WEBVTT

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A used-car market can fail
even when buyers want cars,

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sellers want to sell, and every
possible trade would create value.

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The trouble begins when one
side knows something important

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that the other side cannot see.

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Our question is concrete.

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Sellers know the quality
of their own cars.

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Buyers cannot inspect
quality before buying,

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so every car initially looks
like part of one mixed pool.

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What price can that pool support?

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There are ten cars.

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Quality one is the lowest
and quality ten is the highest,

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with one car at every
whole-number quality in between.

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A seller's reservation price
is the least that seller will accept.

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We write it as s of q:

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one thousand dollars plus eight
hundred dollars for each quality step.

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A buyer's willingness to pay is the
most the car is worth to that buyer.

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We write b of q: twenty-five hundred
plus nine hundred times quality.

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Buyer value rises slightly
faster than the seller's minimum.

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Those are different ideas.

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The seller's number
is a minimum for accepting a sale.

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The buyer's number is a maximum
value from owning the car.

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Their difference
is the value a trade can create.

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Before calculating,
make the assumptions explicit.

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Each seller knows one car's true quality.

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Buyers share the value rule,

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but hidden quality prevents them from
attaching a different offer to each car.

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We also assume competitive
buyers, no transaction costs,

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and no dislike of uncertainty
beyond its effect on expected value.

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These assumptions keep
the arithmetic transparent.

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Later, we can ask what a repair costs.

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With all ten cars offered,
buyers calculate the average quality.

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The average of one
through ten is five point five.

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Buyers insert that average
into their value rule.

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Twenty-five hundred plus

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nine hundred times five point five gives
seven thousand four hundred fifty dollars.

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Competition therefore produces one
pooled offer of seven thousand four

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hundred fifty dollars.

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It is not a guess
about any particular car.

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It is the expected buyer value
of the whole group currently for sale.

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Put all ten cars on the market.

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The red line gives each seller's minimum.

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The blue line gives what a buyer
would pay if exact quality were visible.

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Every blue value is above its red partner,

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so every individual
trade could create value.

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But buyers cannot choose
ten quality-specific prices.

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With every quality present,
average quality is five point five,

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and the common offer is seven
thousand four hundred fifty dollars.

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Now each seller compares that common
offer with the value of keeping the car.

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Quality nine requires
eighty-two hundred dollars.

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Quality ten requires nine thousand.

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The offer is too low
for both, so both leave.

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Buyers understand the withdrawal.

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The remaining qualities one
through eight average four point five,

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so the offer falls to six
thousand five hundred fifty dollars.

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Once that price settles,
qualities seven and eight also reject it.

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Their departure changes
the expected car again.

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Qualities one through six
average three point five,

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and the pooled offer falls to five
thousand six hundred fifty dollars.

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Quality six needs fifty-eight
hundred, so it withdraws too.

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Now only qualities one
through five remain.

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Their average quality is three, so buyers
offer five thousand two hundred dollars.

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This time the next comparison
does not trigger another departure.

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Quality five is the best remaining car.

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Its seller requires five thousand and
receives an offer of fifty-two hundred,

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so that seller accepts.

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Every lower-quality seller has a still
lower minimum and accepts as well.

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Quality six remains outside because
its minimum is fifty-eight hundred,

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above the pooled offer.

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So five is a stable cutoff:

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everyone inside wants to stay, while
the next seller wants to remain outside.

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Read the offer column from top to bottom.

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Seven thousand four hundred fifty
becomes six thousand five hundred fifty,

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then five thousand six hundred fifty,

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then five thousand two hundred.

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This feedback loop is adverse selection.

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A pooled offer is unattractive
to the better sellers,

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their exit lowers expected quality,

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and the lower expectation makes the next
offer unattractive to still more sellers.

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Rational reactions on both
sides produce a worse market.

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The withdrawal process stopped
with qualities one through five trading.

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The blue points are inside the market.

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Qualities six through ten are gray
because their owners prefer keeping them

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at the final pooled offer.

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Now calculate that stopping point
without replaying every round.

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Suppose the pool contains every quality
from one through some highest quality k.

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The average of the whole numbers from one
through k is k plus one divided by two.

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That average is what buyers must value
when they cannot tell the cars apart.

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Insert the average
into the buyer-value rule.

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The pooled competitive offer

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is twenty-five hundred plus nine
hundred times k plus one over two.

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The seller at quality

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k has the highest reservation price
among the people still participating.

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That minimum is one
thousand plus eight hundred k.

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For quality k to remain, the pooled
offer must cover that seller's minimum.

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Substitution reduces the condition

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to three hundred fifty k no
greater than nineteen hundred fifty.

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Divide by three hundred fifty.

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The cutoff can be no greater
than about five point five seven.

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Quality is restricted
to whole numbers here,

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so the largest possible
participating quality is five.

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Check both sides.

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Quality five needs five thousand
and the pool offers fifty-two hundred,

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so five stays.

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Quality six needs fifty-eight
hundred, more than that same offer,

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so six stays out.

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That pair of choices is an equilibrium,

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meaning nobody changes course
after seeing what everyone else does.

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The traded pool justifies the
five-thousand-two-hundred-dollar offer,

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every seller inside accepts it,
and the next seller rejects it.

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Under hidden quality,
only the first five cars trade.

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The five gray cars are not worthless.

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They disappear because one pooled price
cannot keep their better-informed sellers

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in the market.

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Now make quality visible
and verifiable before offers are made.

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Buyers can attach a different
offer to every quality.

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All ten sellers then receive an offer high
enough to trade, so all ten cars remain.

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To measure what information creates,

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do not simply count cars and do not treat
the purchase price as new social value.

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Compare buyer value with the
seller's value of keeping each car.

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The red curve
is the seller's reservation price.

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The blue curve
is the buyer's willingness to pay.

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Their vertical gap is the gain from trade.

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Subtract the two formulas.

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Buyer value minus seller value is fifteen
hundred plus one hundred times quality.

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That number is positive
for every quality from one through ten.

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In the hidden-quality equilibrium,
only qualities one through five trade.

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Add their five gains, and the market
creates nine thousand dollars of value.

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When quality is visible,
all ten positive-gain trades occur.

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Their combined gain is twenty
thousand five hundred dollars.

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The difference is eleven
thousand five hundred dollars.

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That is the value of perfect quality
information in this numerical market:

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five restored trades
and the gains those trades create.

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The price of a car determines how the gain
is divided between buyer and seller,

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but it does not change the total gain.

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A dollar paid by the buyer
is a dollar received by the seller.

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Information is not free in real markets.

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Inspection, certification,
and enforcement use resources.

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So the net value is eleven
thousand five hundred minus the cost

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of producing reliable information.

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This number is a benchmark,

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not a claim that every
information system is worthwhile.

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Keep the failure mechanism in view.

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Hidden quality forces one pooled price.

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Better sellers reject it.

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Their exit lowers average quality,

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which lowers the next price,
and the process repeats.

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A useful repair
must change at least one link.

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Telling buyers to be less
suspicious does not work,

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because their lower offer is a rational
response to the pool they expect.

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Telling good sellers to accept
a loss does not work either.

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First, a warranty.

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If defects appear later,
the seller pays for repair or replacement.

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That shifts some risk
back to the informed side.

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It can also signal quality because a bad
seller expects more expensive claims.

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The warranty changes seller incentives
and can support a higher buyer offer.

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But the promise is weak if the seller
can disappear, exclusions are hard

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to understand, claims are difficult,
or the warranty is too costly to honor.

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Second, inspection and certification
attack hidden information directly.

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A competent independent inspector
can separate cars into quality classes,

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allowing buyers to offer different
prices instead of one pooled price.

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The limits matter.

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Inspection can miss concealed faults.

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Certification can be expensive, vague,
or compromised by conflicts of interest.

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A noisy grade may improve the pool
without revealing exact quality,

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so some adverse selection can remain.

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Third, reputation changes
the payoff from deception.

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A dealer who expects repeat customers,
reviews, and future sales can lose more

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from one bad transaction than
the dealer gains by hiding a defect today.

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Reputation is weakest for one-time
sellers, firms that can change names,

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and products whose
failures appear years later.

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It does not necessarily
reveal quality today.

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It makes dishonesty more expensive
by attaching future consequences.

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Fourth, disclosure duties, return
rights, and liability for concealed

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defects let information emerge after the
sale and reverse some bad transactions.

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They reduce the reward
from passing a lemon as a good car.

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These protections depend on defects
being verifiable and rules being enforced.

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If proving a hidden fault
costs more than the claim,

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or buyers cannot use the remedy,
the written right changes little.

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So apply one diagnostic
to any proposed fix.

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Does it improve information,

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create a credible signal, or change
the incentive to hide low quality?

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Those are three distinct channels.

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Inspection mainly improves information.

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Certification and warranties
can create signals that are harder

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for bad sellers to copy.

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Warranties, reputation,

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and liability also change
the seller's payoff after a poor sale.

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Keep the numerical benchmark
beside those mechanisms.

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Hidden quality created nine thousand
dollars of gains in our example.

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Visible quality created
twenty thousand five hundred.

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A repair should be judged by how much
of the missing trade it restores,

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how reliable its information
is, and what it costs.

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The economic test is not whether
the institution sounds reassuring.

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Its benefit must exceed
the resources used to run and enforce it.

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That is the market for lemons.

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Buyers price what they expect,
sellers act on what they privately know,

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and those actions change
what buyers should expect next.

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Reliable information or well-designed
incentives can stop the downward loop

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and restore trades that create real value.