# Meru’s pricing strategy

Let’s assume I’m writing this post two weeks back when Uber, Ola and TaxiForSure were still running successfully in most places in India. Since then, they’ve been banned to various degrees and it’s gotten harder for customers to get them and for drivers there to find customers leading to a sharp drop in volumes.

Thanks to the entry of app-based taxi booking services such as Uber, Ola and TaxiForSure, entrenched players such as Meru Cabs and Easy Cabs started losing business. This is not unexpected, for the former operated at around Rs. 13-15 per km range (depending on discounts, time of day, etc.) while the latter operated around the Rs. 20 per km price point. This meant that for immediate trips and mostly intra-city movement consumers eschewed the likes of Meru and embraced the likes of Ola.

In the last few weeks I’ve spoken to taxi drivers (mostly Uber; Ola drivers don’t inspire much confidence and so I don’t indulge them in conversation; and I’ve never got a cab via TaxiForSure) who have been affiliated to more than one aggregator, and from that I get what the problem with Meru’s pricing is.

What sets apart Meru, KSTDC and Mega Cabs is that the three are the only operators with a license to pick up passengers from the taxi rank at the Bangalore Airport. Any other taxi that you might book (Ola or Uber or a local cabwallah) don’t have the rights to pick up passengers there and park in the airport’s taxi parking zone. They instead have to park in the space allocated to private cars, paying the parking fees there, and  there is usually a delay from the time when the driver meets the customer at the arrival gate to the customer actually getting into the car. This distinction means that the likes of Meru and Mega offer superior service to the other operators at the airport and thus can command a premium price. Getting into anecdata territory but I always prefer to get a cab from the taxi rank (though the queue occasionally gets long) than to book a cab for which I’ve to wait.

At the city end, the difference between Meru and Uber (Ola is in an intermediate state) is that you can pre-book a Meru, while Uber only accepts “spot bookings”. This difference in service levels means that you can never be assured of getting an Uber at the time you want to leave for the airport – there is a statistically high chance of getting one but you don’t want to take the risk, and thus prefer to pre-book a Meru or a Mega, which lets you know at the time of booking if they are able to service you.

Now, this guarantee from a Meru or a Mega comes at a cost. An Uber cabbie who also drove for Easycabs told me that Easycabs would allocate his trip an hour before it was scheduled to start. Since Easycabs would have assured the customer of a cab reaching his place at the appointed time, this means that they need to account for a sufficient buffer to ensure that the cab does reach on time. Thus the allocation an hour in advance. This cabbie told me that from his point of view that was inefficient, for in the one hour of buffer that EasyCabs would add, he could complete one additional trip through Uber!

So it is clear as to why Meru is more expensive than Uber/Ola – their pre-booking provision means that they have to potentially ground your cab for an hour before pickup, and there is a license fee they have paid the airport for the right to pick up passengers from the taxi rank there. Notice that both these factors also result in increased convenience for passengers. So effectively, Meru is justified in charging a premium. The question is if the current structure is optimal.

The problem with Meru is that their fare structure doesn’t appropriately represent cost. A pre-booked taxi costs as much as a taxi hailed at the time of demand. A taxi from the airport (where they have paid license fee) costs as much as a taxi from anywhere else. So while their cost structure might be optimal for travel to and from the airport, the structure simply doesn’t work out for other rides. And they are getting priced out of non-airport rides.

Assuming that they want to get more non-airport rides for their fleet, how do they do it? The answer is rather simple – let the fare structure reflect cost. Rather than tacking on every piece of cost to the per kilometer fare, they can have a multi-part fare structure which is possibly more “fair”.

A typical trip from the airport to the city is about 40 km, and costs around Rs. 800 (excluding service tax). Instead of charging Rs. 20 per trip, how about charging Rs. 16 (Ola’s rate) per kilometer and an additional Rs. 200 “airport charge”? At the other end, how about charging an additional Rs. 100 or Rs. 200 as pre-booking charge in order to account for driver’s idle time on account of the pre-booking? If they were to charge this way, they will both make as much money as they currently do on airport trips, and also compete with Ola and Uber on intra-city immediate-ride trips.

To take an extreme analogy, this is like asset-liability management – prudent banking dictates that the term structure of your assets reflects that of your liabilities. Similarly, prudent pricing (to the extent it is practically implementable) dictates that your price structure reflects on your cost structure!

# Uber’s surge pricing, Urban Ladder’s Diwali sales and clearing marketplace transactions

I recently bought a bed from Urban Ladder. Since I bought it during their Diwali sale, I got a 20% discount on it. It was supposed to be delivered in three weeks, but it took four. For the trouble caused by the delayed delivery, they gave me an additional 5% discount. As a lay customer, I would have been delighted. As someone with ideas on liquidity and two-sided markets, I’m still delighted by the customer service but intrigued as to why they had to offer the sale at all.
Before we proceed, a word on two-sided markets. By definition, all markets are two-sided, for there is a set of buyers and a set of sellers. The difference between a “traditional market” and a “two sided market” or “platform” as we understand it is that in the former case, the owner and designer of the market is also a participant. Rather the designer of the market is the only participant on the sell side. In a “platform” scenario, the designer of the market is not a participant. The designer makes money by enabling and facilitating transactions. For the rest of this post, however, we will return to the popular definitions and imply “two sided markets” to refer to markets where the market designer is not a participant.
In a two-sided market (by popular definition), the owner of the market usually makes money on a transaction basis. She either takes a fixed sum of money per transaction or more usually a proportion of the value transacted. For example, when you trade stocks, both buyer and seller pay small fees to the exchange (this is in addition to the fees paid to their respective brokers). When you ride an Uber, the marketplace (Uber) takes 20% of the ride proceeds (not currently the case in India, though). Thus, it is in the interest of the designer of the market to maximise the volume/value (usually the latter) of transactions on the market.
Now, two-sided markets have a virtuous cycle/positive feedback built in. The more the buyers you have, the more the sellers want to sell on your “exchange”. And the more the sellers you have, the more the buyers who want to buy. Thus, as a market designer, your job is to “seed” the exchange, to an extent that this virtuous cycle takes off, and then you can essentially relax as the market builds itself and more transactions are transacted.
This necessitates that in the initial stages of building the market, the marketplace will have to make some investments such that buyers and sellers find it profitable to transact. For example, you might choose to take the hit on most of the transaction costs that buyers and sellers face. For example, consider the cab companies in India such as Uber and Ola, which are subsidising both drivers and customers in the hope of building up their respective marketplaces. Once these marketplaces are built and the virtuous cycle kicks in, the platforms can then start making profits.
Building a marketplace is in a sense like climbing two ladders simultaneously, with one foot on each. You have to make constant efforts to beef up both demand and supply, for if at any point in time one goes too far ahead of the other, the market gets unbalanced and you will either have dissatisfied participants (because they could not find a counterparty) or you have to take a hit to ensure that the market gets cleared (to continue the metaphor you either strain your loins or you fall off the ladders ). From this perspective, the recent Diwali sale on Urban Ladder doesn’t make too much sense.
I’m getting into anecdata territory here, but as a customer my main pain point regarding Urban Ladder has been their availability. Every time I’ve wanted to buy something it’s either been out of stock or the delivery cycle has been too long – never has the price been a problem to me. My understanding of their market, thus, has been that demand has been far outstripping supply, and at their current market clearing prices (notice that urban ladder sets the prices at which customers buy on the platform), quantity demanded far exceeds quantity supplied. The normal economic response to this would either be to jack up prices – to a level where the market clears, or to aggressively woo suppliers, such that the market clears at current prices. Instead, Urban Ladder made the problem worse by subsidising customers, which further pushed up the gap between quantities demanded and supplied.
Figure 1 illustrates this problem. In the face of the discount (effectively a subsidy) by Urban Ladder, the demand curve shifted right. There was already a gap between demand and supply at the undiscounted price (which was lower than the market clearing price), and the introduction of the discount only made this gap worse. (the Y axis of this graph refers to the price received by the seller).
In the face of the discount, demand moves downward along the curve, and the demand-supply gap increases as shown in the figure.
During Diwali, Urban Ladder offered a 20% discount. It is unlikely that this discount would have been passed on to their suppliers, which means that the marketplace took a temporary hit in margins in order to grow their market. While it would have grown the market in terms of increasing orders from the buy side, it is unlikely that the market itself would have grown – since the problem with Urban Ladder is supply and not demand.
In the traditional inventory-led model, sales promotions and customer incentivisation are common techniques in order to grow sales – the incentives not only lead you to increase your sales, but also result in a clearing out on your inventory to make room (and working capital) for fresh stocks. In a marketplace model, however, where the bottleneck is clearly on the supply side, it is not clear how a sale results in growth. It seems like Urban Ladder got carried away by the traditional model of growing topline in an inventory-led model.
So does that mean that Urban Ladder’s Diwali sale was wrong? Not really, for they could have done it better. The way to do it would have been to first approach suppliers and lock in an increase in supply. This would have necessitated some subsidies on the supply side – like for example guaranteeing a certain amount of orders during the sale month. Supplies thus guaranteed, Urban Ladder could have then brought on a sale on the demand side to an extent that
1. it would be within their promotional budget and
2. the market would have been cleared.
In fact, it is not even necessary that the discount would have to be entirely monetary – for Urban Ladder could have structured the discount as “10% off sale price and 1 week delivery” or something.
The important thing to consider, thus, is that in a market place model, both demand and supply side are elastic – something that is not the case in an inventory led model where once you have the inventory the supply is largely inelastic. Thus, when demand exceeds supply, one way to clear the market is to actually raise the incentives for the supply side (rather than reducing incentives for the demand side). And this is something that Uber gets right with its surge pricing.
When there is a surge in demand on Uber, prices are jacked up, and more importantly, the jacked up prices are passed on to the drivers. Thus, the jacked up prices help clear the market from two sides – culling demand and increasing supply – for higher prices for a ride would mean that drivers who would otherwise be loathe to venture out into heavy traffic or rain (conditions when surge usually kicks in) would have more incentive to come in and help clear the market!
A market place such as Uber or Urban Ladder is basically a mechanism of matching supply to demand, and the key is in getting the pricing right. Constantly “listening” to both demand and supply helps you do that, and as Uber’s constantly updating surge prices show, adjustments are required. Of course such frequent adjustments are not prudent from the perspective of a company like Urban Ladder. But it is important for them to get at least the direction in the price movement right.
Errata
The original version of this piece indicated the change in price as effecting a shift in the demand curve itself. As those of you know Econ 101 better than I do know, this is simply wrong and the price change results in a movement along the curve. Thanks to Shruti Rajagopalan for pointing this out.

# Valuing loan deals for football players

Initial reports yesterday regarding Radamel Falcao’s move to Manchester United mentioned a valuation of GBP 6 million for the one year loan, i.e. Manchester United had paid Falcao’s parent club AS Monaco GBP 6 million so that they could borrow Falcao for a year. This evidently didn’t make sense since earlier reports suggested that Falcao had been priced at GBP 55 million for an outright transfer, and has four years remaining on his Monaco contract.

In this morning’s reports, however, the value of the loan deal has been corrected to GBP 16 million, which makes more sense in light of his remaining period of contract, age and outright valuation.

So how do you value a loan deal for a player? To answer that, first of all, how do you value a player? The “value” of a player is essentially the amount of money that the player’s parent club is willing to accept in exchange for foregoing his use for the rest of his contract. Hence, for example, in Falcao’s case, GBP 55M  is the amount that Monaco was willing to accept for foregoing the remaining four years they have him on contract.

Based on this, you might guess that transfer fees are (among other things) a function of the number of years that a player has remaining on his contract with the club – ceteris paribus, the longer the period of contract, the greater is the transfer fee demanded (this is intuitive. You want more compensation for foregoing something for a longer time period than for a shorter time period).

From this point of view, let us now evaluate what it might take to take Falcao on loan for one year. Conceptually it is straightforward. Let us assume that the value Monaco expects to get from having Falcao on their books for a further four years is a small amount less than their asking price of GBP 55M – given they were willing to forego their full rights for that amount, their valuation can be any number below that; we’ll assume it was just below that. Now, all we need to do is to determine how much of this GBP 55M in value will be generated in the first year, how much in the second year and so on. Whatever is the value for the first year is the amount that Monaco will demand for a loan.

Now, loans can be of different kinds. Clubs sometimes lend out their young and promising players so that they can get first team football in a different club – something the parent club would not be able to provide. In such loans, clubs expect the players to come back as better players (Daniel Sturridge’s loan from Chelsea to Bolton is one such example) and thus with a higher valuation. Given this expectations, loan fees are usually zero (or even negative – where the parent club continues to bear part of the loanee’s wages).

Another kind of loan is for a player who is on the books but not particularly wanted for the season. It could happen that player’s wages are more than what the club hopes to get in terms of his contribution on the field (implying a negative valuation for the player). In such cases, it is possible for clubs to loan out the player while still covering part of the player’s salary. In that sense, the loan fee paid by the target club is actually negative (since they are in a sense being paid by the parent club to loan the player out). An example of this kind was Andy Carroll’s loan from Liverpool to West Ham United in the 2012-13 season.

Falcao is currently in the prime of his career (aged 29) and heavily injury prone. Given his age and injury record, he is likely to be a fast depreciating asset. By the time he runs out his contract at Monaco (when he will be 33), he is likely to be not worth anything at all. This means that a lion’s share of the value Monaco can derive out of him would be what they would derive in the next one year. This is the primary reason that Monaco have demanded 30% of the four year fee for one year of loan.

Loaning a player also involves some option valuation – based on his performance on loan his valuation at the end of the loan period can either increase or decrease. At the time of loaning out this is a random variable and we can only work on expectations. The thing with Falcao is that given the stage of his career the probability of him being much improved after a year is small. On the other hand, his brittleness means the probability of him being a lesser player is much larger. This ends up depressing the expected valuation at the end of the loan period and thus pushes up the loan fee. Thinking about it, this should have pushed up Falcao’s loan fee above GBP 16M but another factor – that he has just returned from injury and may not be at peak impact for a couple of months has depressed his wages.

Speaking of option valuation, it is possibly the primary reason why young loan signings to lesser clubs come cheap – the possibility of regular first team football increases significantly the expected valuation of the player at the end of the loan period, and this coupled with the fact that the player is not yet proven (which implies a low “base sale price”) drives the loan valuation close to zero.

Loaning is thus a fairly complex process, but players’ valuations can be done in rather economic terms – based on expected contribution in that time period and option valuation. Loaning can also get bizarre at times – Fernando Torres’s move to Milan, for example, has been classified by Chelsea as a “two year loan”, which is funny given that he has two years remaining on his Chelsea contract. It is likely that the deal has been classified as a loan for accounting purposes so that Chelsea do not write off the GBP 50M they paid for Torres’s rights in 2010 too soon.

Every time there is some activity in the football transfer market, you are likely to hear one of two things. Either a particular player was “a steal” or the buyer “overpaid”. You seldom hear that a player was bought or sold at a “fair price”. What drives this?

Note that the issue is not perception – if you look at the transfer dealings, you are likely to find that the general opinion of whether the transfer fee was too high or too low is in most cases fairly accurate. Even if it is not accurate at the time of the transfer, it gets borne out in the subsequent year or two after sale.

Two weeks back I took a class in introductory economics for a bunch of people who hope to get elected to the Bangalore Municipal Council (BBMP). Teaching them about demand and supply, and trade, I mentioned that in any voluntary trade, both the buyer and the seller are “winners”. For example, if Liverpool sold Fernando Torres to Chelsea for GBP 50 million, it means two things: One, the value that Liverpool placed on the future contribution of Torres to the club was less than GBP 50 million. Two, the value that Chelsea placed on the future contribution of Torres was more than GBP 50 million. If either of the above conditions were not true, the deal would not have happened.

So why is it that football transfers usually end up costing too much or too little? The answer lies in “liquidity”. Liquidity is a concept that is normally used in financial markets as a measure of the depth of the market. It measures how many people are willing to buy and sell a particular commodity at a particular point in time. The theory is that the greater the number of buyers and sellers for a particular commodity, the better is the price discovery. I’ve said this several times before – it is unfortunate that the concept of liquidity doesn’t find as much traction in mainstream economics literature.

Coming back to football – why is it that players are typically either undervalued or over valued? Because players are unique, and that makes the market illiquid. Let us go back to the deal that took Torres to Chelsea. Let us say that the value Chelsea placed on his future services was GBP 50 million, and the value that Liverpool placed on his future services was GBP 35 million (numbers pulled out of thin air). Given that Liverpool owned him, this deal could have taken place at any value between these two numbers (note that at any price between 35 and 50 million, both Liverpool and Chelsea would be willing to trade)! So why did the deal take place at one end of the spectrum?

It was a consequence of how badly the two clubs wanted to do the deal. While Torres had lost form and hadn’t been performing in the 2010-11 season, Liverpool were quite happy holding on to him – they were not desperate to do the deal. Even when offered an amount higher than their valuation of the player, they sensed Chelsea’s desperation in doing the deal. So Liverpool’s game here was to hold on long enough until they knew Chelsea had bid an amount they were unlikely to improve on, and then they sold.

Sometimes fans like to sing something like “there is only one Fernando Torres” (typically when he scores). And that is the precise reason that Liverpool was able to get a premium on his sale. There was a certain kind of player whom Chelsea desperately wanted to buy, and Torres was the one who fit the bill perfectly. Given the lack of comparables, and the desperation of the buyer, it became a seller’s market and Liverpool were able to profit from it.

So we have seen here that when the buyer is more desperate to do the deal than the seller, the deal takes place at the higher end of the “value spectrum” (I just made up that phrase at this moment). It can go the other way also. When Liverpool sold Torres, they (rather unwisely) invested most of it buying a player called Andy Carroll from Newcastle United. Carroll turned out to be a dud – he was increasingly injury prone, and when a new manager Brendan Rodgers came in, he found him to be not suitable for the style of football Liverpool wanted to play.

The presence of Carroll in the squad, however, would put pressure on the manager to play him – largely a consequence of the fee that had been paid to purchase him. To this end, Rodgers decided that it was better to cut his losses and remove Carroll from the squad, rather than play a suboptimal brand of football just so that Carroll was played. Rodgers correctly decided that the money that had been spent in buying Carroll was a “sunk cost”.

Now, in his year and a half since his arrival at Liverpool, Carroll had done much to convince people that he was overvalued. His injuries and lack of form meant that clubs were unwilling to value him highly, and given Liverpool’s determination to sell, it was a seller’s market. The GBP 15 million that Liverpool extracted from West Ham for the sale was perhaps exactly the value that Liverpool had placed on Carroll.

To summarize – you sell if the price is higher than your valuation. You buy if the price is lower than your valuation. The buyer’s and seller’s valuations together determine the “value spectrum” along which a sale can be done. Presence of comparable commodities means that people can go for substitutes, and so that shrinks the value spectrum. In case of footballers with few comparables, there are no factors compressing the value spectrum, and the full extent of it is available.

In a large number of cases, one of the buyer and seller is much more desperate to do a particular deal than the other. And that pushes the price of the deal to one of the edges of the value spectrum. Hence people end up either significantly underpaying or significantly overpaying for footballers.

The coming of the internet has led to one round of disintermediation in the travel market, and I hypothesize that review websites such as TripAdvisor are going to lead to another. Let me explain.

In the “good old days” if you wanted to travel there was no option but to reach out to the neighbourhood travel agent who would give you options of a few airlines and hotels. The best you could do to figure out if you were being taken for a ride was to check across multiple agents, but even then the only thing you could compare was price. It was impossible to compare hotels in terms of quality and you would take the word of the travel agent.

And then the internet happened.

Now, with sites such as Expedia or Travelocity, you got more transparency in pricing – especially when it came to airline ticketing. The travel agent could no longer take you for a ride when it came to the air fares – you could cross check online and bypass the agent if he wasn’t offering you a good deal (of course some things such as flexible schedules were best booked via agents, and they continue to hold sway in the corporate segment for that reason). Simultaneously airlines started selling tickets direct, via their own websites (this was led in part by “low cost carriers” who saw this as a good way of saving cost by cutting out agent fees).

This was the  first round of disintermediation in the travel industry. Airlines selling tickets direct and customers being able to book directly online meant the overall business of travel agents reduced. Some of them were cut out completely while others were replaced by large-scale technology enabled agents such as Expedia or Travelocity. Those that survived either have corporate clients (who need flexible schedules and have little time to book online) or have resorted to packages – where they arrange for flights, accommodation and cars, and quote you a consolidated fee – in which there are margins to be made.

The move to large-scale technology-enabled agents meant that some of these agents were now large-scale aggregators. This gave them significant bargaining power vis-a-vis hotels and this allowed them to bargain for deep discounts. While earlier conventional wisdom was that “travel agents” could get you “good deals”, now these large online aggregators were the ones providing the “best deals”. Thus it made eminent sense to book via these aggregators.

Simultaneously most hotels also started direct booking on their own websites. However, the problem was that the hotels themselves did not have the technological capability to implement good revenue management practices on their own websites. They also did not have the technological capability to offer a seamless and smooth booking experience. Thus, large online agents such as booking.com and Agoda prospered.

There are two functions that a travel agent performs – helping customers discover hotels and then actually executing the booking. In the traditional model, agents don’t charge for the discovery process. That service is instead cross-subsidized by the fees they make on the actual booking process. The first level of disintermediation in the travel agency (which we’ve seen above) has chipped away at this model, however. What do I, a travel agent, have to gain if I put in painstaking research and find you a hotel, only for you to find that you can book it for a lower price online? Agents, however, have not figured out a way to charge for the discovery process.

However, it is unlikely that they need to. For you now have websites such as TripAdvisor which have user-generated reviews and ratings for a large number of hotels, and which rank hotels in each city by type and user ratings. TripAdvisor has become so ubiquitous for user-generated ratings for hotels that nowadays travel agents add links to TripAdvisor profiles of hotels that they are recommending. Thus, we can see that the hotel discovery process can exist independently of travel agents.

What of the bookings itself? Don’t we need travel agents for that? Note that irrespective of whether a travel agent is online or offline, the hotel has to pay them a commission for selling their inventory. In the past given their size, hotels (unlike airlines) were unable to effectively sell rooms on their own websites and thus resorted to paying travel agents. However, advances in technology now mean that it is easy for a hotel to adopt a third-party software to effectively manage their inventory and sell tickets on their own website, and at a fraction of the cost they need to pay travel agents.

So, if TripAdvisor helps you discover hotels and then you can book hotels directly through their own websites, who needs travel agents? For now, most large online aggregators have a price matching policy and thus match the prices that hotels quote on their own websites. However, in order to save booking fees (rumoured to be of the order of 17% of the total booking value) hotels are trying to innovate and add freebies to their offering.

For example, a hotel in Cambodia I stayed in last week offered a free massage to guests who had booked through their own website (unfortunately I booked via Agoda and couldn’t avail of this offer). The Bangkok hotel I stayed in last week offered a 10% discount on payments made via American Express on their own website (again we discovered this after we had booked on Agoda, using an AmEx. To their credit, Agoda gave us a refund to the extent of the discount we would have got on the hotel website).

Essentially hotels have figured that with the growing popularity of platforms such as TripAdvisor, they don’t really need travel agents, small or large. As TripAdvisor gets more popular and third party hotel booking softwares gain traction, we are likely to see the decline of large travel aggregators such as Expedia, Travelocity and Agoda.

In essence, the growth of TripAdvisor is going to lead to the partial downfall of its erstwhile parent Expedia.

# Why the rate of return on insurance is low

I’m currently doing this course on Asset Pricing at Coursera, offered by John Cochrane of the University of Chicago Booth School of Business. I’m about a fourth of the way into the course and the beauty of the course so far has been the integration of seemingly unrelated concepts. When I went to business school (IIM Bangalore) about a decade ago, I was separately taught concepts on utility functions, discount rates, CAPM, time series analysis and financial derivatives, but these were taught as independent concepts without anybody bothering to make the connections. The beauty of this course is that it introduces us to all these concepts, and then shows how they are all related.

The part that I want to dwell upon in this post is the relationship between discount factors and utility functions. According to one of the basic asset pricing formulae introduced and discussed as part of this course, the returns from an asset is a positive function of the correlation between the price of the asset and your expected consumption growth. Let me explain that further.

The basic concept is that one’s utility function is concave. If you were to plot consumption on the X axis and utility from consumption on the Y-axis, the curve would look like this:

In other words, let us say I give you a rupee. How much additional happiness would that give you? It depends on what you already have! If you started off with nothing, the additional happiness out of the rupee that I gave you would be large. However, if you already have a lot of money, then the happiness you would derive out of this additional rupee would be much lower. This is known in basic economics as the law of diminishing marginal utility, and is also sometimes called the “law of diminishing returns”.

So, let us say that tomorrow you will either have Rs. 80 or Rs. 120 (the reason for this difference in payoff doesn’t matter). Let us call these as states “A” and “B ” respectively. Now, suppose I’m a salesman and I offer you two products. Product X  pays you Rs. 20 if you are in state A but nothing if you are in state B. Product Y pays you Rs. 20 if you are in state B and nothing if you are in state A. Assuming that you can end up in states A or B with equal probability, which product would you pay a higher price for?

The naive answer would be that you would be indifferent between the two products and would thus pay the same amount for both. However, rather than looking at just the payoffs, you should also look at the utility of the payoffs. Given the concave utility function, you would derive significantly higher happiness from the additional Rs. 20 when you are in State A rather than in State B (refer to appendix below). Hence, you would pay a premium for product X relative to product Y.

Now, from a purely monetary perspective, the payoffs from X and Y are equal. However, you are willing to pay more for product X than for product Y. Consequently, the expected returns from product X will be much lower than the expected returns from Y (define returns as $\frac {payoff}{price} - 1$. Hence, for the same payoff, the higher the price the lower the returns). Keep this in mind.

Now let us come to insurance. Let us take the example of car insurance. Most of  the time this doesn’t pay off. However, when your car gets smashed, you are compensated for the amount you spend in getting it fixed. What should be your expected return from this product?

Notice that when your car gets smashed, you will need to spend money to get it repaired. So at the time of your car getting smashed, the amount of money (and consequently consumption) is going to be lower than usual. Hence, the marginal utility of the insurance payout is likely to be higher than the marginal utility of a similar payout at a point in time when your consumption is “normal”. This is like product X above – which gives you a payoff at a time when your consumption level is low! And remember that you were willing to expect lower returns from X. Similarly, you should be willing to expect a lower rate of return from the insurance product!

Technical Appendix

A standard utility function used in finance textbooks is parabolic. Let us assume that for a consumption of $C$, the utility is $- (200-C)^2$. The following table shows the utility at various levels of consumption:

Consumption          Utility
80  (A)                  -14400
100                        -10000
120  (B)                 -6400
140                        -3600

Notice from the above table that getting the payoff of 20 when you are at A increases your utility by 4400, whereas when you are at B, the payoff of 20 increases your utility by only 2800. Hence, your utility from the payoff is much higher when you are at A than at B. Hence, you would pay a higher price for product X (which pays you when your consumption is low) than product Y (which pays you when your consumption is already high)

# Tata Sky’s Revenue Management (or the lack of it)

Last week Direct To Home (DTH)  television provider Tata Sky launched a new channel called “Star World Premiere HD”. As the name suggests it is a high definition channel, and it broadcasts TV shows from the United States simultaneously in India (as opposed to the usual lag of about a year before a show goes on air in India). The business case for this channel itself is particularly strong – for people are nowadays unwilling to wait for a TV series’ release in India and instead download it from illegal torrents. The availability of the TV Series now through a legal channel will discourage torrents, and also allow the producers to make some money via selling advertisements.

The problem, though, is with the pricing. With great fanfare, Tata Sky had launched this “Mega Pack” a few years ago, where for a fixed annual fee (of the order of Rs. 6000) you would get all channels for an entire year. Built in to this plan was the promise that any channels launched during the year would be available for free for all Mega Pack subscribers. It was like the subscribers were paying a premium for the option of not having to pay for any newly introduced channels.

For the last few years, this plan has been going well. Numbers are not available publicly but based on a small sample of people I know, I know that the Mega Pack has a large number of subscribers (Disclosure: I too subscribe to this). Given the “bundled pricing” (which is what the Mega Pack essentially is), Tata Sky is making more money than it would have with subscribers picking only the channels they wanted.