ARE 201 · Unit 5

Consumer & Producer Surplus

Measuring who gains from a market—and by how much

Before we begin

Announcements

SEP 13

Quiz deadline

Unit 4 Quiz due

SEP 18

Exam

Units 1–5

The exam covers all material from Units 1 through 5.

SEP 20

Quiz deadline

Unit 5 Quiz due

Bridge from the Unit 4 class market

You already computed surplus—we just hadn’t named it yet

Your buyer payoff was

Value − transaction price

Economists call this consumer surplus.

Your seller payoff was

Transaction price − cost

Economists call this producer surplus.

What you were doing

Every bid and ask you placed was an attempt to capture more of the gains from one trade.

Organic strawberries in a market container — Photo: Suzette via Wikimedia Commons · CC BY 2.0 · cropped

Today we scale that idea up from one trader to the whole market.

Before any theory · write one number down

What would you pay for this?

The collectible figure being auctioned in class

Write down the most you would pay for it rather than walk away with nothing.

One numberNot a range. Not “it depends.”

Keep it privateDon’t call it out or change it once you hear someone else’s.

Be honestThe most you’d actually pay—not what you think it’s worth to somebody else.

Four volunteersType the numbers you hear. They save in this browser.

Student 1

$

Student 2

$

Student 3

$

Student 4

$

Four people, four different numbers, one identical toy. Nobody was wrong. That number you wrote down already has a name in economics—and everything in Unit 5 is built out of it.

Willingness to pay · familiar examples

WTP changes across people and situations

🏈

NC State–UNC football ticket

Example maximums

Die-hard Wolfpack fan$120

Friend tagging along$25

Why different? Preferences and expected enjoyment.

🚗

A ride home from RDU

Example maximums

1 a.m. after a flight delay$45

Daytime with a bus option$15

Why different? Urgency and available alternatives.

🧸

A limited-edition Jellycat

Example maximums

Enthusiastic collector$70

Someone who just needs a gift$12

Why different? Tastes and the value of owning this version.

Takeaway: WTP is personal and situational—not the seller’s price or a universal “true value.”

The buyer side · naming what you just wrote

That number you wrote down is your willingness to pay

Willingness to pay (WTP): the maximum amount a buyer would hand over for one unit of a good rather than go without it.

It is a ceiling, not a plan

A buyer with WTP = $22 does not want to pay $22. She will pay as little as the market makes her pay.

It is measured per unit

One toy. One flat of strawberries. WTP is always about one more unit, holding everything else fixed.

It is a number we can add up

Because WTP is in dollars, we can compare buyers and sum across a whole market.

Keep this in mind: WTP reflects both how much you want it and what you can afford. Two buyers with identical tastes but different incomes will report different WTP.

We will return to that caveat next class, when we ask whether an efficient outcome is also a fair one.

Predict before we build

Four buyers, one price: who actually buys?

Buyer	Willingness to pay
Ana	$22
Ben	$18
Carlos	$15
Dee	$11

One flat of strawberries. Each buyer wants at most one flat.

The market price is $14 per flat.

Who buys, and what is quantity demanded?

Commit to an answer, then say out loud what rule you used.

Individual WTP → market demand

Stack the buyers from highest WTP down and you have drawn demand

If the price is…	Buyers who purchase	Q_d
above $22	nobody	0
$18–$22	Ana	1
$15–$18	+ Ben	2
$11–$15	+ Carlos	3
below $11	+ Dee	4

Lower the price and you do not persuade Ana to buy more—you recruit the next buyer.

The key reading rule · LO 5.1

The height of the demand curve is the marginal buyer’s WTP

At any quantity Q, the height of the demand curve is the willingness to pay of the marginal buyer—the last buyer still in the market at that price. Nudge the price up and she is the first one out.

Read it at Q = 3

The third flat is bought by Carlos, whose WTP is $15. So the demand curve sits at $15 when Q = 3.

Raise the price above $15 and Carlos is the first to walk away.

This is why surplus is an area and not just a number. Every unit along the curve carries its own dollar value.

Consumer surplus

Consumer surplus is what you would have paid minus what you did pay

CS = WTP − P

At $14, Ana pays the same $14 as everyone else—but she would have paid $22. That $8 gap is hers to keep.

Stack one rectangle per buyer and the shaded region is the market’s consumer surplus: the area below demand and above the price.

Dee is not in the shaded region at all. A buyer who does not trade earns a surplus of zero—never a negative number.

Method 1 of 2 · from a table · LO 5.2

Compute consumer surplus buyer by buyer, then add

Buyer	Willingness to pay	Price paid	Buys?	Consumer surplus
Ana	$22	$14	yes	$8
Ben	$18	$14	yes	$4
Carlos	$15	$14	yes	$1
Dee	$11	—	no	$0
Market	Q_d = 3 flats			CS = $13

Ask the class for Ana’s number before you click.

Two traps to name out loud: Dee’s surplus is $0, not −$3. And Carlos still counts—his surplus is small, but it is real.

The seller side—same logic, mirrored

Everything you just learned runs backwards for sellers

Buyers

Willingness to pay — the most a buyer would pay.

The height of demand is the WTP of the last buyer still willing to trade.

A buyer trades only if WTP ≥ P.

CS = WTP − P

Sellers

Cost — the value of everything a seller gives up to produce one unit. This is opportunity cost.

The height of supply is the cost of the last seller still willing to trade.

A seller trades only if P ≥ cost.

PS = P − Cost

Producer surplus is what a seller collects above what the unit cost to produce—the area above the supply curve and below the price.

Cost here is not just cash out the door. A grower who plants strawberries gives up the blueberries that land could have grown.

Method 1 continued · the seller side · LO 5.2

Four farms, the same $14, and the market clears

Farm	Cost	Sells?	Producer surplus
Farm W	$5	yes	$9
Farm X	$9	yes	$5
Farm Y	$12	yes	$2
Farm Z	$16	no	$0
Market	Q_s = 3 flats		PS = $16

$13Consumer surplus

+

$16Producer surplus

=

$29Total surplus

At $14, Q_d = Q_s = 3—this little market clears. Note that CS ≠ PS: there is no rule saying the two sides split the gains evenly.

From four traders to a real market

Add buyers and the steps smooth into the curve you already know

4 buyers

12 buyers

A whole market

A staircase with enough steps is a line—and the area under a line is a triangle: ½ × base × height

The economics has not changed. Summing rectangles buyer by buyer and taking the area of a triangle are the same calculation, done at two different scales. Exam 1 allows a basic calculator—these numbers will always come out clean.

Method 2 of 2 · from a graph · LO 5.2

Find P*, then take the two triangles

Strawberries, thousands of flats:
Q_D = 120 − 6P and Q_S = 4P − 20

1

Set Q_D = Q_S → P* = $14, Q* = 36120 − 6P = 4P − 20, so 10P = 140

2

Read the two vertical interceptsDemand at Q = 0: $20. Supply at Q = 0: $5.

3

Consumer surplus = $108½ × 36 × (20 − 14) = ½ × 36 × 6

4

Producer surplus = $162½ × 36 × (14 − 5) = ½ × 36 × 9

5

Total surplus = $270 thousand108 + 162

Step 2 is the one students skip—and you already practiced it in Unit 4: rewrite Q = 120 − 6P as P = 20 − Q/6.

Your turn · LO 5.2

Now you compute one

A different market:
Q_D = 90 − 3P and Q_S = 2P − 10

Find P*, Q*, consumer surplus, producer surplus, and total surplus. Same four steps as the last slide. Three minutes.

1

P* = $20, Q* = 3090 − 3P = 2P − 10, so 5P = 100

2

Intercepts: $30 and $5Demand at Q = 0: $30. Supply at Q = 0: $5.

3

CS = $150½ × 30 × (30 − 20) = ½ × 30 × 10

4

PS = $225½ × 30 × (20 − 5) = ½ × 30 × 15

5

Total surplus = $375150 + 225

Predict first · then check

Demand rises. What happens to consumer surplus?

Same supply. Demand shifts right:
Q_D = 90 − 3P → Q_D = 120 − 3P

The price is about to rise from $20 to $26. Vote before you compute.

1

New P* = $26, Q* = 42120 − 3P = 2P − 10, so 5P = 130

2

CS = $294 (was $150)New demand intercept is $40: ½ × 42 × (40 − 26)

3

PS = $441 (was $225)½ × 42 × (26 − 5)

Buyers paid more per unit and still ended up better off. Consumer surplus is not read off the price alone—the curve itself moved.

Three traps before we move on

Concept check

Question 1 of 3

A buyer whose willingness to pay is $9 faces a price of $14. Her consumer surplus is:

Answer, then say the rule out loud.

Review · read the curves vertically · LO 5.1

Demand records value; supply records cost

Height of demand

At quantity Q, the demand curve shows the marginal buyer’s willingness to pay—the value of that next unit to the last buyer willing to purchase it.

Height of supply

At quantity Q, the supply curve shows the marginal seller’s cost—the opportunity cost of producing that next unit.

At the same quantity, the vertical gap WTP − cost is the potential gain from trading that unit.

Review · one trade, two gains

The market price divides the gain from trade

Buyer: Carlos

WTP = $15 and price = $14

CS = WTP − P = $1

Seller: Farm Y

Price = $14 and cost = $12

PS = P − cost = $2

$1Consumer surplus

+

$2Producer surplus

=

$3Gain from trade

Changing the transaction price reallocates the $3 between buyer and seller; as long as the trade occurs, the total gain remains WTP − cost.

Review check · compute from a graph · LO 5.2

Can you rebuild both surplus areas?

Demand: Q_D = 90 − 3P
Supply: Q_S = 2P − 10

At equilibrium, which statement is correct?

Solve for P* and Q*, then read both vertical intercepts.

New topic · LO 5.3

What if the government places a legal limit on price?

Price ceiling

A legal maximum. Transactions above the limit are not permitted.

Rent caps, regulated maximum prices, and emergency limits on price increases.

Price floor

A legal minimum. Transactions below the limit are not permitted.

Minimum wages, H-2A wage requirements such as the AEWR, and crop-support programs modeled as floors.

Review before drawing the control · LO 5.3

Does a government price limit shift demand or supply?

Assume tastes, income, technology, input costs, expectations, and the numbers of buyers and sellers have not changed.

Commit to an answer before revealing the graph-reading rule.

Government sets a legal price limit

→

Move to the controlled price on the same D and S curves

→

Read the new Q_d and Q_s

Movement along a curve ≠ shift of the curve.

Historical case · United States · 1973–1974

Gasoline price controls during the oil crisis

Cause

Oil supply suddenly fell.

The 1973 Arab oil embargo reduced crude oil reaching the United States, pushing the market-clearing gasoline price upward.

Process

Federal price controls blocked full adjustment.

At the controlled price, motorists wanted more gasoline than stations could provide.

Result

Scarcity was rationed without price.

Drivers faced long lines, purchase limits, and—in some states—odd–even license-plate rules.

Generated historical scene of 1970s cars waiting in a long line at a United States gas station

The key distinction: the embargo changed the market; the price ceiling changed how the resulting scarcity was allocated.

Historical case · European agriculture · 1970s–1980s

Europe’s “butter mountains”

Cause

Europe sought to stabilize farm income.

The Common Agricultural Policy used an intervention price to keep butter prices above the market-clearing level.

Process

Public agencies bought the unsold output.

The supported price encouraged more production than private consumers wanted to purchase.

Result

Warehouses filled with surplus butter.

The stocks became “butter mountains”: farmers gained support while taxpayers financed buying and storage.

Generated historical scene of a European cold-storage warehouse filled with stacks of surplus butter

Why the surplus persisted: the supported price could continue because the government stood ready to buy what private consumers did not.

Price ceilings · strawberries, P* = $14

A ceiling only bites if it sits below the equilibrium price

Ceiling at $18

Above P*. Sellers could never get $18 anyway, so the law never binds. Nothing happens.

$14Price

36Traded

0Shortage

Ceiling at $10

Below P*. The price is forced down and the two sides no longer agree. A shortage opens up.

$10Price

20Traded

40Shortage

Short-side rule: when a control binds, quantity traded is the smaller of Q_d and Q_s. Here 20 flats change hands—fewer than the 36 that traded before the law.

Price floors · same market, P* = $14

A floor only bites if it sits above the equilibrium price

Floor at $10

Below P*. Buyers were already paying $14, so nobody is pushed against the law. Nothing happens.

$14Price

36Traded

0Surplus

Floor at $17

Above P*. The price is held up and sellers want to sell far more than buyers will take. A surplus piles up.

$17Price

18Traded

30Surplus

Short side again: only 18 flats trade. Without a government or other third-party buyer, every binding control shrinks private buyer–seller transactions. Next class we put a dollar value on what that costs.

Class 2 · retrieval before new material

Read the control before you calculate anything else

Choose one statement, then defend every number from the graph.

Nothing shifted. A legal price changes the quantities chosen along demand and supply; it does not move either curve.

From lost surplus to deadweight loss · LO 5.4

Carlos’s missing $1 was only half of the lost trade

	Third buyer	Third farm
Identity	Carlos	Farm Y
Value or cost	WTP = $15	Cost = $12
At P* = $14	CS = $1	PS = $2
With floor = $16	No third trade

Deadweight loss: the reduction in total surplus caused by trades that no longer occur—or by units produced whose cost exceeds their value.

Why Q* is efficient

Keep trading while the next buyer values the unit more than it costs

Possible trade	Buyer WTP	Seller cost	Gain from trade
1 · Ana + Farm W	$22	$5	$17
2 · Ben + Farm X	$18	$9	$9
3 · Carlos + Farm Y	$15	$12	$3
4 · Dee + Farm Z	$11	$16	−$5
Efficient market	Stop after trade 3		TS = $29

Before Q*

Demand lies above supply: marginal WTP > marginal cost. Each additional trade creates surplus.

After Q*

Supply lies above demand: marginal cost > marginal WTP. Forcing another unit would destroy surplus.

At Q*: all positive gains from trade are captured, so total surplus is maximized.

Price ceiling · predict before welfare shading

A $6 ceiling blocks which trades?

Market demand: P = 20 − Q
Market supply: P = Q
Free-market equilibrium: P* = $10, Q* = 10

First find Qs and Qd. Then apply the short-side rule.

Price ceiling · surplus before and after · LO 5.4

The lower price transfers surplus—and the lost trades destroy some

Q = 6Qs = 6, Qd = 14, shortage = 8.

CS = $66Successful buyers pay $6. Efficient rationing is assumed.

PS = $18Sellers receive $6 on the six units produced.

TS = $84Before the ceiling, TS was $100.

DWL = $16The gains from trades 7–10 disappear.

Baseline at P* = $10 and Q* = 10: CS = $50, PS = $50, TS = $100. The ceiling changes who receives surplus and reduces the total.

Price ceiling · winners, losers, and rationing · LO 5.6–5.7

“Consumers win” is too simple—some never get the good

Possible winners

Buyers who obtain the good pay less. In our efficient-rationing calculation, their total CS rises from $50 to $66.

But the low price does not guarantee access.

Losers

Sellers receive less and sell fewer units.
Buyers who would have traded at equilibrium may be shut out.
Future buyers may face lower quality or less investment.

Who gets the six units?

Without price rationing, another rule takes over: first-come-first-served, waiting, purchase limits, lotteries, or seller discretion.

If the highest-WTP buyers are not served, actual CS is lower and DWL is larger than our graph shows.

Assumption behind the shaded graph: the six available units reach the six buyers with the highest willingness to pay.

Price floor · same market, mirrored prediction

A $14 floor blocks which trades?

Market demand: P = 20 − Q
Market supply: P = Q
Free-market equilibrium: P* = $10, Q* = 10

Find Qd first: buyers determine how many units are sold in the private market.

Price floor · surplus before and after · LO 5.4

The higher price transfers surplus—but cannot save the lost trades

Q = 6Qd = 6, Qs = 14, surplus = 8.

CS = $18Buyers pay $14 on the six units purchased.

PS = $66Assume the six lowest-cost sellers make the sales.

TS = $84Before the floor, TS was $100.

DWL = $16The gains from trades 7–10 disappear.

The six sellers who make a sale may gain from the higher price. Sellers left with unsold output do not automatically benefit.

Put the two policies side by side · LO 5.6

Transfers change who gets the surplus; DWL changes how much exists

Outcome	Price	Quantity traded	CS	PS	TS	DWL
Free market	$10	10	$50	$50	$100	0
Binding ceiling	$6	6	$66	$18	$84	$16
Binding floor	$14	6	$18	$66	$84	$16

Transfer

One participant’s gain is another participant’s loss. Total surplus does not change from the transfer alone.

Lost trade

Both the buyer’s potential gain and the seller’s potential gain disappear. Total surplus falls.

Policy evaluation

Name the intended beneficiary, calculate who actually gains, and then identify who pays.

CS under the ceiling assumes the scarce units reach the highest-WTP buyers; PS under the floor assumes the lowest-cost sellers make the sales.

Labor markets · minimum wage · LO 5.5

In a labor market, the wage is the price

Labor demand

Firms decide how many workers or hours to hire at each wage. A higher wage reduces quantity of labor demanded.

Labor supply

Workers decide how much labor to offer at each wage. A higher wage raises quantity of labor supplied.

Binding minimum wage: employment is the short side, L_d. The gap L_s − L_d is a labor surplus—not a shortage of workers.

Farm labor policy · AEWR · LO 5.5

The AEWR applies the wage-floor logic to H-2A farm labor

Adverse Effect Wage Rate (AEWR): a required wage benchmark used in the H-2A temporary agricultural worker program to help prevent the employment of temporary foreign workers from depressing U.S. farm wages.

Hypothetical North Carolina farm-labor market

Suppose the market-clearing wage is $13 per hour and the applicable required wage is $16.

Predict: what happens to the wage, labor demanded, labor supplied, and the gap between them?

Use the same four-step price-floor test—only the axis labels have changed.

The diagram is a simplified policy model. H-2A recruitment rules, corresponding employment, housing, transportation, visas, and other required wage rules also shape actual outcomes.

Agricultural price supports · the government becomes a buyer · LO 5.8

A supported crop price changes the short-side rule

CS = $18Consumers buy 6: ½ × 6 × ($20 − $14).

PS = $98Farms sell all 14 units: ½ × 14 × $14.

Government expenditure = $112Government buys the 8-unit excess: $14 × (14 − 6).

DWL = $96Policy TS = $18 + $98 − $112 = $4, versus TS* = $100.

Welfare assumption: government-held crops have no use or resale value, and storage costs are ignored. If the crops create value later, subtract that value from net government cost. Historical example in the 3B reading: European wheat price supports.

Emergency price caps · information and incentives · LO 5.7

After a hurricane, a high price is both a burden and a signal

If price can rise

Consumers have a stronger reason to conserve scarce water.
Stores and outside suppliers see a reason to bring in more.
But low-income households may be unable to afford essentials.

If an emergency cap binds

The posted price stays affordable for buyers who find water.
Qd exceeds Qs, so shelves empty and a shortage appears.
Waiting, purchase limits, or first-come-first-served replace price.

If price is no longer allowed to ration the scarce water, what determines who receives it?

Choose an allocation mechanism, not a slogan.

Efficiency is not the only value. WTP reflects both preferences and ability to pay, so emergency policy involves a real efficiency–equity tradeoff.

Integrated practice · LO 5.3–5.6

One graph, six decisions

Demand: P = 24 − Q
Supply: P = Q
Government sets a $8 price ceiling.

Which complete statement is correct?

Work in this order: equilibrium → binding? → Qd and Qs → actual trade → surplus → DWL.

Unit 5 checkpoint · explain, calculate, evaluate

Five moves complete the unit

LO 5.4 · Trace the welfare lossFind actual quantity traded, recompute TS, and identify the DWL from missing trades.

LO 5.5 · Translate the labor marketWage is price; firms demand labor; workers supply it; apply the floor logic to minimum wage and AEWR.

LO 5.6 · Name people, not just areasIdentify successful buyers or sellers, excluded participants, taxpayers, and the size of each surplus change.

LO 5.7 · Ask what replaces priceExplain rationing, quality, conservation, supply incentives, and the efficiency–equity tradeoff.

LO 5.8 · Follow the institutionA crop support may make government the buyer of the surplus; H-2A farm labor policy uses a required wage benchmark. The graph is the beginning of the analysis, not the end.

Exit ticket: A crop price support is above P*. Consumers buy 40 units and farms supply 70. If government buys the excess, how many units does government purchase, who benefits, who pays, and why is the government’s expenditure not automatically equal to deadweight loss?