Why do we buy Insurance? Expected Outcomes, Risk pooling and Risk preferences  

In life a lot of events and outcomes are uncertain. Economic risk is the possibility of losing economic security to satisfy an individual’s needs/desires for food, shelter, clothes and other amenities, due to unforeseen events in future.

Thus uncertainty leads to risk. And insurance is just a means to manage this risk. As we will see later, insurance enables you to trade an uncertain outcome/risk (and potential loss) with a known amount (Premium). Behavioral economists have concluded that we humans, buy too less insurance. We don’t anticipate fringe (low probability) outcomes, which may eventually result in a huge payouts (loss).

Let’s take a simple example.
Consider a risk averse car owner has a chance of less than 20% of being in a single accident in a year. And no chance of being in more than one accident. 50% of Accidents are minor and involve repairs worth $500. 40% require repairs worth $5000. And 10% may require replacement of car, which is worth $20,000.

Expected Loss and Standard Deviation

Car Owner’s expected loss is the mean of the above loss distribution
E[X] = 80% * 0 + 20% * (50% * $500 + 40% * $5000 + 10% * $20000)
E[X] = $850

Thus, on an average, car owner spends $850 each year on repair but, the possibility of having to fork out $5000 or $20,000 in medium to severe accidents could create potential concern.

To measure the variability of outcomes, we should also look at the standard deviation of the loss distribution.
Var[X] = 80% * (0 – 850)^2 + 20% * (50% * (500 – 850) ^ 2+ 40% * (5000 – 850) ^ 2 + 10% * (20000 – 850)^2 )
Var[X] = $ 9,302,500
SD[X] = Sqrt (Var[X]) = $3050
CV = Coefficient of Variation of distribution = SD/Mean = 3.6

Thus the variance of outcome (dispersion of possible loss) is pretty high.

Insurance Policies – Issuers and Holders

Now let us see how insurance instruments can be used to reduce/manage individual risk. Insurance is an agreement where, for a stipulated payment (policy premium), one party (the policy issuer) agrees to pay  the policy holder (car owner), a defined amount (policy claim) upon the occurrence of a specific loss (repairs from accident).
The issuer issues the policy to a pool of policy holders, assesses the Expected Total Loss and the Variation and charges a Policy Premium to cover all projected loss claims in the pool. The premium is thus the policy holder’s share of the total premium of the risk pool.

The idea is quite simple. Insurance is all about risk pooling. By subscribing to an insurance policy, the car owners can transfer the risk to the policy issuer. In a given year, not all car owners will be involved in accidents. The issuer pays  these unfortunate few using the premium collected from all the holders. Thus each policy holder exchanges their uncertain losses for a known premium. Also, as seen above, greater the standard deviation, greater the risk, and thus will require higher Premiums (will see again later).

The issuer could restrict the potential loss scenarios by defining or exempting certain “perils” in the contract. For instance, damages from natural disasters like Floods and Earthquakes could be exempted.
Now, extending the earlier example. Assuming, 100 car owners subscribe to an insurance policy which guarantees against all potential losses.
Expected Loss for the insurance pool now is,
E[nX] = n E[X] = 100 * 850 = $85,000

Variance = Var[nX] = n * Var[X]
SD = Sqrt (Var[nX] ) = Sqrt(n) * SD[X] = 10 * 3050 = 30,500
CV = SD/Mean = 30,500/85,000 = 0.36

Had, none of them subscribed to insurance, Expected loss for the group of 100 car owners would still have been nE[X] = $85,000
But, the Variance would have been the sum of their individual variances
n Var[X] = $305,000

Coefficient of Variation is an useful tool to measure variability between positive distributions of different mean. General form of the CV of the group is
CV = Sqrt(n) * SD[X] / n E[X] = SD[X]/ (E[X] * Sqrt (n)
Thus, as number of policy subscribers increases and becomes really large, CV tends to zero. In simple terms, it becomes easier for the issuer to predict expected losses.

Pricing Risk Premium

It should be clear that the existence of the insurance provider does not change the chances of the loss (Ignoring Moral Hazard for now). Since the issuer expects to pay out at least $85,000, the insurance premium would be priced above $85,000/1000 = $850. Generally, it would include some markups for administrative overheads, processing fees, some reserves for uncertainty and a small Profit. In a perfectly competitive market, the Profit margin is generally not that high. Assuming the issuer adds a 30% markup to cover all these, the policy holder ends up paying a premium of $1105 for the policy.
Net Premium = $850
Additional expenses and margins = $255
Gross Premium = $1105

Do note, some risk averse car owners are still willing to pay this amount, even though it is higher than their expected loss ($850) since they can exchange an unmanageable outcome (due to uncertainty) with a non-zero variance for a known amount (Premium) with zero variance. The number of eventual policy subscribers would depend on their risk preference. Had the Gross Premium per holder been $850 (equal to the Expected Loss), the insurance would have been actuarially fair. And all risk averse car owners would have immediately signed up for the insurance.

Issues of Moral Hazard and Adverse Selection

Earlier we mentioned that the insurance provider does not change the chances of the loss. However, studies have found that individuals seem to be more risk-seeking when they know they are insured. For instance, car owners might start driving more recklessly, increasing the chances of accidents and insurance pay outs. This is know as the problem of Moral Hazard.

Adverse Selection occurs when buyers and sellers have asymmetric information. It describes a situation where an individual's demand for insurance (either the propensity to buy insurance, or the quantity purchased, or both) is positively correlated with the individual's risk of loss. Thus, more smokers opt in for health insurance, and more reckless drivers opt in for car insurance. To manage adverse selection, Insurance providers have a differential premium structure where high-risk users (identified from background checks and profile questionnaires) are charged higher Premium than the rest.

Some interesting variations

Modern insurance instruments are really complex. Two simple variations are Deductions and Benefit Limits (Ceilings). In Deductions, the issuer pays out after a minimum threshold. In our earlier example, if the minimum deduction is $500, and if the repairs are worth $5000, the issuer pays out only $4500. For any repair below $500, the owner has to pay from his own pocket. As expected, the probability of claim drops from 20% to 10% and so does the risk premium. Some stand-out advantages are –Lower Premiums, A check against Moral Hazard (since owners will be more careful due to the first $500 out-of-pocket payment) and Lesser overheads –Admin and Processing Fee (since small claims are not processed).

In Benefit Limits, the issuer sets an upper bound on the claim pay-out. Policy holders can subscribe to additional coverage by paying incremental Premium. It also provides a safety net for the issuer and reduces the risk burden. Though a thing to note is that the additional Premium per holder is generally not that high since, as seen earlier, the risk pool is shared among a large number of subscribers.

Well, that’s the basics. The model discussed above was between an issuer and a policy holder. Insurance portfolios are also traded by the issuer in the financial sector (Securitization).  There is a lot of interesting literature out there on premium/insurance pricing. We briefly touched on the risk preference of the consumer. What we did not discuss was the optimal amount of insurance to buy. Intuitively, a consumer would want to maximize his Utility under uncertainty, that is, maximize his Expected utility -with and without the probability of loss, inclusive of his premium payouts and claims. Thus, the coverage or Premium that maximizes the solution will rely on individual utility and risk preferences. Let us leave it for a later post.

Risk and Insurance: Society of Actuaries - http://www.wsc.ma.edu/ecke/342/P-21-05.pdf
Premium Calculation and Insurance Pricing - http://www.econ.kuleuven.be/insurance/pdfs/premium3.pdf
Applications of Expected Utility Theory - http://econport.gsu.edu/econport/request?page=man_ru_applications_insurance
An Introduction to Risk-Aversion - http://econport.gsu.edu/econport/request?page=man_ru_basics4

Why economists hate giving gifts and why you should too

Why is giving gifts socially inefficient? And why do we continue doing it?

As an aspiring economist, the act of giving gifts has always intrigued me. From a personal experience, my gifts have often received mixed reaction from the recipients. Be it my addictive compulsion to buy books to signify the thoughtfulness or my lazy yet cautious purchase of popular music CDs to play it safe.

In most cases, giving gift is a laborious exercise. It involves high search cost (unless you know exactly what to get), price you pay to obtain the gift, and an often unmet expectation that it would provide high satisfaction to the recipient. From a pure utility standpoint, this dissatisfaction creates disutility at both our ends, making you wonder if there is any economic rationale to buying in-kind gifts.

Economists argue that since people typically know their own preferences better than others do, so we might expect everyone to prefer cash to in-kind transfers. It reflects the problem of asymmetric information where I do not have perfect information about the wants of my friend, to match it with an appropriate gift. Thus the intimacy of my relationship with the recipient eventually decides whether I create or destroy value. Thus the ideal gift is as good as cash which let's "them" purchase the gift of their choice.

For instance, the $100 I paid to get a plaid sweater for a friend could be valued as low as $75 by her, with an instant erosion of 25% of the actual value. The $25 is a dead-weight loss. Deadweight loss, which is also part of the name of Waldfogel’s widely noted 1993 paper on the topic, refers to a loss to one party that is not offset by a gain to another. To think of it in terms of total Surplus, the Consumer Surplus to me and my friend is -$25 (assuming no emotional significance). The Producer surplus is a small amount above $0, assuming in a competitive market, the sweater is priced at its marginal cost. The Total Surplus to the society for the 1 unit of sweater is -$25. The Negative amount signifies deadweight loss.

Wharton Professor Joel Waldfogel estimated that Deadweight loss from Christmas Holiday gifts, on an average is around 18%. In an absolute Dollar terms, in 2007, where US spent $66 Billion on Holiday gifts, resulted in value destruction close to $12 Billion. Globally he estimates Christmas yuletide spending in 2006 to be close to $145 Billion and a staggering $25 Billion of value destruction.

Assuming, these numbers were plausible, this Annual figure outmatches annual disbursements of Bill-Melinda foundation, which has a total endowment of US $33.5 Billion (in 2009) and could eradicate infectious diseases and malnutrition in all third world countries. Waldfogel’s noble arguments as misstated by a lot of sources is not about stopping the traditional act of giving gifts. Rather, in his book “Scroogenomics” requests readers to think about the problem carefully, before rushing to buy your gifts. He articulates that the ideal Christmas gift is a carefully chosen item that delights the user and opens a new world of consumption choices. Below is his suggestion to a carefully selected, efficiency increasing selection of gifts.

Relationship Waldfogel's estimate of value Children Adults Rich Adults
1 Partners, Siblings, Parents 102%-97% Gifts Gifts Charity cards
2 Friends 91% Gifts Gifts/Gift cards Charity cards
3 Aunts/Uncles/Grandparents 80%-75% Cash/Gifts Cash/Gift cards Charity cards

He reasons that people who know our preferences well, should give in-kind gifts. In some exceptional cases, process of giving gift could outperform their retail values in cash. Firstly, they will chose gifts which we know we need. Secondly, behavioral economics show that contrary to our expectation, people do not always have rational preferences. They constantly forget/change their preferences. And quite often do not know what they really need. Thus, paternalistic instinct of the givers could promote new and better consumption choices which were previously unknown to us. Studies have found that we as individuals like to be pleasantly surprised by new consumption choices. For instance, the first keyboard from my dad which triggered my interest in music, or Steven Levitt’s “Freakonomics” from my friend which has prompted me to take up Economics in my grad school (not sure if this can be considered positive). This is also true especially for kids, who may not make rational decisions on using cash appropriately and may positively benefit from new consumption choices.

In cases where givers are not that aware of the recipient's preferences, the next best choice is cash. However social awkwardness in giving and receiving cash could also devalue the gift to as low as 50%. Thus $100 in cash could eventually only signify $50. A way around it is gift-cards. Depending on the recipient's general interest in music, electronics or clothes, you could gift him gift cards from iTunes, Apple Store/Amazon or GAP. Waldfogel is quick to point out that in US alone, ~10% of the value of gift cards are destroyed either due to people forgetting/loosing the cards, cards expiring before use, disinterest in the shop’s merchandise or inability to fully redeem the total value. The latter happens when on a gift card of $100, you purchase a sweater for $95 and find nothing to purchase for the remaining $5. Unused gift-card values are also dead-weight but since the issuing merchant eventually declares it as a revenue (after the card expiry), the value is not all lost. Legislature in some states makes it liable for merchants to redeem buyers in cash for unutilized gift-card amounts. There is also a secondary market for buy-sale of gift cards.

The most interesting case is for richer recipients. Economics teaches us the law of diminishing marginal returns. As we have more of a specific good, our marginal value for each additional unit of the good decreases. Same goes for money. A poor man values every $1 more than a rich man. Thus no matter what gift we give to a rich friend or a relative, he will always value it lower than the original price. Thus rather than giving materialistic gifts, Waldfogel suggests altruistic gifts like a charity card. A market of charity pledge cards is fast catching steam where the issuer is liable to donate a certain amount to the charity of your choice. One could argue that charity donations also are subject to diminishing returns, but since charitable organizations generally produce multifold results for each dollar donated, it is the most efficient gift. For instance, $1/day/kid donated to improve nutrition in diet of impoverished kids in sub-Saharan Africa could result in their improved health and productivity facilitating the growth and development of the impoverished Societies.

In most cases, I do agree with Joel Walfogel and his rationale on selecting the most optimum gift for your recipients. However I am still wary of his estimation of an average 18% value loss from gifts. I have the following concerns -

1. His 18% is made up of different relationships, each with their estimated efficacy of value creation.
2. He discounts the sentimental value created for the giver and the recipient. Agreed that there is a disutility from disappointing gifts but remember it’s the “thought” that most often counts. A poor gift could also be a great source of memory.
3. A gift could lead to high transactional efficiency. For instance, a Kindle which retails in the US for $130 is not available in Singapore. I value it as high as $250. If a friend in States gifts me a Kindle, there is ~100% increase in value.
4. He discounts the value creation for the giver. Giver could have ulterior motives in giving a specific gift. For instance, a Dad gifting his young son, a book on mathematics in a hope he becomes an engineer, me gifting “Scroogenomics” to a friend, in a hope of having an intellectually stimulating discussion on this very topic, or you getting a movie ticket just to ask someone out on a date. These are not always selfish as seen from the examples. The son enjoying maths, my friend enjoying the book and the date enjoying the movie, without the possibility of having a chance to experience them in the first place (without gifts).
5. Gifts as tool to signal your care and affection for the person to the society, should not be discarded
6. Since people voluntarily continue to give and receive gifts, does that mean it is pareto-optimal. If there was any way to improve the benefit, society would have already moved towards that equilibrium (Jef Ely)
7. Finally, the entire process of searching and thinking about the gift, makes you  know the person better and hopefully be better gift givers in the future, thereby increasing the return in subsequent years

Phew, I know this post was really long, but the economics behind it is really fascinating. Economists and social scientists are still on the fence, on how socially efficient, gift giving is. I would also like to include a nice illustration from WePay’s blog on the “Holiday Misgivings”.
Happy Holidays, enjoy all the gifts. But Remember, the next time you shop for one, put in a bit of thought in your gifts ;)

List of great resources on the same subject:
WePay: http://www.wepay.com/blog/2010/12/21/holiday-misgivings-the-real-dynamics-behind-holiday-gifting/
Jeff Ely: http://cheeptalk.wordpress.com/2009/12/23/the-real-economics-of-holiday-gift-giving/

The Deadweight Loss of Christmas: (Joel’s original paper)
The Deadweight Loss of Christmas: Comment : http://www.idc.ac.il/publications/files/393.pdf

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Why do we leave tips for some service but not for others?

It has become customary at most places to leave 15-20% of the total bill as a tip for good service at restaurants. But it is illegal to tip some service providers. For instance, the clerk at your immigration office.
Why this distinction?

If we go back, tipping in restaurants originated to induce better service. Restaurant owners are willing to reward attentive and courteous servers, since better service leads to repeat customers. And the reward incentivizes waiters to put in extra effort to improve the dining experience.

One way to achieve this is that owners monitor their staff and reward them accordingly. However, this is painstakingly difficult. An elegant solution devised by restaurant owners was to reduce the price of food slightly and leave the onus to the diners by announcing that they leave a bit extra if they are pleased with the service. Diners are perfectly positioned to monitor service quality.

From a diners perspective his willingness to pay remains the same as earlier as the reduction of list price of the meal compensates for the tip.
They are at an advantage since competition in restaurant industry makes it difficult for servers to exploit less generous customers by withholding quality service. Customers can always choose a different place to dine, the next time.

Now imagine you go to your Immigration and Checkpoint Office (ICA) to renew your residency permit. ICA is what you would call a monopoly. If tipping was made customary, due to lack of competition, clerks would refuse to serve you without a generous tip. Thus tipping is illegal in services without market competition.

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Hot or Not? Rating Chicks at bars and the notion of Collective decisions – Field study

Me and my college mates were thinking of ways to kill time, this Friday evening. And we decided to play a simple game. Each of us would take turns in spotting a member of the opposite sex, and we would rank her purely on her appearance. Then we would compare our scores and see who was the biggest fan and who was the harshest critic. I consolidated the scores and the results are quite interesting.

Rationality of choice and preferences were introduced long back. Adam Smith was of the notion that each individual/entity is driven by his/their own preferences. Each of them take decisions which will maximize their outcome, and collectively the economy of Suppliers and Consumers moves towards an efficient equilibrium. Also famously known as the “Invisible hand”, forms the foundation of microeconomics.

The reason why the above mentioned idea works, is that each of us have our own unique preferences, which may or (quite often) may not be similar to the rest of the group. However, preferences and perceptions can be changed over time by peer influence, societal changes, information, advertisements, etc.

Firms know this. Hence they can group similar consumers together, and based on their willingness to pay, form the demand curves.A homogenous perfect group implies that any individual can effectively represent the entire group.

 I have always been been fascinated by the uniqueness in individual perception, and how groups are formed. A lot of key societal decisions and policies are formed on group consensus. What interests me is the variance of the group decision versus the optimal individual decision, and how it influences society, people and the economy.

Now back to to the fun part.

Let me first describe the raters here. It is 4 of us, each in our mid 20s, with a similar educational background (a college degree in engineering) , similar professions (Banking, Technology, Finance) but from 4 competing MNCs. We will call them, LD, PJ, AS and RK. We managed to select 16 subjects to rate. And each individual was subjected to a diligent discussion before the final ratings were given (on a total of 10).

Average 6.1 5.2 4.7 5.6 5.4
Highest 8.0 8.0 6.5 9.0 7.6
Lowest 3.5 1.0 2.0 1.5 2.9
Range 4.5 7.0 4.5 7.5 4.8

LD, on an average gave a score of 6.1/10 to the subjects, with a high of 8/10 and a lowest of 3.5/10. RK gave an average of of 5.6/10 with his highest being 9/10 to a certain individual and lowest 1.5/10.
Where RK and PJ represent a highly critical group, with a variance of 7+ between their best and the last. LD and AS had a more consistent rating, with a moderately extreme opinions.

Now let us drill down into the scores, in a descending order of their averages.

# Subjects LD PJ AS RK AVG Highest Lowest
1 MW 7.5 8 6 9 7.6 RK AS
2 SH 7.5 7.5 6.5 6.5 7.0 PJ Tie
3 RB 5.5 7 6.5 8.5 6.9 RK LD
4 NS 6 8 6 7.5 6.9 PJ Tie
5 DB 6.5 6 6 8 6.6 RK Tie
6 RBB 8 6.5 5 6 6.4 LD AS
7 SN 6 6 5.5 7.5 6.3 RK AS
8 DK 8 5 5 6 6.0 LD Tie
9 PB 6.5 5 4 5.5 5.3 LD AS
10 MK 7.5 4.5 4 3 4.8 LD RK
11 AD 5 7 3 3 4.5 PJ Tie
12 LM 5.5 3 5 5 4.4 LD PJ
13 AN 4 3 5 4.5 4.1 AS PJ
14 TR 3.5 1 4 5.5 3.5 RK PJ
15 AG 6.5 2 2 2 3.1 LD Tie
16 BM 4 4 2 1.5 2.9 Tie RK
The highest group average went to MW ~7.6/10 and lowest to BM, where the scorers were quite consistent in their preference.

Table Highest Table Lowest Variance
LD 6 1 0.7
PJ 3 3 (0.2)
AS 1 4 (0.7)
RK 5 2 0.2
Tie 1 6
16 16
Let us look at the table toppers. LD gave 6 high scores closely followed by RK. AS gave 4 lowest score, followed by PJ.

So who do you think was the best judge? Do you see a certain bias in scores of some select individuals? Is there inconsistencies in the group v.s. individual preference? Do you think not all of the judges were equally Rational?

As I work more on the analysis. You would notice, there are 2 subjects who are statistical outliers. One benefited a lot from the irrationality of the judges and the other got the harshest result :)

Art of Bargaining

I find bargaining with street peddlers and merchants highly challenging. My mom on an average can haggle 30% lower than my very best effort.
Interestingly, I am far more educated and professionally qualified than my mom. And I am often called upon at work to analyse multi-million dollar procurement deals and help them negotiate the best possible price.

Bargaining is an art and as I try to understand this failure of mine and the uncanny success of my mom, it is an interesting problem nevertheless.

Let's assume I am walking on a narrow stretch in South Delhi in my home country India when suddenly my eyes fall upon the most beautiful scarf. It's bright orange with beautiful hand crafted glass pickings. I know I have to get one and gift it to a certain someone. So I ask the merchant, how much is one, and he immediately replies " 500 Rupees Sir" (~11 USD).

Obviously my gut feel says it shouldn't be more than 100, so I reply back in our local language "Bhaiya hum to yehin ke hain. Sau rupai le leejiye. Usse zyada nahin ( Brother, I am from here. I am not paying more than 100) ". Our discussion continues and 5 mins later, we seal it at 150. I return home satisfied with a neat 70% reduction from his initial quoted price, but before I can celebrate, my mom returns with two such scarves at 80 Rupees each.

Amazing right. To deduce the above, I follow my mom, the next time to find out how she did it and construct my hypothesis. So here it is.

Defining Bargaining
Let's define two parties- A Buyer  and a Seller. Both of them have personal incentives to negotiate for the best possible price. Assuming this a niche good, and no one else in the vicinity sells exactly the same scarf, we would call the Seller a Monopolist.

This single buyer and seller situation is trickier than a competitve market, since competition can drive prices towards an equilibrium, nullifying any need for negotiation. And the goods in question are niche, non comparable items with no fixed marked price.

Perceived Value of the traded good
Compared to my mom, I value the scarf more, for it's an opportunity to impress the ladies. Imagine this pickup line, "Well, I was rushing for some urgent work when I saw this and thought how wonderful it would look on you. Hope you like it".

I would love to get the scarf (with all the other ancillary benefits) at 100Rs, but I can compromise till 150. This is my utility enhancing, perceived value of the scarf. Anything less, I would be happier. Anything more, I am better off not purchasing.
On the other hand, the only reason my mom is interested in it is a fact that long back I had told her to help me get something nice for my colleagues at work, each time I visit India. Her perceived value is my emotional gratitude to her for remembering my request. Let's not quantify mother's love by assigning a value to it.

This difference in perceived value leads to two things. Firstly, it makes me quote a higher first lowest bid (100 in my case whereas it was 50 in my mom's), after which I can only bid up. Secondly, I have a higher risk of losing the scarf if the exchange falls apart with the seller deciding not to sell, or not to quote below 150 ( my price tolerance limit). On the other hand, my mom has nothing to lose.
We economists call it a first degree price discrimination where the Seller (Monopolist) tries to ascertain our individual price tolerance, in order to extract the maximum value that each of us are willing to pay. The bargaining process is just a tool to assist him in deducing this perceived value.

Perceived Value of money
Living away from India has definitely spoilt me. For 150 Indian rupees, you can get 7 liters of milk, or 2 Big Macs (called Chicken Maharaja here) or a month of mobile talk time, or a 25 km cab trip from airport to home. Whereas for 5SGD in Singapore, I can only get 1 Big Mac or 2 cartons of milk or a 4 km cab ride from the nearest food court to home or just a small cafe latte at starbucks.

Hence, it's easier for me to part with a 100 than my mom to part with her 50, for a scarf which has a higher perceived value to me.

Uncertainty and Rational Behavior of the Seller
Economics teaches us, a rational individual will maximize his utility given certain constraints. For the seller, his utility is proportional to his profit function.
Say, he procured 100 scarves from a craftsman for 50 rupees each. Let's assume his transportation cost was 500, his other fixed costs add up to 15 more for each scarf. For him to earn profit, he must sell all of them at an average price above 70.

His range of negotiable price would be as high as he can quote to, and as low as 50 (variable cost), keeping in mind, he can sum a neat profit in the end.

But why quote 500 then, when it is a whooping 614% profit? I guess, a couple of reasons for it. Firstly, his nett investment on the 100 scarves is 7000 INR. When he starts selling, he is a bit unsure on how many he will sell. Assuming, before me, he managed to sell only one. He safely estimates if he can sell off 20 at a premium, and remaining 80 at a loss, he can still pocket a good profit.
If we do the math 7000/20= 350

Now even if he sells the remaining at 20 each, he gets 1600 which is a 23% profit.
Interestingly, he starts his quote at 500 and not 350, knowing that his customers would always bargain and try to pitch a lower price. Also, as he starts selling more scarves with profit, his confidence of recovering his investment increases, and he is more forthcoming to bargaining. Thus if you buy later, you might end up with a better price but as a tradeoff you have lesser colors to chose from, since all the better ones have already been bought with a slight premium.

The starting quoted price (500 in this case) is also a function of the economic condition of the society. In a relatively poor society like in India, sellers will often try to cheat the more affluent customers who find it hard to guage the true value of the commodity. It is also a lot easier for the seller to price discriminate based on the appearance and personality of each buyer. Were all buyers alike, it would have made the Seller's job a lot harder.

Also, merchants are often required to bribe their local authorities and mobs to do a hassle free trade. This corruption increases their fixed cost. And now add to it the customer's higher percieved value of the good and their lower percieved value of money. This results in merchants often quoting a lot more to rich or new buyers. Foreigners are privy to such unfair experience. 

Based on the above discussion, there is a reason why my mom is more successful in this ancient art of haggling. So words of wisdom, the next time you shop, don't forget to bring your mom along. Happy shopping!

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