A Risk Adverse Economist’s Guide to Dating

Though this could also be titled: “My Normal Approach is Useful Here“

I guess it’s just a math heavy day today, mixed with a light sprinkling of rather standard insomnia. As I study for midterms and do my Econ-105A homework, I must have some internal desire to ground myself in things that I can attach more directly to myself. I had a conversation with a friend the other day that involved why I never ask anyone out. I claimed that the reason must be that I am highly risk adverse. Even though I meant this as a (albeit true) joke, as I sit here tonight doing way too much math, I distracted myself by thinking about how exactly I would model my own aversion to asking someone out on a date.

Since I’ve moved to Irvine, the old concept that there’s no such thing as a single woman has been pretty much entirely dissolved. This is a bizarre and foreign land where women seem to be, for no apparent reason that I can fathom, involuntarily unattached. Furthermore, the women here are of the highest quality in both beauty and intelligence, making the idea that any one of them would be involuntarily single all the more strange. I would say that perhaps it’s because the men don’t live up to their standards, but the men here are also of the same quality, so this seems unlikely at first glance.

All of this  is, of course, just a round about way for me to say that my usual excuse of “I can’t ask anyone out, because everyone is already taken” may not actually hold. I need an objective way to think about asking out women so that I can use it as a good rational for why I never do, and can thus maintain my well earned reputation as a cranky, lonely hermit.

So, for this model, we’ll assume that we’re presented with a choice between two options. The first option is to ask a girl out and the second option is to do nothing. For the do nothing option, we’ll assume that the expected utility of that option is zero. Some may say this is unfair, since you may suffer or may gain by choosing to do nothing. However, since we are only interested in the choice (or opportunity cost of doing one over the other), we only need to know if the expected utility of the ask-her-out choice is greater than or less than the expected utility of the do nothing choice. Said another way, we want to know if it’s better to have loved and possibly lost or to have never loved at all, and we’re measuring that based off of having never loved at all.

For the ask-her-out option, there are two potential outcomes. She can say yes, or she can say no. Let A represent the event that she accepts your offer, and A^c represent the event that she rejects your offer. Now, let U_A > 0 represent the utility gained by her accepting your offer and U_R > 0 represent the disutility caused by her rejecting your offer. The expected utility of asking her out is then given by the following equation:

EU = P(A)*U_A – P(A^c)U_R

Now, let k = U_R/ U_A. We’ll call k the heartbreak proportionality constant. The equation then becomes:

EU = P(A)*U_A – k*P(A^c)*U_A

EU = [P(A) - k*P(A^c)]*U_A

Now, we must examine the sign of the expected utility of asking her out. If negative, it’s better to do nothing rather than ask her out. If positive, it is better to ask her out. Since we know that the utility gained by asking her out, U_A, is always positive, the sign of this equation can be determined entirely by analyzing the sign of P(A) - k*P(A^c). Essentially, we can now say that the choice of whether or not to ask someone out can be determined entirely by two things. First, the probability that she will accept your offer. Second, by the heartbreak proportionality constant, k.

In this model, k represents how much one dislikes being turned down relative to how much one prefers being accepted to go on a date. First, consider a k = 1. This would represent a person that puts equal weight on being accepted and rejected. If it feels good to be accepted, then to this person it would feel just as bad if they got rejected. A person with a k = 1 would need to perceive that asking out his love interest would have at least a 50% chance of success in order for him to be at least indifferent between asking her out and not asking her out. If k > 1, then this person is strongly hurt by potential heartbreaks and would need greater than even odds in order to find the courage to ask someone out. A person with k < 1 is someone with a certain amount of courage. They value a potential relationship more than they value being hurt by rejection and will thus ask someone out even if they believe there is less than a coin toss chance of it being successful.

From this idea, it makes sense to determine the indifferent probability. Given a certain k, we must find the probability that a man would need to believe he would be successful in order for him to be indifferent to asking her out and not. This can be found using a little algebra:

P(A) - k*P(A^c) = 0

P(A) = k*P(A^c)

P(A) = k*[1 - P(A)]

P(A) = k – k*P(A)

(1+k)*P(A) = k

P(A) = k/(1+k)

If we know the person’s heartbreak constant, we can then determine by the above equation what probability of acceptance would be necessary in order to be indifferent to asking someone out.

And that’s where we can get back to me. I estimate that I dread getting embarrassed and rejected about twice as much as I like the idea of being accepted. Therefore, I must believe that the probability of someone accepting my offer would have to be greater than 2/3 in order for me to actually make an attempt. Since, however, I likewise believe that I am fundamentally undesirable to women since I am in fact a cranky, lonely, hermit economist secluded in my ivory tower, it is unlikely that I would ever believe, unless presented with extreme evidence to the contrary, that P(A) would ever be even close to 2/3.

And that, ladies and gentlemen, is a mathematically elegant explanation of why I will be single for the rest of my life. I guess my usual approach still doesn’t work here…

Game Theory Approach to the Pitcher’s Duel

I’ve been kind of drawn in by the NLCS this year. I’m a long time Giant’s fan and seeing them actually winning games and having a good chance at going all the way is a bit of an uplifting experience. On top of this, baseball is a highly strategic game. The choice of pitcher in one game will limit the choice of pitcher in the next game. Offensive lineups must sometimes be changed to optimize a variety of scoring strategies. My team winning, combined with a chance to think about strategic behavior, is always a good way to get me interested.

So, all this got me to start thinking about the so called pitcher’s duel. My question is: Why open a series with two ace pitchers? This is a pretty common practice that two top pitchers go head to head, but is there a reason that coaches would want to do this? Couldn’t a team put a lousy pitcher up against a great pitcher and throw the first game in order to give themselves a better shot at later games by wearing out the top pitcher early? Of course, if one team knew that the other team was going to do this, nothing would stop them from switching their pitching strategy, and on and on like that.

The choice of pitchers is a simultaneous game. For my thought process, we’ll assume that pitchers are chosen in secret by each coach. I start with a simple model. There are two teams and they will play one game against each other. Each team can either play their ace pitcher or their second-tier pitcher. If an ace plays and ace, there’s a 50% chance that either will win. If a second plays a second, the same thing will happen. If an ace plays a second, the ace will have a 75% chance of winning the game.

I could draw the payoff diagram, but I’m a bit lazy so I’ll just spoil the punchline. In this single game, both teams have a strongly dominant strategy to play their ace pitcher. The game, however, gets quickly complicated if you consider multiple plays. First off, to avoid the possibility of ties, you’d have to play three games. You’d give each team a first, second, and third ranked pitcher, and assign probabilities based on each pitcher facing each other. The complication then comes in even harder because each opening match up leads to its own sub-game for the next two games.

While working out what would happen in this three game situation would be difficult, there are a few things that can be thought about. First, the probability of winning the three game series, given that you already lost the first game, is lowered even if you do have a pitching advantage in later games. If you think about a seven game series, where ace pitchers may re-enter in later games, then a dominant strategy for all seven games might not exist.

Given that it is almost impossible then to find a dominant seven game strategy, it is probably a useful rule of thumb to simply try to win every game as if that game stands on its own. Winning game one does have a dominant strategy (choose the ace pitcher). So, it’s entirely reasonable then that we often see the opening of any given series start off with a pitcher’s duel between two ace pitchers. A pitching strategy that gives the highest probability of winning each individual game as if they are played one at a time is likely the optimal strategy for winning a series. Proving this is a bit beyond my scope of practice at the moment, but perhaps I might follow up on this idea when I have more skills and time.

Thinking About Zipcars at the Beach on Irvine’s Hottest Day

Today, there was a record breaking heatwave across Southern California. Here in the OC, three cities (Santa Ana, Fullerton, and Yorba Linda) apparently cooked right past their old records by several degrees. They still manged to fall cold of Los Angeles however, whose 113 degree temperature apparently broke the thermometer at the National Weather Service downtown. My exposure to the heat wave was luckily very short before I was back in my thankfully air-conditioned apartment. Irvine, though still way up there, peaked only at 106.8 compared to our less fortunate neighbors. However, it’s easy to see why the claim that heat is one of the great killers holds so much weight. By the time I went from the student center back to my apartment, I was already feeling mild symptoms of heat exhaustion and dehydration. I wish I had some way to measure exactly how much water I was able to lose in that short period of time. Combined with only 17% humidity, the heat is oddly pleasant, until you realize that it is draining you of your precious bodily fluids at an alarming rate. Luckily, later in the day, I replenished myself with a large frozen yogurt waffle cone from Strickland’s.

Around 3 pm, despite the fact that my every waking moment should be spent trying to get ahead in statistics, I felt that this epic heat wave was quickly calling me to do something with the warm temperatures. Around Newport Beach, weather stations were only registering around  88-ish degrees, and the general trend was already starting to drop as the evening winds started to tepidly pick up again. I decided that I should go to the beach, because during a record setting heat wave that just what you’re suppose to do. I grabbed a Zipcar for 20 bucks and change and headed to my favorite spot at Newport Beach. It was beautiful. The water was the perfect temperature, the waves were filled with surfers catching perfect curls, and the low evening sun was was distant enough that is didn’t turn me into a sunburned mess. I swam in the cool waters for 40 minutes, felt the waves wash over me, and then headed homeward.

With that, this is the second time that I’ve used the Zipcar, and it certainly provides an entirely different way of thinking about transportation. You have to be extraordinarily conscious of how you’re managing the time that you’ve allowed for having a car, and yet at the same time it’s completely liberating in that the only time you need to concern yourself with anything having to do with a car is during those blocks you’ve specifically allocated.

I have no doubt at this point that my monthly automobile expenses will be lower (much lower) using the Zipcar than actually owning a vehicle. However, that’s not entirely a fair assessment. Much of the decrease in costs comes from the fact that I use the Zipcar substantially less than I would if I owned my own car. Here is the part where my inner economist begins to chime in. I think it would be fascinating to develop or see some kind of normative model of Zipcar usage. There would essentially be two models here. The first model would involve the choice of modes of transportation. It would be about how the consumer choses to either own their own car and use that, or to use a Zipcar in combination with other alternate modes of transportation such as the bus/train. The second model would then be the decision of when to actually use a Zipcar and for how long (I’m sure Zipcar probably has their own version of this model worked out, as it would help determine pricing, profitability, scheduling, etc).

I find the choice model to be the most interesting for a few reasons. First, we hardly ever consider the opportunity costs involved with what is essentially having our car sit in a parking lot. A car is a somewhat expensive piece of capital equipment, and yet we never think to ourselves, “Well, while I’m at work for 8 hours, I could be renting out my car rather than having it sit unused in a parking lot.” One of the correct ways to think about this problem in economics is to consider the value of the car and determine how much could be made off of the next best investment as the opportunity cost of ownership. That, however, would involve not owning the car at all, rather than simply having the car be used while you’re not using it. So, thinking about Zipcars might provide a deeper understanding of what the opportunity cost of having a car sit in a garage or parking lot is. In the case of a Zipcar user, the opportunity cost is $8 an hour. If you choose to have your Zipcar sit in a parking lot, you’re having to pay $8 an hour to maintain rights over that car while it sits there.

Which brings me to my second interest, Zipcars make the marginal cost of driving very apparent to the driver. As I mentioned above, the cost of having a Zipcar for an hour is $8. Most of the time, I think, drivers that own their own car think about driving as if the marginal cost of driving were close to zero. We all make estimates of gas millage, registration costs,  insurance costs, repairs, etc. but how many people could reasonably say how much their morning commute costs? Or, put better, how much does that detour down the scenic route cost compared to the regular grinding commute? How much does it cost to go through the Starbuck’s drive thru on the way to work? And, once again, how much is being paid to have your car sit in the parking lot waiting for you until the exact moment when you’re ready to leave? Being a part of a shared car program puts a real marginal cost on driving that the consumer has to confront every time he or she gets behind the wheel. These kinds of things change behavior and it would be worth some careful study to see just how much. Since I’m considering doing my undergrad research in urban transportation, it certainly would be worth my time to think about it more. I’m hoping it will involve more trips to the beach.

More Grocery Thoughts

I’ve managed to think even more about my upcoming grocery situation, and started to think a lot more about a comment I made at the end of my last grocery store post. I said,

“I think I can reasonably conclude that Albertsons self-interests are aligned with my own. If everybody else decides to throw away their car though… well then… I’ve got my eye on you Albertsons.”

In my last pondering of what determines the pricing at grocery stores, I considered a demand side perspective of how the Albertsons might decide to set its prices. However, I think there can be some interesting things discovered by considering another idea that I hinted at called “limit pricing.” From this perspective, let’s consider the market for groceries having only one demanding group like the walkers. In the short run, our fictional grocery store has a complete monopoly on this group. It cannot achieve profits by luring in customers from outside of this group. It’s my dreaded scenario where everyone is a walker.

However, that’s in the short run. Let’s assume that there is free entry into the market for transporting goods.  The walkers may not be able to escape their horrid situation, but perhaps there are other ways to alleviate their stresses. If it is assumed that our fictional grocery store starts out as a monopoly, the potential profits from starting a competing store would be huge. I’d imagine that little corner shops might start to appear, chipping away at our grocery’s hard earned monopoly on the walkers. What’s a monopoly grocery store to do?

The answer, perhaps, may be limit pricing. Rather than set the prices at the absolute monopoly price, the grocery could lower the prices to the point that it wouldn’t be profitable for other stores to open and compete with it. Even if that means lowering its prices all the way to the perfectly competitive price, all of a competitive priced market is still better than only some of that market. The walkers might still be saved from monopoly prices. This time, not from the influence of other sources of demand, but from other potential sources of supply. It’s an amazing feature of markets that they often work both ways like this.

However, that’s not even the most interesting part of thinking about this. An added question, I think, is how transportation costs might affect the economic geography of an area. In places where people walk a lot, San Francisco or NYC perhaps, stores do tend to form more as small scale corner stores it appears. The urban areas natural seem to form institutions that take advantage of their densities. Transportation, once in the city, is probably highly costly, since it’s often preferred to walk rather than drive. Economies of scale come from density of consumers, rather than from high fixed cost, low marginal cost suppliers.

My prediction is then that in places where cars are cheap and prevalent, you’re more likely to see high fixed cost, low marginal cost mega stores. In places where walking is more prevalent and population density is the order of the day, I think you’d be more likely to see low fixed cost, high marginal cost corner stores. To think more about this however, I think I’ll need a research grant or two.

My Friendly Neighborhood Grocer

As I prepare to move to Irvine in about two weeks, I’m also contemplating my future life without a car. I’ll be “living the dream” of being an eco-friendly, health-nut walker and such, and the $100+ a month that I’ll put back in my pocket certainly doesn’t hurt. Living directly across the street from an Albertsons makes this an especially easy sacrifice.  At this point, owning a car would be purely a luxury item,  and living alone for the first time in several years is enough luxury to last me for some time.

However, I wouldn’t be a very good economist if I didn’t consider all the ways that my friendly neighborhood grocer might be plotting to take all those hard earned car-free gains away from me. My local Albertsons is a happy little Monopolistically Competitive firm,  and given the proximity of not just myself, but a large, also-walking student population, Albertsons might want to catch itself some monopoly profits by raising prices, reducing my own profits from eliminating my car.

When I lived in Cutten, I lived about two blocks away from the local Murphy’s Market. You might think that, given the closeness of the Murphy’s, I would never shop anywhere else. However, that would be wrong. I had a car, could afford to use it, and Murphy’s was expensive relative to most of the other groceries a short drive away. Why would Murphy’s turn away a customer like me with high prices? The answer lies in that whole monopolistically competitive thing again. Murphy’s could exclude me, and still come out ahead, because many people were willing to shop at Murphy’s because it was so close. Murphy’s had a monopoly on proximity, much like my new Albertsons, and they used it to great effect.

The question then comes: what is the right way to model this walker exploitation? The way I see it, there are three groups of people involved. If one could determine their respective demand curves,  one could predict in advance how the Albertsons will price their groceries. The first group consists of students and nearby population that have almost no other choice than to walk to Albertsons (me). This group likely has a highly inelastic demand curve as it would involve high opportunity costs to go to an alternate grocer (take the bus to Whole Foods, or walk much further to the Trader Joe’s in the university plaza). The second group consists of local residents that have an inexpensive way to transport groceries to their homes (people with cars), but would enjoy the convenience of walking to get their groceries. Their demand curve depends on how much this group values that convenience. If the price goes too high, that group exercises their alternatives and the demand curve becomes rapidly elastic. The final group are people that would be willing to come from out of the area to the Albertsons from out of the area if offered a good price. Competing for these customers will be essentially determined by the market price of groceries in the whole Irvine area, so their demand curve is elastic as well. Put these things together, and you could determine where Albertsons can set its profit maximizing prices.

What made Murphy’s prices so high relative to others was that Murphy’s could gain more by charging the first group high prices than it would gain by lowering its prices to attract the other groups. Will Albertsons be a high priced local monopoly, or will other forces push their prices into line? This is, of course, ignoring a plethora of other economic effects (Possible limit pricing, Albertsons being a chain that has brand value to lose if it overcharges customers, etc.), but it would still be interesting. My guess is that Albertsons will likely offer competitive pricing since the surrounding UCI community is very large. At a student population of over 25,000, and with Irvine itself having a population of over 200,000, the benefits of serving groups two and three far outstrip the benefits of exploiting the first group (me).  Eureka, on the other hand, has a population equal to about the student population of UCI. It’s easy to see how the small, and somewhat disconnected, community of Cutten might lend itself to exploitation of group one.

So, assuming Albertsons does not engage in impossible to implement price discrimination (how would you identify people that walked in order to charge them higher prices? And if you did that, wouldn’t you kind of look like a total dick?), I think I can reasonably conclude that Albertsons self-interests are aligned with my own. If everybody else decides to throw away their car though… well then… I’ve got my eye on you Albertsons.