I wrote the original when the Occupy movement was enjoying its first wave of enthusiasm. There was a popular photo meme of people holding up placards giving some facts about their financial situation and then I Am the 99%. And then, of course, came the reaction; photos of people holding up things saying Im not the 99%, I worked to get where I am, get a job you hippie (Im paraphrasing, but not unfairly I think).
This narrative goes way beyond a few photos on Facebook. It is written deep into our societys economic philosophy. Choose to work hard and exercise your talents, and you will be rewarded with wealth. Choose to complain and protest instead of knuckling down and getting things done, and you will be rewarded with poverty, for which you will have no-one to blame but yourself.
It would be hard to deny that, other things being equal, you will achieve (and acquire) more if you work than if you dont. Thats kind of the definition of work, really (if youre expending effort but not achieving anything, youre not working, youre faffing about). But thats not enough to settle the question. Just because youll get more if you work than if you dont work, doesnt mean that the difference between someone with money and someone without is that the first person is working and the second one isnt. It could instead, for instance, be simple luck.
When economists want to test an idea, they use mathematical models. I shall have more to say on economists and their models another time. But I thought the hypothesis that luck cannot make the difference between a rich person and a poor one in a capitalist system was worth testing, and it turned out to be really easy. With a little algebra, you can do it yourself in Microsoft Excel. As I have done, and will now demonstrate.
First, lets set up our scenario. Angela, Barry, Cathy, Dave, Ellie and Frank work in competing businesses, making the same product. All of them have exactly equal talent and exactly equal work-ethics when it comes to selling their product, so which one actually makes a sale to any given customer is purely random. So we can assign each one, at each sale, a random number. In cell A2, write
=rand()and fill across six columns to cell F2. Then fill down as many trial opportunities as you want; I picked 1024, that being a nice round number if youre a computer geek. The command rand() in Microsoft Excel generates a random number between 0 and 1.
Columns A to F represent how well each of our six competitors did, as it turned out, towards making the sale. But each customer will only buy one product, so only the best of the six competitors will win in each column. To figure out how many sales each competitor makes in the course of the 1024 trials, youll need another set of columns, G to L. Column G represents Angelas sales, column H Barrys, column I Cathys, and so on. We need to set them to add 1 to that persons sales total if their random number happens to be the highest. In cell G2, write
=if(a2=max($a2:$f2),g1+1,g1)and fill across to L2, and down for however far youve decided to run it. Let me explain that formula. An if() statement in Microsoft Excel has three parts. First you set the condition, which in this case is If cell A2s value is the highest of the cells A2 to F2.... Then a comma, then what happens if the condition is true, which in this case is Add 1 to the running total; then another comma, and then what happens if the condition is false, which in this case is Keep the running total the same as it was. As you fill the cells across to L2 with the same formula, it does the same test on columns B to F and adds 1, or not, to the appropriate total. Be careful to put the dollar signs in the phrase max($a2:$f2), so that all six new columns still run their test against the first six columns. Fully translated into English, what it does is If cell A2 has the highest value of A2 to F2, then add 1 to the running total, otherwise leave it as it is.
What happens? This happens:
But weve forgotten something: this competition takes place in a capitalist environment. That means our six competitors arent starting from scratch every time; the profits from each sale become capital for the business thats why its called capitalism which can then be directed into advertising, promotions, tidier premises, or whatever, and make it easier to make the next sale. We need a slightly more complex formula to model this. Well keep the random numbers and the same test column, but well change the references in that test column so that it now says
=if(m2=max($m2:$r2),g1+1,g1)and now we have to fill in a third formula in columns M to R to make it work. Column M will take the random number representing Alices luck that day, and multiply it by the number of sales shes already made,
=a2*g1except, of course, the first row will be all zeroes because G1 is zero (which will then screw everything up below it). Dont try changing it to =a2*g2, youll get a circular reference error. So why are we multiplying them? Why not add them (=a2+g1)? Well, capital doesnt automatically add itself to your success; you still have to deploy it appropriately. Your talent, work, and luck the random number in columns A to F is a factor modulating the effect of capital, not merely something slapped on the top. Also, remember, the rand() keyword in Excel generates a number between 0 and 1, and if you multiply a whole number by something less than 1, the result is smaller than your original number; so multiplying actually has a more conservative effect on the end result than adding, and I want to see if I can make the point with the most conservative numbers possible.
Heres a workaround. Type in to cell M2
=a2*(g1+1)and fill across and down as before. Now, I set things up so Im using the same random numbers each time to make my graphs (I start a new page each time, and fill in columns A to F with sheet1!a2 instead of rand()), and this is the result:
Whats going on? Well, each time Barry makes a sale, he has more capital to compete against the others with, which makes the next sale surer, and the next surer still, and so on. Within quite a short time, the chances of anyone else beating him, no matter how hard they try, dwindle away to practically nothing.
If youre not comfortable with that arbitrary +1, lets suppose that it represents help, or money, or whatever, over and beyond the profits from sales. Public services, perhaps. Public transport for goods, free water, stuff like that. But that immediately suggests an additional question. What happens if this outside help gets bigger or smaller? Or, equivalently, what happens if the contribution of capital is proportionately smaller? We needn't model both of these, since they will both do exactly the same to the maths. Lets set the formula to
=a2*(g1+20)and see what happens:
=a2*(g1+0.05)then we get this:
Next I want to deal with an objection that one or two commenters raised in response to my Note. My models so far have Angela, Barry, Cathy, Dave, Ellie and Frank doubling their businesses startup capital with their first sale hardly a realistic scenario. Perhaps, given more plausible starting conditions, my argument would no longer hold?
Fair enough, I guess. And easily tested. Simply fill in cells G1 to L1 with the value 100, to represent their startup cash, and see what difference that makes. This is what happens now if the competitors dont avail themselves of the early-luck-magnifying effects of capital: a2*(g1+1)) level of public services: a2*(g1+20)), this happens: a2*(g1+0.05)), its this: 100 because I havent bothered to simulate their startup investors demanding their money back.
Now were ready for the real test. In the real world, some people are more talented than others, and some people do work harder than others. Perhaps that talent and industry do make a difference, even given the massive skewing effect of capital. For convenience sake, I decided to set our six salespeoples talent in alphabetical order; Angela would be the best, and Frank the worst, of them. But how to insert it into the formula? Should it be something we multiply the random number by, or something we add to it?
I went with add. I figure what an industrious genius achieves on a bad day is still a lot better than what a cognitively limited layabout achieves on a bad day; if talent were a multiplier, then they would both do exactly the same if the randomizer happened to come up with 0. So, first, we string six numbers across the top row:
The formula for columns A to F looks like this:
=rand()+a$1as before replacing rand() with sheet1!a2 if you want to use the same numbers for each test. And what happened?
Without capital, it looked like this: 100. By hypothesis, this distribution is the fairest possible, assuming a meritocratic standard of fairness (which it would take us too far off track to argue about here). With capital accumulation factored in (and moderate public services), that became this:
But theres another thing we havent been bothering to vary, up until now: theyve all been starting at the same time. What would happen if talented, hard-working Angela were new to the market, and lazy, mediocre Frank were the old guard? Would her talent win out over his early luck? I set up the same model again, but this time I had them enter the competition in reverse order of skill. Frank is there from the start, but I replaced Ellies first 128 randomly generated numbers with -2, to make it that she hadnt come in yet for those first 128 sales; then did the same to Daves first 256 numbers, Cathys first 384, Barrys first 512, and Angelas first 640. (It had to be -2 rather than 0 because Dave, Ellie, and Franks random numbers all dip below 0 from time to time.)
This was the result if no-one can accumulate capital (once again, I havent bothered to simulate what happens to each of them before they get enough cash to enter the stakes): a2*(g1+100) or a2*(g1+1000), our hypothetical society might even become tolerably fair. What is absolutely clear, however, is that laissez-faire capitalism creates undeserving élites by rewarding early luck over merit.
Now, if Ive made a mistake in any of my assumptions or algebra, please feel most free to point it out. I would welcome debate and commentary on this. But by that I mean debate and commentary. If your contribution is going to be along the lines of I cant find an error in your methods or premises, but your conclusion has to be wrong because get a job hippie dont bother.