September 23, 2013
Posted by gtaniwaki under Real Numeracy
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by George Taniwaki
While in school, we often learn about a particular subject through textbooks that make it seem that the body of knowledge for that area is neat and tidy and always has been. As students we may take for granted that the ideas presented by our instructors and textbooks are static, or at least follow a linear progression of always increasing. Rarely is it ever discussed how ideas change over time, the controversies, errors, and long lead time for new information to be incorporated into the body of knowledge.
Even in graduate school, where critical analysis is considered an important skill to teach, very little time is spent on the historical context in which important ideas were formed. Very little time is spent describing how radical new ideas are vetted and if found useful, replace entrenched older ones, a process called a paradigm shift. The term comes from the excellent book by the philosopher Thomas Kuhn entitled The Structure of Scientific Revolutions (1962).
Even rarer than a historical description of how a new idea replaces an old one is a description written by the very people who were responsible for the paradigm shift. That’s why I was interested to read a paper entitled Ball and Brown (1968): A Retrospective. written by Ray Ball and Philip Brown.
Mr. Ball and Mr. Brown were PhD students at the University of Chicago in the 1960s. They were the first researchers to show that on the day that accounting information (like earnings) is released, it will affect stock prices. This seems obvious today and nearly all researchers believe it is true and base their own research on the assumption that it is true. Today this belief even has a well-recognized name, called the semi-strong form of the efficient market hypothesis. But in 1968 the idea was considered radical and many experts dismissed the paper.
The paper was groundbreaking in another respect. The basis of their paper was not theoretical, it was experimental. The authors looked at actual companies and conducted a statistical analysis of the historical stock price data on the days before and after each “event”, in this case the company’s release of accounting information. (This technique was championed by Eugene Fama, also of the U. of Chicago.) Again, this seems obvious today, but was radical in 1968. The story of how they came to write the paper is quite interesting. (Or it is to me or anyone else interested in the history of economic theory.)
Their original paper is entitled “An empirical evaluation of accounting income numbers” and appeared in J. Acct. Res. 1968. To give you an idea of how important this paper is, below is a citation graph for this paper. It has been cited a total of 941 times since it was published 45 years ago, with the number of citations growing almost every year (the drop at the end is likely due to recent papers not yet indexed).
Citations for Ball Brown (1968). Image from Microsoft Research
Much thanks to my wife, Susan Wolcott, for sharing this paper with me. Her PhD dissertation in accounting is based on a test of the semi-strong form of the efficient market hypothesis.
As a follow-up to a recent blog post marking the passing of the Nobel prize-winning economist Ronald Coase, I want to feature two fine obituaries.
The first is by the Economist, in an article entitled “The man who showed why firms exist”.
Coase is dead, long live the firm. Photo from U. of Chicago
Another tribute was published by UChicago News, an official publication of Mr. Coase’s employer. The article has a link to a YouTube video that includes short excerpts (3:40) of a longer interview of Ronald Coase from 2012.
Accidental Economist. Video still from YouTube
Ronald Coase was active until his death. In 2012, he published a book with a U. of Chicago PhD graduate named Ning Wang. The book entitled How China Became Capitalist describes the economic transformation in China over the past 35 years. It argues that the credit for this change belongs to individual entrepreneurs, not to the central government. China’s new economic freedom has not been matched by the free flow of ideas. Until that changes, China will never reach its full potential.
A short (3:30) discussion of the ideas behind the book by its two authors is posted on YouTube. It is from the same interview from the video described above.
Coase and Wang discuss their book. Video still from YouTube.
Disclosure: George Taniwaki is a graduate of University of Chicago’s Booth School of Business. The opinions expressed in this blog post are his own and do not reflect those of any organization.
September 18, 2013
by George Taniwaki
In a Dec 2011 blog post, I critiqued an article in The Fiscal Times that compared the cost of eating a meal at home against dining out at a restaurant. The article purported to show that eating at a restaurant was cheaper. I pointed out the errors in the analysis.
One of the errors was in the way data for expenditures for grocers and restaurants were shown in a line graph. The two lines were at different scales and aligned to different baselines making comparisons difficult. The original and corrected charts are shown below. Correcting the baseline makes it clear that restaurant expenditures are significantly lower than for groceries. Correcting the scale shows that restaurant expenditures are not significantly more volatile than for groceries.
Figures 1a and 1b. Original chart (left) and corrected version (right)
Another error in the article I pointed out was that the lower inflation rate of meals at restaurants compared to meals at home should not favor eating more meals at restaurants. I didn’t give an explanation why. I will do so here.
Consider an office worker who needs to decide today whether to make a sandwich for lunch or to buy a hamburger at a restaurant. Let’s say she knows that the price of bread and lunch meat has doubled over the past year (100% inflation rate) while the cost of a hamburger has not changed (0% inflation rate). Which should she buy?
The answer is, she doesn’t have enough information to decide. The inflation rate over the past year is irrelevant to her decision today, or at least it should be. What is relevant is the actual costs and utilities today.
Let’s say she likes shopping, making sandwiches, and cleaning up, so the opportunity cost for the sandwich option is zero. Let’s also say she likes sandwiches and hamburgers equally and values them equally and doesn’t value variety. Now, if the price today for lunch meat and bread for a single sandwich is 50 cents while a hamburger is 75 cents, then she should make a sandwich. Next year if inflation continues as before, making a sandwich will cost $1.00 while a hamburger remains 75 cents. In that case, she should buy a hamburger. But that decision is in the future.
Let’s consider an extreme case where inflation rates may affect purchase decisions today. What if the price of sandwich fixings are 50 cents today but inflation is expected to be 100% during the work week (so prices will be $.57, $.66, $.76, and $.87 over the next four days) . Such high inflation rates are called hyperinflation and can lead to severe economic distortions.
Let’s also assume hamburgers are 75 cents today and will remain fixed at that price by law. (Arbitrary but stringent price controls are another common feature of an economy experiencing hyperinflation.) Further, let’s assume that sandwich fixings can be stored in the refrigerator for a week for future use but hamburgers cannot be bought and stored for future consumption.
Finally, let’s assume it is early Monday and our office worker has no sandwich fixings or hamburgers but has $5 available for lunches for the upcoming week. What should she buy each day?
I would recommend trying to buy $3.75 in sandwich fixings today (enough for 5 sandwiches). Here’s why. During a period of hyperinflation, you want to get rid of money as fast as possible because cash loses its value every day you hold it. Thus, buying as much food as possible today is a good investment (called a price hedge).
Ah, you say. Why not make sandwiches the first two days of the week and then switch to the relatively cheaper hamburgers for the last three days? That is unlikely to work because the restaurant is caught between paying rising prices for the food it buys while getting a fixed price for what it sells. Long lines will form as customers seek cheap food. The restaurant will either run out of food, go bankrupt, or close its doors. Regardless, our office worker shouldn’t rely on her ability to buy cheap hamburgers later in the week.
So why am I updating a blog post from almost two years ago? Well, it’s because I noticed a big spike in traffic landing on it last week. It turns out my wife, Susan Wolcott, assigned it as a reading for a class she is teaching to undergraduate business students at Aalto University School of Business, in Mikkeli, Finland. (The school was formerly known as the Helsinki School of Economics.)
Normally, this blog receives about 30 page views a day. On days that I post an entry on kidney disease or organ donation (pet topics of mine) traffic goes up. Of a typical day’s 30 hits, I presume about half of that traffic is not human. It is from web crawlers looking for sites to send spam to (I receive about 15 spam comments a day on this blog).
But check out the big spike in page views for my blog on the day my wife assigned the reading. This blog received 264 page views from 91 unique visitors. That’s the kind of traffic social media experts die for. Maybe I’ve hit upon an idea for generating lots of traffic to a website, convince college professors to assign it as required reading for a class.
Figure 2. Web traffic statistics for this blog
Naturally, I expect another big spike of traffic again today when my wife tells her students about this new blog post.
September 17, 2013
by George Taniwaki
Back when I was in high school, every summer my friends and I would go to the amusement park. One of the attractions we visited was the hall of mirrors. Ten points worth of tickets allowed you to go through the hall once. The goal is to go in through the entrance and find the exit before you starved to death. ( I’ve been told that there are numerous bodies of lost patrons still stuck inside the hall, but I digress.)
The hall of mirrors consists of a room with a series of tracks on the floor and ceiling laid out in an equilateral triangular array, called an isohedral tiling pattern (Fig 1).
Figure 1. Isohedral tiling. Image from Wikipedia.org
Each triangular cell is about 3-foot to a side. The tracks on some of the sides have a floor-to-ceiling partition inserted in them. The partitions form walls creating a maze with a single entrance, a single exit, and exactly one path between them. Solving a maze of this type is a great mathematics problem.
The maze is called a hall of mirrors because the partitions are not just solid opaque panels. Instead, they are all of one of two types, either mirrored on both sides or clear plastic.
I had never been in the hall of mirrors. While waiting in line, one of my friends urged us to go twice. The first time would be figuring the maze out. The second time we would race through. He then bet me he could get through it faster than me both the first and second times.
I eagerly accepted because I knew a trick for solving simple mazes called the wall follower algorithm. In the wall follower algorithm, you place one hand (say your left hand) on the wall as you enter the maze and never take it off. As you move through the maze, if you reach an intersection, keep your left hand on the wall, meaning you take the leftmost turn. If you reach a dead-end, keep your left hand on the wall, meaning you will return to the intersection and take the next path. Eventually, you will reach the exit.
If you remember the series of correct paths you took, the next time you enter the maze, you will not need to keep you hand on the wall. You just need to remember the turns you took at each intersection. For example, left, right, center, right, right, left, right.
Seeing how eager I was, all my other friends also made the same bet and I accepted. After giving our tickets to the operator, my friends ran into the maze. I was surprised that they would dash off without caution. I was determined to show them that I could beat them and solve the maze faster by simply walking through the maze using my logical skills.
What I didn’t know were three facts. First, because of the mirrors and clear walls, as you stepped into each triangular cell, you couldn’t be sure which direction would lead you to an adjacent open cell and which led you into a wall. Using the wall follower algorithm by placing your hand on the wall definitely helped, but it was slow going moving around.
Second, the maze was crowded. There were lots of other people who were moving around, sometimes in the opposite direction as me, and it was difficult to navigate around them. To do so, I often had to take my hand off the wall and as I was getting jostled, I couldn’t be sure I placed my hand back on the same wall. Similarly, it was difficult for me to remember if I had returned to the same point as before. This meant I couldn’t memorize which turn I should make at each intersection.
After a few minutes of trying to solve the maze, I noticed that all of my friends were already outside the maze watching me. I began to panic and became disoriented. Eventually, feeling sorry for me, they began shouting and pointing the directions for me to take. Finally, with their help, I reached the exit of the maze and stepped out to be with them. Except, I wasn’t quite at the exit yet and bam, I walked right into a clear wall mashing my eyeglasses into my face. So much for my superior maze solving skills.
Upon exiting the maze, I learned the third fact. My friends had all been to the amusement park previously that summer and had memorized the path through the hall of mirrors.
As we agreed, we went through the hall a second time. I did a lot better, but still made several wrong turns and became disoriented a couple of times. I was the last one out of the maze again. I had to pay off on two losing bets with each of my friends that day.
However, I did learn an important lessons about gambling (and investing in the market too). First, don’t place a bet on a game of skill simply because you know something your opponent doesn’t (like the algorithm to solve a maze). Only place a bet if you have actual experience winning the game you are betting on (like having run through the maze before). Second, if someone challenges you to a contest (who can run through the maze fastest), they probably already have the skills needed to win and you should avoid the bet.
Solving a maze using pencil and paper is another interesting problem. And is one that should not induce panic attacks about getting lost. One way to study a maze is to first identify the walls. A maze with a single entrance and single exit must have at least two separate walls as shown on the left of Figure 2.
In the case of a maze with exactly two walls, you can solve it using the wall follower algorithm described earlier. But a faster solution exists. Notice that any path where the wall on both sides is the same color ends in a dead-end. By following the path that has one wall of each color on each side you will quickly find the solution. Notice that this technique is faster only if the walls are already color coded.
Figure 2. Three simple mazes with two walls (left), three walls adjacent to each other (center) and three walls where one is enclosed (right) Image by George Taniwaki
A maze may have more than two walls. If there is only one entrance and exit, there will still be only two exterior walls. Any additional walls will be totally enclosed within the exterior walls. If an interior wall is at any point adjacent to two walls that are part of a solution, then a path following this wall will also add a solution. A wall that is adjacent to only a single wall (is totally enclosed within a wall) will not add another solution. An interior wall that is adjacent to one or fewer walls that is part of a solution will not add another solution either.
In Figure 2 above, the center maze has three walls and has two solutions. You can turn either left or right at the blue wall. The right maze has three walls but only a single solution since the blue wall is totally surrounded by the red wall.
For a more complex example, consider a maze (Fig 3a) that is included in a recent advertisement for Dropbox, a cloud file sharing service.
Figure 3a. Dropbox print ad. Image from Dropbox
It is hard to see the solution to this maze just by inspection. But if we color code all the walls we will discover there are four separate walls (Fig 3b, to save time I only added color at the turns and intersections). The two interior walls (in blue near the top of the puzzle) are both completely contained within a single wall (in red), so they do not add any new solutions, so there is only one solution. The solution is the path that stays between the two exterior walls (green and red). The solution is easy to recognize when the walls are color coded (assuming you do not have red/green color deficient vision). Try it and see how easy it is.
Figure 3b. Dropbox print ad with color coded walls and enclosed paths highlighted. The solution is the path that keeps walls of different colors on each side.
Notice that there are two errors in the maze. There are two paths (filled in yellow) that are completely enclosed, meaning they are not connected to the entrance or exit and so cannot be reached. Despite the errors, this is a nice maze. A good maze has the following attributes:
- The path for the solution is quite long and traverses all four quadrants of the grid, meaning that finding the solution path is not obvious if the walls are not color coded
- There are many branches off the solution path, meaning that there are many potential places to make an error
- Many of the dead-end branches are long and also have branches, meaning that discovering whether a path is a dead-end branch or part of the solution takes a long time
September 16, 2013
by George Taniwaki
I recently came across a series of articles about one very generous man. A man who decided to help a distant relative he barely knew. A man who donated his kidney to a stranger he didn’t know at all. And a man who despite being only a mediocre swimmer is now in training to swim across Lake Ontario to raise money and awareness for a camp for dialysis patients and their families.
Mike Zavitz of Pickering, Ontario was 43 years old when he offered to donate his kidney to a distant relative in 2010. They were not a match, but Canada had just introduced a new Living Donor Paired Exchange (LDPE) program that year (see Dec 2010 blog post).
The program is small resulting in a perhaps a dozen kidney swaps (see Kidney swaps explained below) per year, meaning the chances of finding a match are slim. But Mr. Zavitz and his relative were lucky enough to find a match and became one of the first participants in the Canadian LDPE program and the first one at St. Joseph’s Hospital in Hamilton, Ontario.
The story of Mr. Zavitz’s donation appeared in The Hamilton Spectator Dec 2011. Mr. Zavitz’s kidney ended up saving a young man he never met and whose name he didn’t know. In exchange, that man’s father donated a kidney to Mr. Zavitz’s relative. The surgeries occurred on Feb 2, 2011.
Mr. Zavitz met his recipient, Jesse Hunt, for the first time a year-and-a-half later (The Hamilton Spectator May 2012).
When explaining why he did it, Mr. Zavitz said it was in response to a lifetime of second chances he has received since he was abandoned as a baby and later adopted. “They don’t make Hallmark cards saying, ‘Thank you for rescuing me from a lifetime of foster care and possibly death.’”
Figure 1. Mike Zavitz interviewed. Video still from Hamilton Spectator
Mike Zavitz keeps on giving
The story of Mr. Zavitz’s generosity doesn’t end with his donor surgery. In an Aug 2013 story, The Hamilton Spectator reports that Mr. Zavitz plans to swim 22 kilometers (14 miles) across Lake of Bays near Algonquin Park.
His swim has two purposes. The first is to raise money for the Lions Camp Dorset, a camp designed for dialysis patients and their families. It is a place where they can get away for a week, while still receiving treatment. His goal was to raise CAN$10,000 for the camp.
In a quote in the Hamilton Spectator article, Helen Walker, administrative coordinator of the camp said, “To have somebody who has been involved in a transplant want to give back is amazing. Without Camp Dorset, it would be next to impossible to have a getaway at an affordable price.”
The recipient of Mr. Zavitz’s kidney, Jesse Hunt, had this to say, “I think it’s awesome. When you are not on dialysis, you realize the freedom you have. You can’t travel [on dialysis] or go to a cottage or get on a plane. If you can get away, it’s very important.”
Mr. Zavitz’s second goal is to raise awareness for organ donation, and especially living donation. His long distance swim shows people that organ donors can still live incredibly active lifestyles. In fact, becoming a donor may be a life changing event that actually makes you more mindful and more active.
A follow-up report on CKLP FM radio Aug 2013 says Mr. Zavitz completed the swim in 10 hours and 45 minutes. He exceeded his goal and raised CAN$11,000 for Lions Camp Dorset.
Next year, Mr. Zavitz plans to swim Lake Ontario, a distance of about 52 km (32 miles). To follow Mr. Dorset on Facebook, his page is at Tied Together Swim. To learn more and to make a donation go to tiedtogetherswim.com. The video featured on the website was produced by his recipient Mr. Hunt, who is a filmmaker.
Figure 2. Screenshot of the Tied Together Swim website
A list of camps for children with special medical needs in the United States is available at the Transplant Living website.
Kidney swaps explained
A kidney swap begins with a patient who needs a transplant and has a willing donor who is healthy but is not blood type or HLA compatible. Through a matching service, called a kidney exchange, they can find another patient-donor pair in the same situation where the donors in each pair match the patient in the other pair (Fig 3a).
Finding pairs that match each other is sometimes difficult. Matching becomes easier if a nondirected donor, that is a person who does not have a patient in mind but just wants to donate a kidney enters the exchange. Then all the matches only have to be one-way (Fig 3b).
Figures 3a and 3b. An example of a kidney swap (top) and kidney chain (bottom). Images by George Taniwaki
The use of kidney swaps and kidney chains to facilitate kidney transplants is a recent phenomena. The first multihospital kidney chain occurred in the U.S. in 2007 (see Sept 2009 blog post). These kidney swaps are getting more common in the U.S. (see June 2010 blog post) but are still fairly rare outside the U.S.
Canada started up a Living Donor Paired Exchange (LDPE) program in Oct 2010 (see Dec 2010 blog post). It only allows swaps. Chains starting with a nondirected donor are not yet permitted in Canada.
September 3, 2013
by George Taniwaki
Two announcements made yesterday seem to point to a cosmic convergence, or at least a law and economics convergence. First, is the death of Ronald Coase. The other is Microsoft’s plan to acquire the mobile handset business of Nokia.
Ronald Coase 29 December 1910 – 2 September 2013
Why are there firms? Why doesn’t everyone just work for themselves and contract out their labor to each other whenever and wherever it is needed? Conversely, why doesn’t everyone work for a single large employer that tells everyone what to do and produces everything that consumers want to buy?
The answer to this question of firm size is the basis of a branch of economics called the theory of the firm. Theory of the firm sounds like a single idea. But actually there were many competing explanations regarding why firms exist. The most important contribution is by Ronald Coase, a British economist who taught at the University of Chicago who proposed that the ratio of internal transaction costs to external transaction costs drove firm size.
In 1937, Mr. Coase published a paper “The Nature of the Firm” in Economica which outlines his is ideas about how in certain cases transaction costs can be reduced by replacing a market driven contractual relationship between a buyer and seller with an internal non-market relationship. (Also called insourcing as opposed to the current controversy about firms getting smaller by shedding operations in a practice called outsourcing.)
All transactions involve a contract, either explicit or implicit, written or verbal. Complex contracts often require expensive lawyers who consider possible contingencies and carefully define the outcomes. In addition to legal costs, contracts have to be monitored and enforced to ensure both parties get what they expect in the relationship. The more complex the task, the more complex and expensive the contract is likely to be over its lifetime
Much of the effort in using a contract is to ensure that all risks are explicitly defined and divided between parties. This effort can be eliminated if the parties join into a single firm. Then the risk where one party’s gain is another’s loss can be shared.
We live in a world with many sized firms, so thinking about two extreme cases posed at the beginning of this blog post may seem silly. But they lead to important questions. What factors determine the size of a firm? What is the “ideal” size of a firm? Given that we see lots of firms of different sizes, is the current distribution of sizes “efficient”? If not, what should we do, if anything, to help owners, managers, and workers “right size” their firms? Finally, can we predict the effect of technological and social changes on firm size?
These are important questions worth investigating. And all of them can be analyzed using the framework first developed by Mr. Coase.
In 1960, Mr. Coase again used transaction costs to develop a framework to study the problem of externalities (the failure of the market to capture all benefits or costs of a transaction, such as pollution). He showed that if the resource being impacted (such as clean air) could be well-defined and protected as a property right, and if transaction costs were low, then rights owners could bargain for use of the property. Further, he showed that it didn’t matter who owned the property rights initially. As long as all parties bargained fairly and rationally, the utility maximizing outcome would prevail.
It is on the basis of his groundbreaking work on transaction costs that Mr. Coase was awarded the Nobel Memorial Prize in Economics in 1991.
Figure 1. Ronald Coase in 2011. Image from Wikipedia.org
Microsoft and Nokia, better together?
How big should a mobile computing firm be? The biggest firms in the market today are huge. How should a firm profit from the mobile computing market? Should it make its software and hardware available only in combination like Apple with iOS and iPhone? Should it make software and license it to a small set of select vendors, like Microsoft with Windows Phone? Or should it make software available to all comers including itself, like Google does with Android?
Well, it’s pretty obvious that the licensing strategy for Windows Phone has not worked. The only licensee of volume is Nokia, and that is about 3.5% of the market. Handset manufacturers were not willing to pay the estimated $10 per handset fee for it. Instead they licensed Android for free, plus an estimated $5 per handset patent royalty to Microsoft and Apple. (Given that Android has 12 times the market share of Windows Phone, that means Microsoft makes most of its mobile computing revenue from Samsung and other makers of Android phones.)
Now Microsoft has announced it will acquire Nokia for $5 billion plus $2.1 billion to license its patent portfolio. What explains the belief that the performance of a combined Microsoft + Nokia will be superior to Microsoft and Nokia as independent entities? Ronald Coase would probably say that using transactions cost analysis is a good place to start.
In the 1980s, Microsoft made an enormous amount of money realizing that it could sell its operating system software to many hardware manufacturing firms with little or no customization. In the desktop computing era, Microsoft paid for nearly all the research and design for desktop computers and charged it to manufacturers as part of its license fee for Windows. These licensees competed mostly on price and ended up with slim margins. What R&D they did pay for was focused on improving supply chain management and manufacturing efficiency. Almost nothing was spent on new computer designs or user experience.
Apple guessed wrongly that people would pay a premium for computers where the software and hardware worked together better and were a joy to use. They didn’t.
Keeping software and hardware as separate firms made sense for Microsoft. All the profit was in software and there was little innovation or value added in hardware.
Then in the late 2000s, mobile computing took off. Unlike desktop computers where size, shape, weight and design are not particularly important, mobile devices are all about pushing the technical limits of computing while fitting it into a handheld package. Apple, which already had an experienced design staff and a CEO who prized good design, immediately had a hit with the iPod and later the iPhone.
Microsoft revamped its mobile OS (was called Windows Mobile, now called Windows Phone) but had difficulty finding licensees that could create phones with compelling designs. One solution is to include a subsidy to the hardware manufacturer to pay for improved software and hardware integration. But contracts to guarantee innovation are hard to write and nearly impossible to enforce. Thus, Microsoft (and Google) found itself in a difficult position. How can a manager at a software company make hardware innovation a priority at its licensees? One solution is to insource it.
Horace Dediu has an excellent blog post that asks, Who’s buying whom? He states that firms are the sum of three values, resources, processes, and priorities (RPP). He says that, “When one company buys another, it’s the equivalent of one set of RPPs trying to engulf or swallow another set of RPPs.”
It is pretty easy to see that when one company buys another for its resources (people, plants, patents, store locations, customer lists) or processes (workflows, algorithms, supply chains) that it wants to incorporate them into its existing infrastructure.
However, Mr. Dediu states that acquiring another company’s priorities is different. “A company typically only has room for one set. If there are conflicting priorities, they need to be sorted out else the company can end up in a state of internal conflict and dysfunction. So if you’re acquiring a set of Priorities, it’s likely that you’ll have to discard your own… So, in a way, an acquisition of Priorities is almost a reverse acquisition.”
Microsoft has stated its intent to make devices central to the user’s experience. By buying Nokia and making Nokia become the new face of Windows Phone, it would definitely reinforce that priority. Farhad Manjoo on Slate Sept 2013 states it even more forcefully. He says the purchase of Nokia will kill Microsoft’s software licensing strategy, including for Windows.
Figure 2. Ownership share of mobile phone OS for Symbian (Nokia’s old mobile OS), Windows Mobile (Microsoft’s old OS), and Windows Phone (Microsoft’s new OS for which the largest licensee is Nokia). Image from Wikipedia.org
Disclosures: George Taniwaki is a graduate of University of Chicago’s Booth School of Business. He has been employed at Microsoft both as a full-time employee and as a contractor. The opinions expressed in this blog post are his own and do not reflect those of either organization.