, but the space on it isn't. A city can't create another downtown lot, but it can allow a taller building on it, or apartments where only single-family homes were allowed, or a backyard cottage behind an existing house. Building up and building more densely increases the supply of housing and office space even when the land underneath can't grow.

Not just more housing · more homes per acre

Where people most want to live, the land near the jobs is the fixed input, so the only way to add homes there is to put more of them on each lot. Suppose a lot near downtown costs $1,000,000. If one house is built on it, that home carries $1,000,000 of land cost. With four townhomes, each carries $250,000, and with a 40-unit apartment building, each carries $25,000. The land costs the same; density spreads it across more households. Building outward at the edge of a metro area helps too, but it adds homes where land is cheap and far from the jobs, which means longer commutes and little relief where demand is highest. The housing debate is mostly a density debate.

That is where zoning comes in. Rules that ban apartments, require large lots, cap building heights, mandate parking, or make permits slow and uncertain all make housing supply steeper: less able to respond when more people want to live somewhere. This is the NIMBYism from the start of the chapter, written into law. Economists across the political spectrum broadly agree that tight limits on building raise housing costs.

One proposed fix is a right to build. In many cities, every project needs permission, and every hearing is another chance to say no. A right to build flips the default: unless there is a clear and significant reason to block it, an owner who meets written standards may build homes and sell or rent them. The argument rests on a distinction about rights. Neighbors have the right to buy and sell, to vote, and to speak at a hearing. What they lack, on this view, is a right to stop a deal between two other people, a landowner and the family who wants to live there, just because they would rather it didn't happen.

Building allowed Homes Rent ($) D₁ D₂ S P₁ Q₁ P₂ Q₂ Building restricted Homes Rent ($) D₁ D₂ S P₁ Q₁ P₂ Q₂
Fig 12.5 The same increase in housing demand in two cities. Where building is allowed (left), supply is flat: rent rises a little and many more homes get built. Where building is restricted (right), supply is steep: rent rises a lot and few homes get built.
What to notice: these are the two cities from the start of the chapter. Both get the same demand signal; only one lets its land respond.

None of this makes the local concerns silly. Traffic is real. So are crowded schools, strained pipes, and environmental worries, and so is the sense of loss when a familiar neighborhood changes. Economists don't claim that every project is a good one. Their objection is that blocking nearly all new building is an expensive and exclusionary way to handle those concerns. It protects people who already own homes, and pushes out renters, newcomers, young families, and workers who would have moved toward better jobs.

Policy rule · let land move

Allow more homes where people want to live, especially near jobs and transit. Let land shift from lower-valued uses to higher-valued ones instead of freezing today's uses by default. Solve real congestion and infrastructure problems directly, rather than treating them as reasons to ban housing. Remember who pays for scarcity: renters, newcomers, young families, and people who never get to move where the opportunity is. When in doubt, let them build.

Quick check A coastal town becomes more popular, but the buildable land is fixed. What happens to land rent and to the quantity of land? ▸
Rent rises; the quantity of land doesn't change. With a vertical supply curve, the higher demand shows up entirely in the price.
Quick check If physical land is fixed, how can a city increase its supply of housing? ▸
By allowing more housing on the same land: taller buildings, apartments, duplexes, backyard cottages. Physical land is fixed; usable space is not.
Quick check A $600,000 lot near a train station is zoned for one house. The city rezones it for 12 apartments. How much land cost does each home carry before and after? ▸
Before: $600,000 for one home. After: $600,000 ÷ 12 = $50,000 per home. Density doesn't make land cheaper; it spreads its cost across more households.
Retrieval practice Explain why restricting housing construction raises rents when demand rises, and define economic rent. ▸

Restrictions make housing supply steeper, so when demand rises, quantity can't expand much and the pressure goes mainly into higher rent. Economic rent is any payment to an input above what it would take to keep it in its current use; for fixed land, almost all of a rent increase is economic rent.

On the exam

The moves you can now make

Four questions at exam level: MRP from a table, the hiring rule, an investment decision, and a factor-market shift. Try each on paper first, then reveal.

Type A · calculate MP and MRP

A firm sells its output in a perfectly competitive market for $8. When it goes from 3 to 4 workers, total product rises from 54 to 64 units. Calculate the marginal product and marginal revenue product of the fourth worker.

Show model answer ▸
  1. MP = 64 − 54 = 10 units.
  2. MRP = MP × P = 10 × $8 = $80.
The fourth worker adds $80 of revenue.

Type B · the hiring rule

A wage-taking firm pays $80 a day. Its first six workers have MRPs of $140, $118, $96, $80, $62, and $35. How many workers should it hire? What if the wage falls to $60?

Show model answer ▸

At $80, hire 4: the first three have MRP above $80, the fourth's MRP equals $80, and the fifth's ($62) is below it. At $60, hire 5: the fifth worker's $62 now covers her cost, and the sixth's $35 doesn't. A lower wage moves the firm down its MRP curve, its demand curve for labor, to a larger quantity.

Type C · investment and the interest rate

A firm can fund any of five one-year projects. Each costs $50,000, and their expected rates of return are 18%, 14%, 11%, 8%, and 5%. The interest rate is 10%. Which projects should it fund? What changes if the interest rate rises to 12%, and why?

Show model answer ▸
  1. At 10%, fund every project whose return is at least 10%: the 18%, 14%, and 11% projects.
  2. At 12%, the 11% project no longer covers the cost of the funds. Fund only the 18% and 14% projects.
  3. The 11% project returns $5,500 on $50,000, but at 12% the money costs $6,000.
A higher interest rate raises the cost of funds, so fewer projects pass and the quantity of capital demanded falls.

Type D · derived demand and fixed supply

Demand for restaurant meals in a city rises sharply. Explain what happens to the demand for commercial ovens and to the wage of cooks. Then, using a correctly labeled graph, show what happens to the rent on downtown land, where restaurants want to locate.

Show model answer ▸

Demand for ovens and cooks is derived from demand for meals, so both demands shift right: restaurants want more ovens at every rental rate and more cooks at every wage, and the cooks' wage rises. For downtown land, put rent on the vertical axis and quantity of land on the horizontal. Supply is vertical because the land is fixed. Demand shifts right, so rent rises while the quantity of land stays the same. (Restaurant space can still grow if taller buildings are allowed.)

Capstone · free response

Put the moves together

AP-style free response · ~10 points · graph required · model answer and scoring below

A firm sells its output in a perfectly competitive product market at $6 per unit and hires workers in a perfectly competitive labor market at $72 per day. Its total product schedule is: 0 workers, 0 units; 1 worker, 18; 2 workers, 34; 3 workers, 46; 4 workers, 56; 5 workers, 63; 6 workers, 67.

  1. Calculate the marginal product and the marginal revenue product of the third worker. (2 pts)
  2. State the rule a profit-maximizing firm uses to decide how many workers to hire. (1 pt)
  3. How many workers will the firm hire? Explain, using MRP. (2 pts)
  4. Draw a correctly labeled graph for this firm showing its MRP curve, the wage, and the number of workers hired. (2 pts)
  5. Demand for the firm's product increases, raising its price. Explain what happens to the firm's demand for labor. (1 pt)
  6. The firm can lease a new machine that lets each worker produce more units per day. Explain what happens to the firm's MRP curve and to the number of workers it hires, assuming the wage stays at $72. (2 pts)
Reveal a full-credit response ▸

(a) MP = 46 − 34 = 12 units. MRP = 12 × $6 = $72.

(b) Hire until MRP = MRC. For a firm that takes the market wage, hire until MRP equals the wage.

(c) MRPs are $108, $96, $72, $60, $42, $24. Hire 3 workers: the third worker's MRP ($72) equals the wage, and the fourth worker's MRP ($60) is below it.

(d) Dollars on the vertical axis, workers on the horizontal. A downward-sloping MRP curve, a horizontal wage line at $72 (which is also MRC), and the quantity hired, 3, where they meet.

(e) Demand for labor is derived demand. A higher product price raises each worker's MRP (MP × P), so the MRP curve, the firm's labor demand, shifts right.

(f) The machine is capital that complements labor: it raises each worker's marginal product. Since MRP = MP × P, MRP rises at every quantity of labor, so the MRP curve shifts right. With the wage unchanged at $72, more workers now have MRP at or above the wage, so the firm hires more workers.

Workers hired Dollars per day $0 $20 $40 $60 $80 $100 $120 1 2 3 4 5 6 $108 $96 $72 $60 $42 $24 wage = MRC = $72 MRP = demand for labor hire 3
Model graph MRP falls from $108 to $24. The $72 wage line meets it at the third worker, so the firm hires 3.
Reveal the scoring rubric ▸
  • 1 pt (a) MP of the third worker = 12.
  • 1 pt (a) MRP of the third worker = $72.
  • 1 pt (b) Hire until MRP = MRC (or MRP = wage).
  • 1 pt (c) Hires 3 workers.
  • 1 pt (c) Explains: the third worker's MRP equals the wage, and the fourth's ($60) is below it.
  • 1 pt (d) Correctly labeled axes with a downward-sloping MRP curve.
  • 1 pt (d) Horizontal wage (MRC) line at $72, with 3 workers marked where it meets MRP.
  • 1 pt (e) MRP (labor demand) shifts right because a higher price raises MP × P.
  • 1 pt (f) MRP shifts right because the machine raises marginal product.
  • 1 pt (f) The firm hires more workers at the unchanged $72 wage.

Ten independent points. A wrong MRP in (a) doesn't cost the (c) points if the hiring decision follows correctly from it.

Reveal what loses points ▸
  • Conceptual Multiplying total product by price. That is total revenue, not MRP; MRP uses the change in output.
  • Precision Hiring the fourth worker because total product still rises. The test is MRP against the wage, not whether output grows.
  • Exam craft Saying the machine "replaces" workers by default. Capital that helps workers produce more raises their MRP; only capital that does their job for them reduces labor demand.
Market thesis

Markets price every input at the margin. A firm pays for a worker, a machine, or an acre up to what the next unit adds, interest puts a price on waiting for capital to pay off, and fixed land turns rising demand into rising rent.


If economists ruled the world…

we would let capital and land move to wherever they add the most value: far more room to build homes and offices where people want to be, and no subsidies propping up projects that can't beat the cost of the money.

Positive
what economists agree on
  • Demand for an input is derived from demand for the output it helps make.
  • Firms hire any input until MRP = MRC; for a wage taker, until MRP equals the wage.
  • A higher interest rate means fewer investments clear the bar, so less capital is demanded.
  • When supply is fixed, as with land, higher demand raises rent, not quantity.
Normative
what citizens must decide
  • How much say should current residents have over who gets to build and live nearby?
  • When land gains value because a city grows up around it, should the owner keep the whole gain, or should some of it be taxed?

Takeaways
In your life

Time has a price. Money you borrow costs interest, and money you hold could be earning it, so a big purchase or a plan should beat that bar before you commit to it.

In your work

Give your people better tools. Capital that makes each hour more productive raises MRP, and that is what makes higher pay possible.

Learn more
Khan Academy
Introduction to labor markets
~7 min · derived demand and the factor-market graph · Pairs with Concept 1 · Khan Academy

Khan Academy
A firm's marginal product revenue curve
from a total product table to MP, MRP, and the firm's demand for an input · Pairs with Concepts 2–3 · Khan Academy

Elasticity of Supply: Why Housing is Unaffordable
Elasticity of Supply: Why Housing is Unaffordable
why restricted housing supply turns demand into higher rents · Pairs with Concept 5 · Marginal Revolution University
Chapter 12 homework

Chapter

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