Production Function (A Quick Overview)

So I have been meaning to write more about what is happening to labor and capital as we transition from industrial society to information society. To do that well I need lay some groundwork first though by talking about the idea of a production function. A function as you may recall from math is something like f(x) = 3x + 1 which takes a value (here x) and transforms it into a different value (here into 3x - 5, so that f(1) = 4, f(2) = 7 …)

A production function then is the mathematical abstraction of the production processes of a single firm, or an industry, or even an entire economy into a function that captures how the inputs get transformed into the outputs. We will write Q = f(x1, x2, x3, …) where Q is the output, eg bicycles and x1, x2, x3 … are the inputs such as labor, raw materials, machines, buildings that go into making the bicycles. We will use the words inputs and factors (of production) interchangeably. At the level of the overall economy the output measure is generally taken to be GDP (which is problematic but that’s not the point today).

This mathematical abstraction turns out to be useful because it lets us give more precise definitions for a bunch of terms and capture some basic intuitions. Let’s start by considering a linear production function of the form Q = a + b*X1 + c*X2 + d*X3 … We will use it to define our first term, the marginal product of an input factor. This is simply the change in output that results from using more of a particular input. In the linear example it easy to see that when you use 1 more unit of X1 you always get b more units of output. That’s completely independent of how much of X1 you are already using and also independent of how much of the other factors you have. That seems wrong for most types of production because it is saying that you can make more bicycles simply by using more labor or more rubber or more steel or more buildings.

Now consider Q = a * X1^b * X2^c * X3^d …, the so called Cobb Douglas production function. Let’s look again at the marginal product of X1, which we find by taking the derivative of Q with respect to X1 to get a * b * X1^(b-1) * X2 ^ c * X3 ^ d … which now depends on how much of the other factors we are using. If b < 1 then we have an example of a declining marginal product, which means as we use more of X1 (for any given level of the other inputs) we get less and less additional output. That conforms better to our intuition about most production processes.

We can also use the Cobb Douglas production function to illustrate the concept of returns to scale or economies of scale. What happens to output if we use twice the amount of every input? There are three possibilities decreasing, constant and increasing returns to scale if we get less than twice, exactly twice or more than twice the amount of output. In the Cobb Douglas case it is easy to see that if the exponents b, c, d … add up to less than 1 we have the decreasing case, exactly 1 gives us constant and greater than 1 increasing.

Another important question to ask is to what degree we can substitute one factor of production for another. For instance, it is pretty clear that in many cases we can either use more machines (capital) and fewer humans (labor) or the other way round and achieve the same output. The quantity which captures this tradeoff is the so-called Marginal Rate of Technical Substitution (sorry, I didn’t pick the terms, just explaining them). We find it by taking the ratio of the marginal products for the two factors. With just a tad of math you can see that for the Cobb Douglas case, the rate between x1 and x2 is (b/c) * (x2/x1), meaning if we use 1 unit of x1 less then we need to use (b/c) * (x2/x1) units more of x1 to maintain the same output. You can also go back to the linear case and check that the rate of substitution there is simply b/c, i.e. doesn’t depend on how much of the inputs we are currently using.

What about factors of production that cannot be substituted for each other? For instance, if you make a bicycle you generally can’t substitute the rubber of the tires for the metal in the frame. Instead if you make more bicycles you will always need more rubber and more metal. These two factors would be called technological complements. The Leontief production function captures this notion in the extreme with Q = a * min(x1/b, x2/c, x3/d …). The marginal product of any factor by itself is 0 as increasing it does nothing when the other factors don’t increase also. The rate of substitution is undefined (it goes off to infinity), instead factors x1 and x2 will always be used in the ratio b/c.

So far we have not said anything at all about the cost for each of these factors of production. That will be the subject of a separate post, which will introduce the cost minimization problem at the level of the firm. Our eventual goal with all of this is to link changes in production technology to the determination of the factors prices in the economy overall. That will allow us to examine the impact of technology on wages and the return on capital.

Posted: 19th May 2014Comments
Tags:  economics production function

Some Thoughts on Surge Pricing

I am sympathetic to Uber’s basic argument that surge pricing is the market at work as (a) nobody is being forced to take an Uber and (b) raising prices puts more Ubers out on the street. On Saturday evening, close to the height of the storm I had to go to the Upper East Side to pick up one of our kids. I quickly decided to take the subway which was running on time and only cost $2.50 each way, even though that meant I had to walk about a dozen blocks in the storm. As an avid skier and lover of snowstorms the latter was just a question of bundling up which I did. The walk through a deserted Upper East Side was in fact magical.

But once you dig a bit deeper there are a couple of things worth examining. The first is whether or not people are good judges of what a 10x surge means. I for one would be interested in seeing the results of an AB test that compares announcing a surge multiplier with asking people to also put their destination in and then giving them a fare estimate. My gut is that quite a few people will say “yes” to 10x but “no” when they see $250. Now you might say tough noogies — they should have figured it out but we are creatures full of cognitive biases and so appealing to strict rationality in your customers may be a mistake. Fortunately, this would seem to be easily AB testable.

The second point is a bit more technical but equally important. A uniform price mechanism works extremely well with commodities which have a single unified market. As price goes up supply increases and demand drops until the two are in balance. With transportation the situation is trickier thought because during a snow storm an Uber that’s in downtown is not really relevant for someone trying to get a ride in uptown. It is not one market but many local mini-markets. In some of these it is likely that demand exceeds supply at any price level (supply simply doesn’t have enough elasticity). In those instances price increases do more to transfer wealth than to clear the market. By the way, I am not making a value judgement here — just clarifying the economics.

In this context it is worth mentioning that the fixed base charge and per mile incremental charge on taxis is also deeply flawed. It is not really effective to ask a taxi driver to work for the same rate at night in a snow storm as on a sunny afternoon (which is why there were very few taxis on the road). There are no really easy answers here and this is very much a debate worth having as long as we are willing to get down into the nitty gritty of it.

Posted: 19th December 2013Comments
Tags:  markets economics uber pricing surge

More on Basic Income Guarantee: Minimum Wage is Not a Longterm Solution

On Monday I posted about looking for a Research Assistant primarily to look into questions around using Basic Income Guarantees as a way to deal with what I believe is the end of work as we know it. Then yesterday Fred wrote a terrific post on the Limits of Capitalism and linked to my earlier post driving more traffic to it. The net result is that I now have many wonderful folks interested in helping out and will be sorting through that over the weekend.

In the meantime though I wanted to address an important point that came up in several of the comment threads where people asked about minimum wage. While the motivation behind a minimum wage is to help people make enough money to be able to live it winds up causing distortions that effectively reduce rather than increase the work that can clear in the market. That’s of course a known problem but at a time when automation is becoming a real alternative the distortion effect of a minimum wage is going way up.

Basic Income Guarantee (assuming for a moment that it can be made to work, this is what my research project is about) is a much more elegant solution. Why? Because it shifts the bargaining position for *all* labor as it gives everyone a credible walk away point. Yet it still allows for the labor market to clear effectively. For instance, if someone wants to do an unpaid internship (e.g., at a startup) because they value what they will learn this can now happen, whereas a minimum wage requirement will effectively eliminate a whole bunch of these internship opportunities.

The same is true for many other jobs, such as say bicycle messenger. A good friend of mine spent a year between college and graduate school as a bicycle messenger in Manhattan. He loved to cycle, loved the adrenaline rush of doing so on busy city streets. A minimum wage may eliminate a bunch of these jobs entirely whereas a Basic Income Guarantee makes it an individual choice.

This becomes especially interesting in the context of a potential migration of work into marketplaces such as Postmates. Without a Basic Income Guarantee these might quickly become a race to the bottom. But applying a minimum wage approach here would easily result in essentially arbitrary price floors. One of the arguments against a Basic Income Guarantee ist that it would reduce the labor supply so much that these marketplaces collapse entirely — I will have more to say about this in future posts.

Posted: 13th December 2013Comments
Tags:  economics basic income wages

Russell Brand and the Revolution

Russell Brand helped edit the latest issue of New Statesman. He leads off the magazine with an epic rant that is worth reading in its entirety. If you need some motivation, watch this 10 minute clip of him. Essentially, Brand is calling for a revolution.

It would be easy to dismiss Brand as a slightly lunatic comedian who lives a very comfortable life. But I think that would be a mistake. Aside from having a wonderful way with words, I find that Brand gives expression to a sentiment that seems very much pent up among a lot of people: the existing system has failed and is beyond repair. The net result of that is either apathy or violence. Or flipping back and forth between the two.

Brand is not really offering a coherent alternative vision. While that is a big open question, it doesn’t really invalidate his basic point about the pressures that are building up and why that is happening. And I sure wish that more people were speaking as frankly as he is about it as our politicians do seem to be largely in denial.

A big chunk of Brand’s critique is based on the assessment that we do in fact have the capabilities today to take care of our basic needs. This is a point I have made several times on Continuations — just look for my posts on abundance. What that means is that we should be focusing on such pressing matters as income inequality and the environment instead. And we should be tending to our spiritual health. Having watched a few minutes of an episode of the Real Housewives of Beverly Hills this morning while exercising I couldn’t agree more.

Here is a wonderful quote (among many that could be pulled) from Brand’s piece:

Fear and desire are the twin engines of human survival but with most of our basic needs met these instincts are being engaged to imprison us in an obsolete fragment of our consciousness. Our materialistic consumer culture relentlessly stimulates our desire. Our media ceaselessly engages our fear […]

That pretty much nails it. Go read the whole thing. It’s worth it. And I will come back to writing more about abundance and with that Basic Income Guarantee as the basis for a possible alternative structure for society.

Posted: 25th October 2013Comments
Tags:  economics russell brand revolution society

Micropennies: The Beginning Not the End

I have been meaning to write about the NY Times piece on royalties in the age of streaming music. People have talked about how real dollars have turned into digital nickels when music went online and sales went from records to individual songs. With streaming, the argument goes, “the river of nickels looks more like a torrent of micropennies.”

The first big gaping whole in the article was that it made no attempt at unpacking what part of the economics goes to labels versus individual artists. I am a big believer that services such as Spotify should enable individual artists to make their music available directly on the service without being intermediated by a record label. Our portfolio company Soundcloud already makes that possible. The NY Times writer apparently got so much feedback that this wound up being the first point in a subsequently published “footnotes" piece.

A second important point though that is not addressed in either the original article or the footnotes is that we are still at the beginning of a world of consumer surplus. When lots of content is free or nearly free the consumers of that content get a lot of benefit. Only once we provide new and innovative ways (above and beyond pay for the song and/or pay a subscription) for consumers to give back some of that benefit will we know what the new economy actually looks like. Kickstarter is one glimpse of that but there are many more yet to come.

We are at the beginning of the structural change in the music industry, not the end. I am quite optimistic that the end state will look better for artists than before. But much like the changes in the labor market, getting there will be painful.

Posted: 8th February 2013Comments
Tags:  music economics

Work and Value in the Digital Economy

Yesterday I attended MIT's Roundtable on the Digital Economy. It was a gathering convened by Erik Brynjolfsson and Andrew McAfee, the authors of Race Against the Machine, to discuss “Work and Value in the Digital Economy.” The gathering brought together an interesting mix of academics, startups, investors (yours truly) and policy experts.

I don’t have time this morning for more detailed thoughts, but I came away with a clearer grasp of some of the central questions:

1. Is work actually diminishing more permanently or do we just have a disappearance of “jobs” as we know them? The latter might be easier to deal with than the former.

2. Do people need jobs or can we deliver what jobs provide some other way and in a potentially unbundled fashion? The “jobs of a job” include income, structure, social connections, meaning, and at least in the US, access to healthcare.

3. Are emerging marketplaces such as Etsy, Airbnb, ODesk, Relayrides (these were all present) a potential solution? There are important differences between markets that potentially drive down the payout to (commodity) labor (a la Amazon Mturk) and those that may create sustainable activities with the potential for a stable income. More on that in a future post as I had a big Aha moment.

4. How meaningful is the shift from producer surplus (profits) to consumer surplus (value creation) in the digital economy (eg Khan Academy) and how should it be measured? This is an important question as we think about how to regulate some of these emerging providers and marketplaces.

Unfortunately I could not stick around for the last session on regulation, so I have to wait to see some of the transcribed notes from that.  All in all it was a very thought provoking day on a topic that I care a great deal about, ie how do we get the transition that’s before us right instead of winding up with massive social unrest.

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Posted: 12th December 2012Comments
Tags:  MIT work employment economics

Thinking About Employment (Part 4)

In part 3 of this series I argued that the changes in employment are the main driver behind the massive rise in inequality in the US.  That inevitably brings out a number of responses for how to address inequality, none of which I believe will actually work.  At the end of that post I already showed a graph that debunks the notion that this can be solved through better education (at least of the traditional variety).  Similarly we now have calls for better labor organizing and higher minimum wages. Unions played an important role during industrialization so why not now? As even Robert Reich concedes, if there are too many people without a job it becomes very hard to organize those who have one. And even though I am sympathetic to an increased minimum wage as a short term measure, in the long run it will only hasten the demise of jobs as machines do not qualify (ditto for healthcare).

What all of these old solutions have in common is that they are premised on the continued growth of traditional jobs. If we want to make progress we first have to abandon that notion and have to think about a world in which there are fewer and fewer traditional jobs. Here then are three proposed solutions aimed at such a world:

1. Encourage and support the creation of new marketplaces that support micro-entrepreneurship, such as Etsy, Airbnb, Taskrabbit, Kitchensurfing, Sidecar, Skillshare and Shapeways to name just a few (including several USV investments).

2. Stimulate demand in areas of the economy that are mispriced or underpriced and hold significant employment potential for instance by taxing carbon and problematic food ingredients and providing prizes for space exploration and medical innovation.

3. Take measures aimed directly at inequality and its consequences, such as unbundling healthcare from employment and changing the tax code to affect some level of redistribution.

Each of these will eventually get its own detailed treatment in a separate blog post.  But for now I want to provide some more justification for each and more importantly point out how they work together given the changes in employment.

Micro-entrepreneurship is exciting because it allows people to earn an income often with minimal need for capital. Many (but not all) of these marketplaces are aimed at providing unique products or experiences or otherwise ad hoc tasks that will not easily be substituted by machines any time soon. So from a regulatory perspective we should be encouraging the growth of these marketplaces and the creation of new ones. Instead, we are seeing a fair bit of hasty action, such as the cease and desist orders against Lyft and Sidecar, that could harm the development of these marketplaces.

The second part of the approach is likely to be more controversial. But I firmly believe that it is the central role of government to deal with externalities. And we have a bunch that are not properly addressed today that could create significant net new employment. When people protest a carbon tax by pointing to jobs that would go away they fail to point to the new jobs that would get created. In fact, a carbon tax would mostly hit industries that are heavily substituting machines for humans whereas it would benefit efforts such as reforestation that are labor intensive. The same goes for processed foods compared to local farming and farm-to-table. I strongly favor approaches such as taxes and prizes where the government just sets the framework and lets private activity unfold over having this activity be part of the government itself. In fact, this is a strong complement to the micro-entrepreneurship. For instance, taxing highly processed foods while simultaneously fostering farm-to-table marketplaces (e.g. Farmigo and Good Eggs) will push economic activity from capital intensive to labor intensive which is what we need. Similarly, posting prizes for medical innovation and space exploration will help foster collaboration in emerging research networks such as Research Gate.

Some of the likely criticism of both of these recommendations is that people cannot earn enough money via micro-entrepreneurship and that taxing carbon and processed foods will make staples more expensive thus compounding the inequality problem. Which is exactly why we need to attack inequality and its consequences more directly. In fact all indirect approaches which make labor more expensive are the exact opposite of what we need in a world which is substituting away from labor. Direct approaches aimed at making healthcare accessible and affordable (one of the major issues with inequality) and redistribution through the tax code don’t have that problem.

The goal for today’s post was to get these three pillars of what I think of as the “new new deal” out there. I will provide more meat on each of these in subsequent posts.  But I want to address one other immediate question as to how we can afford all of this. Leaving aside for a moment that we cannot afford the alternative, which ultimately heads towards massive social unrest, I am proposing new revenue sources for government.  I also believe that by shifting more activity into new and emerging marketplaces we can actually reduce some costly government programs. In fact, re-inventing how we tax and allocate budgets to avoid the silliness that is the Washington’s fiscal cliff could and should be a fourth component.

What I am most hoping for with this post is to move the debate past the old solutions and past the old divisions towards a different set of approaches that do not fall along existing party lines.  All of the proposals above really are aimed at moving us away from the hierarchical organization of production which is dominated by a substitution of capital for labor towards a peer economy and society.

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Posted: 3rd December 2012Comments
Tags:  employment economics politics innovation peer

Thinking About Employment (Part 3)

This is the third post in my mini series on employment.  Part 1 illustrated how agriculture and manufacturing, the two historically large areas of employment, have collapsed over time.  Part 2 drilled into the services sector which today accounts for the bulk of employment to show that many categories there have stopped to grow and are under pressure from the twin forces of automation and globalization. Why does all of this matter? My overriding argument is that we have not found a new source of jobs. The result is an unprecedented pressure on wages that is the primary driver of the astounding growth in inequality in the United States.

Much has been written recently about inequality but still the numbers are so extraordinary that it is worth calling some of them out.  Maybe the most radical summary came in the form of a tweet by Senator Bernie Sanders in which he claimed that the Walton family owns more wealth than the bottom 30% of Americans.  Subsequent fact checking showed that he was off with the real number being above 40%.  For some more similar examples see this post.  How is such an extreme situation possible? Of course on one end it is the exceptional fortunes at the top of the pyramid.  But these wouldn’t be so much a problem in isolation.  

The real issue, as fas as I am concerned, is just how tough things have gotten for a large and growing part of the population.  A recent report by the Census Bureau showed a further decline in median household income (image taken from the full PDF report which is worth studying)

When looking at this chart it is critical to keep in mind that these are median household incomes.  That means half of all households make *less* than that and in some cases by a lot, with almost 10 million households living in poverty.

To see how inequality is driven by what is happening in the labor market consider first the following chart from a terrific blog post titled “Is Decoupling Real?" that investigates the relationship between GDP and income growth:

The chart shows average household income tracking GDP growth but median and Q3 (middle quintile) income detaching around 1980 and slowing down substantially.  The only way for the average to grow faster than the median (for any measure) is for the high end of the distribution to grow faster.  Translation: incomes at the top have been rising while incomes at and below the media have been stagnant or declining.

But what is behind that decoupling?  The next chart shows what has happened to labor’s share of national income.  It is from a great post from two researchers at the Federal Reserve in Cleveland titled “Labor’s Declining Share of Income and Rising Inequality

The two obvious questions are: why is labor’s share declining and what is growing in its stead?  Let’s start with the second question as it is covered by the same set of statistics: income from capital has been rising rapidly. The answer to the first question are the forces I have described in part 1 and part 2 of this series: globalization and automation.  Both of these will make capital more important than labor.  And that is exactly what the statistics show!

The rising importance of capital is a double whammy for inequality.  First, wealth is already highly unevenly distributed which means that the returns to capital are highly concentrated among a small part of the population.  Second, the shift is responsible for the decoupling between average and media wages shown above.  For those with jobs that are complementary with capital (eg, investors, CEOs) incomes have been rising with the increased importance of capital.  The latter effect is made even more pronounced as automation is driving increasing returns to scale with winner-take-all (or nearly all) effects in many markets.

And to tie all of this back to the basic premise of my series of posts: traditional remedies simply won’t do.  We are experiencing a fundamental restructuring of economic activity on par with the shift from agrarian to industrial society.  Pressure on labor will only rise from here on out. We need to think beyond fiscal stimulus and even beyond a simplistic and unreflected mantra of “more education” as the following chart shows (taken from a post title “It’s the distribution, stupid”): 

The red and blue lines indicate that a growing percentage of the population has at least completed high school (blue) and even more gains have been achieved in the percentage of the population with a college degree (red).  Over that time period productivity (yellow, measured here in change in GDP per capita) has also grown substantially due to automation. All the while median wages (green) have stagnated as we have already seen.

What is the answer then?  I don’t know either but in the next post I will take some stabs in what I think is the right direction.  It should come as no surprise to regular readers of this blog that much of it will involve the peer progressive agenda.

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Posted: 25th November 2012Comments
Tags:  employment economics innovation

Inequality, The Movie

I am still working on my third post about employment.  As part of that I have been reading up on the rise of inequality in the US and its effects on society.  In that process I came across this interesting chart from a Morgan Stanley research report:

It shows that rising income inequality has been highly correlated with increased political polarization since the mid 1970s (found via Business Insider).

Then just a few minutes ago I saw in my Tumblr dashboard that Robert Reich is making a documentary movie about inequality and is raising money for it on Kickstarter. I just backed the movie because this topic needs all the attention it can get. The chart above shows why it presents not just an economic and moral challenge but also a political one that has in the past lead to violent social convulsions.

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Posted: 16th November 2012Comments
Tags:  economics inequality movie kickstarter

Information Technology and Hybrid Organizations (Thesis)

This is the second post in my little project of self publishing my PhD Thesis.  Last week I introduced an econometric analysis of the impact of Information Technology (IT) firm size.  This time it is a more theoretical paper that presents a model for examining the impact of different types of IT on the structure of organizations.  In particular, it compares having no IT, with centralized IT (think mainframes) and networked IT (think Internet and Intranet).

I was particularly happy with how this paper came out because it addresses a fundamental problem in economics: the organization of economic activity in firms versus markets.  In re-reading the paper I found that I don’t actually bring this point out very well at all because I focused the paper too much on different organizational forms (inside of firms).  So I will try to do a better job in this little recap / introduction.

Ever since Coase published his seminal essay on The Nature of the Firm, there has been a long running inquiry into a fundamental question of economics: why are some activities carried out in the market and others inside of firms? Coase and subsequent writers focused on the idea of differing transaction costs, but the precise mechanism by which transaction costs would be different in a market versus inside firms were hard to pin down. That changed with the work on principal agent problems and incentives.  Tons of different economists contributed to this. I was fortunate to have one of them, Bengt Holmström, as one of my thesis advisors.

One of the key insights coming out of Bengt’s and others’ work is that firms exist to reduce incentives.  Why would you want to reduce incentives?  In order to get better coordination.  If you pay people a flat wage then you can direct what problems you want them to work on and how you want them to work together on those problems.  In fact, much of what companies do in HR and compensation, such as reviews, goals, options, bonuses, etc. is aimed at restoring some additional motivation in the face of much reduced incentives. Effectively you can think of this issue as a coordination - initiative tradeoff frontier.  You can get more coordination inside of a firm than in the market by reducing individual initiative.

What my paper does is explore the shape of the coordination - initiative frontier based on different types of information technology.  I distinguish between three different scenarios: no IT, centralized IT and networked IT.  I examine how these three different scenarios would play themselves out in the absence of incentive problems, i.e. when everybody does the “right” thing to maximize joint production.  That analysis provides a baseline for looking at the incentive case.  In the incentive case people look to their own benefit first and thus exert less effort if their incentives are muted.

The key findings are summarize in the following diagram

The diagram shows the location and shape of the coordination - initiative frontier.  The first key finding is that having information is a good thing as the frontier for both IT cases dominates the one without IT.  The second key finding is that that networked IT dominates central IT case: it is possible to achieve full coordination at a much higher initiative level than with centralized IT.

In the paper I interpret this result along different organizational forms inside the firm.  But it would be just as correct (and looking back at it more relevant) to classify this as the historical change that we have experienced from mostly individuals in the market (agriculture, crafts, trading), to having large hierarchical firms (industrial society), to replacing those hierarchies with networks (now).  That of course is a very nice fit with what I and others have been arguing in the Peer Progressive agenda.

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Posted: 12th November 2012Comments
Tags:  thesis information technology firm organization economics model

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