Efficiency & Welfare
Economics & Law - NIT Northern Institute of Technology / TUHH, Hamburg · part of my Technology Management MBA · study notes for revision.
Chapter 2 got a market to settle on a price and a quantity. This chapter asks the follow-up question a lawyer and an economist both care about: is that a good outcome? To answer it we need a way to measure how much value a market creates - and then a definition of what “good” even means. That second part is where economics and law start to pull in slightly different directions, and the last section is about how to reconcile them.
1 · Consumer surplus: getting more than you paid for
Section titled “1 · Consumer surplus: getting more than you paid for”Start with a simple observation. When you buy something, you often would have been willing to pay more than you actually did. You would have paid 8 euros for that coffee on a freezing morning; the café charged 3. That leftover 5 euros of value you pocketed is your consumer surplus - a bonus you keep because the price was lower than what the coffee was worth to you.
Consumer surplus - the gap between what a buyer was willing to pay for a good and what they actually paid. Summed across all buyers, it is a measure of the welfare consumers gain from a market.
Where does the “willing to pay” number come from? The demand curve. Recall from Chapter 2 that the demand curve traces, for each unit, the most someone would pay for it. The first units go to people who value the good highly (high willingness to pay); later units go to people who barely value it above the price. Everyone, though, pays the same single market price. So for almost every unit sold, buyers paid less than their personal maximum.
Worked example: finding the triangle
Section titled “Worked example: finding the triangle”Numbers make this concrete. Suppose the demand curve for some good is
P = 8 − 2QP the price (in euros)
Q the quantity demanded at that price
and the market clears at a price of P = 2. To measure consumer surplus we find the corners of the wedge, then use the area formula from school geometry.
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Top corner (point A). Where the demand curve hits the vertical axis, nobody has bought anything yet, so Q = 0. Plug in:
P = 8 − 2(0) = 8. The very first, most eager buyer would have paid 8. -
Bottom corner (point B). At the market price P = 2, how many units sell? Set
2 = 8 − 2Q, which gives2Q = 6, so Q = 3. Buyers purchase three units when the price is 2. -
The height of the wedge is the drop from the top corner’s price down to the market price:
8 − 2 = 6. -
The base is the quantity traded:
Q = 3. -
The area of the triangle is
½ × base × height = ½ × 3 × 6 =9.
So consumers, as a group, walk away with 9 euros of surplus - value they enjoyed beyond what they handed over. That single number is the market’s gift to the buying side.
2 · Producer surplus: the seller’s half of the pie
Section titled “2 · Producer surplus: the seller’s half of the pie”Sellers get their own version of the same bonus. A producer has some cost of making each unit - the supply curve traces those costs. If the market price sits above what it cost to produce a unit, the seller keeps the difference. That difference, summed over all units, is the producer surplus (also called supplier surplus).
Producer surplus - the price a seller receives minus the cost of producing the good. On the diagram it is the area above the supply curve and below the price line - the mirror image of consumer surplus.
Put the two wedges together and you have measured the entire value the market created:
- Willingness to pay minus price
- Area under demand, above price
- The gain to the buying side
- Price minus production cost
- Area above supply, below price
- The gain to the selling side
Total surplus = Consumer surplus + Producer surplusThis total surplus is the number economists reach for when they ask “how much is this market worth to society?” A rule, tax, or intervention that shrinks the pie is destroying value; one that grows it is creating value. That framing - the pie - is what the rest of the chapter is built on.
3 · Two ideas of efficiency
Section titled “3 · Two ideas of efficiency”Economists say an outcome is efficient when it makes good use of scarce resources - but there are two different, precise versions of that idea, and they disagree. Getting the difference straight is one of the most useful things in the whole course.
3.1 · Pareto efficiency - nobody can win without someone losing
Section titled “3.1 · Pareto efficiency - nobody can win without someone losing”Pareto efficiency (named after Vilfredo Pareto) - an allocation is Pareto efficient when you cannot make anyone better off without making at least one other person worse off. Every possible gain has been squeezed out; the only way left to help one person is to hurt another.
The gentler, everyday cousin of this is a Pareto improvement: a change that makes at least one person better off and nobody worse off. A Pareto improvement is an unambiguous win - literally no one can object, because no one loses. The catch is that in the real world, almost every interesting policy creates some loser, so pure Pareto improvements are rare. Pareto efficiency is a demanding, cautious standard.
3.2 · Kaldor-Hicks efficiency - grow the pie, worry about slices later
Section titled “3.2 · Kaldor-Hicks efficiency - grow the pie, worry about slices later”Kaldor-Hicks efficiency loosens the rule. A change is a Kaldor-Hicks improvement if the winners gain so much that they could hypothetically compensate the losers and still come out ahead. The crucial word is hypothetically - the compensation does not actually have to be paid. All Kaldor-Hicks asks is that the total pie grows; it stays silent on who ends up with the slices. This means a Kaldor-Hicks improvement can genuinely leave some people worse off in practice.
- Improvement = someone gains, nobody loses
- Efficient = no more free wins left
- Losers can veto; hard to satisfy
- Cares about winners and losers
- Improvement = total pie grows
- Winners could compensate losers…
- …but need not actually do so
- Some people may end up worse off
3.3 · Worked example: Homer, Bart and one slice of bacon
Section titled “3.3 · Worked example: Homer, Bart and one slice of bacon”The classic teaching example nails all four terms at once. Homer loves bacon and values a slice at 10 euros. Bart also likes it, but values the same slice at only 5 euros. You hold one slice and must decide what to do with it. The baseline is that nobody has any bacon (everyone at 0).
| Option | Homer’s value | Bart’s value | Total (the pie) |
|---|---|---|---|
| Baseline - no one gets it | 0 | 0 | 0 |
| 1 · Give it all to Homer | 10 | 0 | 10 |
| 2 · Give it all to Bart | 0 | 5 | 5 |
| 3 · Split it in half | 5 | 2.5 | 7.5 |
| 4 · Half to Homer, bin the rest | 5 | 0 | 5 |
Now read the definitions off the table:
Walk through the logic:
- All four options are Pareto improvements over the baseline - each gives value to someone (Homer, Bart, or both) while leaving the other person no worse than their starting 0.
- Options 1, 2 and 3 are Pareto efficient, but Option 4 is not. Why? Because from Option 4 you can switch to Option 3, which raises Bart from 0 to 2.5 without touching Homer’s 5. A free win still exists at Option 4, so it fails the Pareto test. Throwing half the bacon in the bin is exactly the kind of pure waste Pareto efficiency rules out.
- Only Option 1 is Kaldor-Hicks efficient - it produces the biggest total pie (10). Because Homer values bacon more than Bart does, putting it all in Homer’s hands squeezes out the most total value. In principle Homer could give Bart a euro or two as compensation and still be ahead - but Kaldor-Hicks does not require him to.
4 · Efficiency versus justice
Section titled “4 · Efficiency versus justice”The bacon example exposes the fault line. Kaldor-Hicks efficiency is a utilitarian goal: it tries to maximise the sum of everyone’s utility - the total pie - and is deliberately indifferent to how that pie is divided. If handing everything to one person makes the total biggest, so be it.
Utilitarianism - the ethical view that the best outcome is the one that maximises the total of everyone’s welfare (utility) added together. Distribution between people is not, in itself, a concern.
A lawyer’s instinct often runs the other way. Jurists tend to care about distributive justice - how fairly wealth and welfare are shared out, and especially about equality. To a lawyer, an outcome that maximises the total but leaves someone with nothing can be a bad outcome, no matter how big the pie. So how do we settle these two views?
4.1 · Rawls and the veil of ignorance
Section titled “4.1 · Rawls and the veil of ignorance”The philosopher John Rawls offered a famous thought experiment for thinking about fairness. Imagine you must design the rules of society before you know who you will be in it - rich or poor, healthy or sick, talented or not. You choose from behind a “veil of ignorance” that hides your future position.
Veil of ignorance - Rawls’ device: pick the rules of society as if you had no idea which slot in it you will occupy. Because you might turn out to be the worst-off person, self-interest itself pushes you to protect that position.
The striking conclusion Rawls draws is a very different welfare rule from the utilitarian one. Behind the veil, a rational, risk-wary person cares most about not being destitute if they land at the bottom. So social welfare, on this view, rises only when the worst-off person is made better off. Giving more to the already-comfortable does nothing; giving more to the poorest is what counts.
- Goal: maximise the sum of utilities
- The total pie is all that matters
- Blind to distribution - a loser is fine if the total rose
- Bacon → give it to Homer (biggest total)
- Goal: lift the worst-off person
- Welfare rises only when the poorest gains
- Deeply concerned with distribution and equality
- Bacon → worry that Bart got nothing
4.2 · Reconciling the two
Section titled “4.2 · Reconciling the two”These look like rival worldviews, but economics is more flexible than it first appears, and two moves bring them much closer together.
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Economics can maximise any welfare function - not only the utilitarian sum. The mathematical toolkit for “find the allocation that makes some objective as large as possible” does not care what the objective is. Feed it the utilitarian sum and you get Kaldor-Hicks. Feed it Rawls’ rule (“make the worst-off person as well off as possible”) and the very same machinery optimises that instead. Efficiency is a method; the goal is a choice you plug in.
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Utility functions can include altruism. The homo economicus from Chapter 1 was assumed purely self-interested, but that assumption can be relaxed. If I genuinely gain utility from helping the poor, then me “selfishly” maximising my own utility will automatically channel resources toward the poor - because their well-being is now part of what I value. Selfishness and fairness stop being opposites once caring about others is written into the preferences.
Revision summary
Section titled “Revision summary”Next: Game Theory → - what happens when my best move depends on yours.