Harberger Triangle

Yglesias has a absolutely impenetrable explanation of the Harberger triangle. However, on thinking things through, it may not be that complicated. Here is what I think it all means.



The chart above depicts the theoretical supply curve for some commodity. For simplicity it is shown as a straight line. As the price in the market increases, the quantity available for sale will likely increase, and so the the curve has a positive slope.

What determines how much supply will be there for a given price? Well, for a quantity like that shown on the graph and the price as shown (Market Price), the producers have a surplus. It is advantageous for the producers to put additional supply on the market. Of course, as they do so, the costs to themselves tend to increase, and so the surplus eventually goes to zero. At that point, producers will not put any more supply on the market, and you've got a point on the supply curve.

In reality, given the nature of production, the supply curve for any one producer probably looks like this, a staircase.

Once the price crosses a threshold, it is economical for the producer to add on certain production capacity. Incremental costs of increasing production remain constant upto a certain point, so the producer will put as much as they can on the market. The overall market is a sum over all producers who have different staircase curves. Looked at a fine scale, a sum of staircase curves remains a staircase. However,

1. A smooth curve is a good enough approximation. The uncertainties/errors of measurement of the staircase is probably larger than its discontinuities.

2. Doing efficient market theory becomes mathematically very inefficient without this approximation.

______________

We can in a similar way, look at the demand curve for the commodity. In this case, as the price goes up, we expect the amount consumers are willing to buy goes down, and the demand curve has a negative slope.



In exactly the like fashion as in the supply curve, we have the notion of a consumer surplus. Consumers keep buying until at some point, the benefit to additional purchases among consumers is zero.

Putting it all together, we have the efficient market equilibrium.


The colored areas - which really should extend all the way to the price axis - represent the net benefit to the economy (the consumers and producers) at this equilibrium. Every consumer that had a benefit that still existed at the market price makes purchases, those purchases that had no economic benefit (at the market price) for the consumers don't happen. Similarly only the sales that had a net benefit for the producers happened.

Now suppose something (some government intervention) moves the market away from its efficient equilibrium. A situation like that below might obtain (it is one of several possible scenarios. In general, both the supply and demand curves will move from their efficient market instances. In my diagram, we simply moved along the efficient market curves.) The quantity sold/consumed and the price at which it is consumed is represented by the point C.

Because of the higher price, the demand quantity is lower than it could have been. The yellow and orange colored areas are the net loss to the economy because it is no longer efficient. The technical term, I believe, is deadweight loss. One or both of those triangles BCD or BDE, or the overall large triangle BCE is the Harberger triangle(s) (pure reason does not enable one to determine which.)

BDE represents lost value to the producers, BCD represents the lost value to the consumers, compared to the efficient market scenario. The hatched area between the Forced Price and the Efficient Market Price appears to be a loss to consumers or gain to producers. It depends.

Suppose the departure from the market equilibrium is because the government imposed as sales tax. One would expect the tax to be partly borne by producers and partly by consumers. I think (but can't currently prove) the price received by the producers is represented by the price at point E, the price paid by consumers is represented by the price at point C, and the ratio of the burden of sales tax on consumers to producers is CD/DE. The revenue collected by the government is represented by the rectangular region to the left of the line segment CE.

Suppose C was the price set by a monopoly. C would be set by the monopoly producer maximizing price * quantity, with C on the demand curve. BCE still represents the loss to the economy compared to the efficient case. In this case the producer is reaping additional benefit represented by the hatched area minus BDE.

Overall I don't understand what Yglesias is writing. Maybe CIP or someone will be able to explain.

PS: I think BCE is The Harberger Triangle.

PPS: Wiki is unclear. They seem to imply government revenue is represented by some fraction of the Harberger triangle. But it seems to me that BCE represents economic activity that simply doesn't take place - it doesn't represent government revenue. Now I'm totally confused.

PPPS: Uncharitably, I tend to think Yglesias is the hopelessly confused one. When I read Krugman's paragraph that started off Yglesias, then it doesn't seem to be saying anything like what Yglesias or Wiki writes. The Harberger triangle is not captured by government revenues, etc.

Now, a key point in all this is that the emissions tax or, equivalently, the rent on emissions permits, does not represent a net loss to society. It’s just a transfer from one set of people to another — from the emitters, and ultimately those who buy their products, to whoever collects the taxes or gets the permits, and ultimately whoever benefits from the revenue or rents thus generated. The only net loss is the Harberger triangle created by the reduction in emissions — which has to be set against the benefits of reduced pollution.

To Krugman's larger point: not taking into account the costs of pollution (i.e., assuming that the efficient market is one in which pollution is costless) is a mistake. I.e., today's "efficient market" really embodies a pollution subsidy.

Fast computers

After a super-duper fast Nehalem Mac Pro, it is very painful to use any other computer.

Intense Debates

Commenter RK suggested this. To install it I had to upgrade from classic templates to layouts in blogger. Let's see if it works.

Reflection on John Norton's argument

Here and referred to below.

Suppose we have a physical quantity Q that must take its value between 0 and 1, inclusive. Let us stipulate that our current knowledge has absolutely nothing to say about the possible value of Q. It is very tempting to say that a priori, Q is uniformly distributed on [0,1]. This is nothing but a theoretical prejudice. We would in effect be saying that our utter lack of evidence means that it is nine times more likely for Q to lie between 0 and 0.9 than for Q to lie between 0.9 and 1. In reality the support for Q to take on some set of values is exactly equal to that for Q not to take on that set of values (as long as the set is not the entire set or equivalently we do not try to assert that Q takes on no value whatsoever.)

This may be easier to see if we map [0,1] to [0,infinity). There is no uniform distribution on [0, infinity); and our theoretical prejudice explicitly manifests itself when we try to assign a probability measure for Q on [0,infinity).

In a physical theory, we need a physical reason to believe that Q has a probability distribution. In Norton's language, we need a randomizer in order to induce probabilities. E.g., in many situations we have a good reason to believe that a quantity follows a normal distribution, because it arises as an aggregate from a large number of underlying processes and the law of large numbers holds. In statistical mechanics, we have good reason from Hamiltonian mechanics to assume that a system in thermal equilibrium is well represented by assuming a uniform distribution over its microstates. And so on.

The Trouble With Physics

Heretical punchline: cosmic parameters can’t be judged as “improbable,” so long as they’re consistent with theory and observation.

The trouble in physics is that the punchline above was judged to be heretical.

John Norton's paper, "Cosmology and Inductive Inference: A Bayesian Failure" is available here. It is both a pity and a blessing that this was formalized.

(emphasis added)

John Norton talks about the “Bayesian failure” of cosmology and inductive inference. (He admits off the bat that it’s kind of terrifying to have all these cosmologists in the audience.) Basic idea: the Bayesian analysis that cosmologists use all the time is not the right tool. Instead, we should be using “fragments of inductive logics.”

The “Surprising Analysis”: assuming that prior theory is neutral with respect to some feature (e.g. the value of the cosmological constant), we observe a surprising value, and then try to construct a framework to explain it (e.g. the multiverse). This fits in well with standard Bayesian ideas. But that should worry you! What is really the prior probability for observing some quantity? In particular, what if our current theory were not true — would we still be surprised?

We shouldn’t blithely assume that the logic of physical chances (probabilities) is the logic of all analysis. The problem is that this framework has trouble dealing with “neutral evidence” — almost everything is taken as either favoring or disfavoring the hypothesis. We should be talking about whether or not a piece of evidence qualifies as support, not simply calculating probabilities.

The disaster that befell Bayesianism was to cast it in terms of subjective degrees of belief, rather than support. A prior probability distribution is pure opinion. But your choice of that prior can dramatically effect how we interpret particular pieces of evidence.

Example: the Doomsday argument — if we are typical, the universe (or the human race, etc.) will probably not last considerably longer than it already has (or we wouldn’t be typical). All the work in that argument comes from assuming that observers are sampled uniformly. But the fact that 60 billion people have lived so far isn’t really evidence that 100 trillion people won’t eventually live; it’s simply neutral.

Heretical punchline: cosmic parameters can’t be judged as “improbable,” so long as they’re consistent with theory and observation.

PS: at least the beginning of the paper was very readable for me. BTW, this also requires a climbdown from me - I have to admit that philosophers can be useful.

PPS: While the conclusion, as reported by cosmicvariance, is intuitively satisfying ("obvious"), Norton's paper is deep.

A few thoughts

Reminder to self - need to make the comments on this blog more useable. Haloscan, maybe?

Bee wrote in the comments to my previous post: "Unless you are talking of a mathematical proof, right and wrong are context dependent. If you want to reach xyz, something might be the right thing to do, something else the wrong thing. Even if you know that, the question remains, do you want to reach xyz in the first place?"

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Yes, right and wrong can be context dependent - but they are more or less absolute within the context. There is a right way (or a few right ways) to start a car, for instance. That doesn't change, regardless of the purpose for starting the car - going somewhere, or running over someone. Right and wrong are for dealing with "factual" reality.

"Why do you want to reach Atlantic City in the first place?"
"To bet at the blackjack tables".

That may be good or less good (morally bad) depending on your perspective.

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Bee's question - why do you want to reach xyz in the first place, also reminds me of the question - why be good?

"Why be good (moral)?" is a perennial problem in Western systems of ethics. This was Glaucon's challenge to Plato. Apparently this question cannot even be meaningfully framed in most Indic systems - at least, so I understand. In Indian thought there is simply that which is life-sustaining and that which is not. By life-sustaining, I do not simply mean the physical body, but include the psyche,mind,etc., and the family/community/society,etc. One's actions are more or less conducive to the health of these things. The question "why be good?" morphs into "why should I choose to live?". But that is a private question, not susceptible to universalist answers.

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Anyway, I picked up at the library, what from the first few pages seems like an interesting read: "A Case for Amorality: The Moral Fool" by Hans-Georg Moeller.

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Thought for the day

There is no good and evil — or rather, good and evil are subjective, not objective. There is however, right and wrong. (Paraphrase of Swami Dayananda Saraswati from a Q&A session at Arsha Vidya Gurukulam on its 23rd anniversary.)

WTC 7

From the NIST report on the collapse of World Trade Center 7 (this building collapsed hours after the two main towers went down):


The important point is that during Stage 2, the collapse was accelerating at 32 ft/sec^2, i.e., it was essentially in free fall.

The 9/11 truthers claim that this could happen only if the building was deliberately demolished (i.e., it requires simultaneous catastrophic failure of structural members all over the building, and therefore the free fall indicates that the building fell for some other reason than being damaged by falling debris from the main towers and the fires that raged uncontrolled for six hours.

This article on implosionworld.com by a building demolition specialist says that a collapse due to structural damage is consistent with all the known facts.

The truthers also claim that the NIST did not do the analysis summarized in the graph above, until pressed by them, and that this is a sign of a cover-up.

Your mileage may vary.

The text from the NIST report states the following:

3.6 TIMING OF COLLAPSE INITIATION AND PROGRESSION

The timing of global collapse of WTC 7, as indicated by downward motion of the north exterior face, was investigated using a video of the collapse taken from the vantage point of West Street near Harrison Street (Camera No. 3, Figure 5-183 of NIST NCSTAR 1-9). An initial analysis compared the observed time it took for the roofline to fall approximately 18 stories to the free fall time under the force of gravity. A more detailed analysis examined the vertical displacement, velocity, and acceleration through different stages of the collapse process. (NIST NCSTAR 1-9, Chapter 12)

The time that the roofline took to fall 18 stories or 73.8 m (242 ft) was approximately 5.4 s. The theoretical time for free fall (i.e., at gravitational acceleration) was computed from
t=sqrt(2 h/g)
where t = time, s; h = distance, m (ft); and g = gravitational acceleration, 9.81 m/s2 (32.2 ft/s2). This time was approximately 3.9 s. Thus, the average time for the upper 18 stories to collapse, based on video evidence, was approximately 40 percent longer than the computed free fall time.

A more detailed examination of the same video led to a better understanding of the vertical motion of the building in the first several seconds of descent. NIST tracked the downward displacement of a point near the center of the roofline, fitting the data using a smooth function. (The time at which motion of the roofline was first perceived was taken as time zero.) The fitted displacement function was then differentiated to estimate the downward velocity as a function of time, shown as a solid curve in Figure 3- 15. Velocity data points (solid circles) were also determined from the displacement data using a central difference approximation. The slope of the velocity curve is approximately constant between about 1.75 s and 4.0 s, and a good straight line fit to the points in this range (open-circles in Figure 3-15) allowed estimation of a constant downward acceleration during this time interval. This acceleration was 32.2 ft/s2 (9.81 m/s2), equivalent to the acceleration of gravity g.

For discussion purposes, three stages were defined, as denoted in Figure 3-15:

• In Stage 1, the descent was slow and the acceleration was less than that of gravity. This stage corresponds to the initial buckling of the exterior columns in the lower stories of the north face. By 1.75 s, the north face had descended approximately 2.2 m (7 ft).

• In Stage 2, the north face descended at gravitational acceleration, as the buckled columns provided negligible support to the upper portion of the north face. This free fall drop continued for approximately 8 stories or 32.0 m (105 ft), the distance traveled between times t = 1.75 s and t = 4.0 s.

• In Stage 3, the acceleration decreased somewhat as the upper portion of the north face encountered increased resistance from the collapsed structure and the debris pile below. Between 4.0 s and 5.4 s, the north face corner fell an additional 39.6 m (130 ft).

As noted above, the collapse time was approximately 40 percent longer than that of free fall for the first 18 stories of descent. The detailed analysis shows that this increase in time is due primarily to Stage 1. The three stages of collapse progression described above are consistent with the results of the global collapse analyses discussed in Chapter 12 of NIST NCSTAR 1-9.

Full-blown Corporatocracy

The NYT editors fear that the Supreme Court is about to strike down all limits on corporations' involvement in elections.

The court, which is scheduled to hear arguments on this issue on Wednesday, is rushing to decide a monumental question at breakneck speed and seems willing to throw established precedents and judicial modesty out the window.

After establishing that the court is in an unseemly rush, the editors continue:

The scheduling is enormously troubling. There is no rush to address the constitutionality of the corporate expenditures limit. But the court is racing to do that in a poorly chosen case with no factual record on the criticalquestion, making careful deliberation impossible.

Most disturbing, though, is the substance of what the court seems poised to do. If corporations are allowed to spend from their own treasuries on elections — rather than through political action committees, which take contributions from company employees — it would usher in an unprecedented age of special-interest politics.

Corporations would have an enormous say in who wins federal elections. They would be able to use this influence to obtain subsidies, stimulus money and tax loopholes and to undo protections for investors, workers and consumers. It would take an extraordinarily brave member of Congress to stand up to agents of big business who then could say, quite credibly, that they would spend whatever it takes in the next election to defeat him or her.

Rahu and Ketu

The traditional Indian astrology/astronomy is concerned about the following nine objects

# 1 Surya
# 2 Chandra
# 3 Mangala
# 4 Budha
# 5 Brihaspati
# 6 Shukra
# 7 Shani
# 8 Rahu
# 9 Ketu

In English, Surya is identified with the Sun, Chandra the Moon, Mangala Mars, Budha Mercury, Brihaspati Jupiter, Shukra Venus, Shani Saturn, and Rahu and Ketu the lunar nodes - the two points of intersection of the moon's orbit and the ecliptic (i.e., points of potential solar and lunar eclipses). Rahu is the ascending node (the point where the moon moves to the north of the ecliptic), and Ketu is the descending node (the point where the moon moves to the south of the ecliptic). Further reading here.

The interesting thing about this organization is how Rahu and Ketu are reified (Wiki: "Reification in thought occurs when an abstract concept describing a relationship or context is treated as a concrete "thing"").

There is a case to be made that Hindus reified virtually every concept. That may be the basis of murti puja ("idol worship"), the source of its "polytheism" and their sacred geography (scare quotes around concepts that make sense only in the context of the Abrahamic religions).

Not Even Wrong

Browsing through the pages of "Conceptual Foundations of Quantum Field Theory" edited by Tian Yu Cao, I see the following (in John Stachel's essay):

Others were less cautious in their approach to quantum gravity. In their first paper on quantum electrodynamics, Heisenberg and Pauli asserted that:

quantization of the gravitational field, which appears to be necessary for physical reasons [in a footnote, they refer to works of Einstein and Klein cited above], may be carried out without any new difficulties by means of a formalism fully analogous to that applied here.

Almost seventy years [1999] have elapsed since this casual prediction, and we are still without a quantum theory of gravity!

Well, strictly, Pauli was wrong, rather than not even wrong.

More Princeton

Princeton University campus has great potential for photographic exploration. My primary expedition was to the Borders bookstore near Princeton for some Photoshop and cookbooks that were in stock there. I then stopped at the bridge, and then feeling hungry, stopped for a meal. So I squandered much of the light. So, apart from Hogwarts, on which I got lucky, the following are random uncorrected snapshots, put here as a reminder of a promise. There is a nice interactive map here which also provides a photographic glimpse of the buildings.

Nassau Street, in front of the restaurant where I ate.


Firestone Library:




University Chapel:


One of the chapel doors:


Crop from the above:



Whig Hall:


Books - detail of the Witherspoon statue. What amused me is that Principia is used rather than Newton.

Bridge

Washington Road Bridge over Lake Carnegie at Princeton.

Another try: uncropped and less sharpened.


The whole bridge - had I arrived earlier, maybe the whole bridge would be glowing in the sunlight. Heavily cropped and heavily sharpened.

Hogwarts

Actually Princeton. But that is what the atmosphere was on the end-of-summer evening.

Bill Moyers to the President: We need a fighter

via dailykos:

BILL MOYERS: The editors of THE ECONOMIST magazine say America's health care debate has become a touch delirious, with people accusing each other of being evil-mongers, dealers in death, and un-American.

Well, that's charitable.

I would say it's more deranged than delirious, and definitely not un-American.

Those crackpots on the right praying for Obama to die and be sent to hell — they're the warp and woof of home-grown nuttiness. So is the creature from the Second Amendment who showed up at the President's rally armed to the teeth. He's certainly one of us. Red, white, and blue kooks are as American as apple pie and conspiracy theories.

Bill Maher asked me on his show last week if America is still a great nation. I should've said it's the greatest show on earth. Forget what you learned in civics about the Founding Fathers — we're the children of Barnum and Bailey, our founding con-men. Their freak show was the forerunner of today's talk radio.

Speaking of which: we've posted on our website an essay by the media scholar Henry Giroux. He describes the growing domination of hate radio as one of the crucial elements in a "culture of cruelty" increasingly marked by overt racism, hostility and disdain for others, coupled with a simmering threat of mob violence toward any political figure who believes health care reform is the most vital of safety nets, especially now that the central issue of life and politics is no longer about working to get ahead, but struggling simply to survive.

So here we are, wallowing in our dysfunction. Governed — if you listen to the rabble rousers — by a black nationalist from Kenya smuggled into the United States to kill Sarah Palin's baby. And yes, I could almost buy their belief that Saddam Hussein had weapons of mass destruction, only I think he shipped them to Washington, where they've been recycled as lobbyists and trained in the alchemy of money laundering, which turns an old-fashioned bribe into a First Amendment right.

Only in a fantasy capital like Washington could Sunday morning talk shows become the high church of conventional wisdom, with partisan shills treated as holy men whose gospel of prosperity always seems to boil down to lower taxes for the rich.

Poor Obama. He came to town preaching the religion of nice. But every time he bows politely, the harder the Republicans kick him.

No one's ever conquered Washington politics by constantly saying "pretty please" to the guys trying to cut your throat.

Let's get on with it, Mr. President. We're up the proverbial creek with spaghetti as our paddle. This health care thing could have been the crossing of the Delaware, the turning point in the next American Revolution — the moment we put the mercenaries to rout, as General Washington did the Hessians at Trenton. We could have stamped our victory "Made in the USA." We could have said to the world, "Look what we did!" And we could have turned to each other and said, "thank you."

As it is, we're about to get health care reform that measures human beings only in corporate terms of a cost-benefit analysis. I mean this is topsy-turvy — we should be treating health as a condition, not a commodity.

As we speak, Pfizer, the world's largest drug maker, has been fined a record $2.3 billion dollars as a civil and criminal — yes, that's criminal, as in fraud — penalty for promoting prescription drugs with the subtlety of the Russian mafia. It's the fourth time in a decade Pfizer's been called on the carpet — and these are the people into whose tender mercies Congress and the White House would deliver us?

Come on, Mr. President. Show us America is more than a circus or a market. Remind us of our greatness as a democracy. When you speak to Congress next week, just come out and say it. We thought we heard you say during the campaign last year that you want a government run insurance plan alongside private insurance — mostly premium-based, with subsidies for low-and-moderate income people. Open to all individuals and employees who want to join and with everyone free to choose the doctors we want. We thought you said Uncle Sam would sign on as our tough, cost-minded negotiator standing up to the cartel of drug and insurance companies and Wall Street investors whose only interest is a company's share price and profits.

Here's a suggestion, Mr. President: ask Josh Marshall to draft your speech. Josh is the founder of the website talkingpointsmemo.com . He's a journalist and historian, not a politician. He doesn't split things down the middle and call it a victory for the masses. He's offered the simplest and most accurate description yet of a public insurance plan; one that essentially asks people: would you like the option — the voluntary option — of buying into Medicare before you're 65? Check it out, Mr. President.

This health care thing is make or break for your leadership, but for us, it's life and death. No more Mr. Nice Guy, Mr. President. We need a fighter.

Not just the economists

As I see it, the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth. - Paul Krugman

The physicists, too.

Only in America

In the "First World", the following kind of thing happens only in America. When I first read it in Nicholas Kristof's NYT column, I thought maybe it is a one-of-a-kind.

This is a nation that some constituents trumpet is based on "Christian values". About marriage:

The Bible, Matthew 19:6 (King James Version):

Wherefore they are no more twain, but one flesh. What therefore God hath joined together, let not man put asunder.

IMO, it is pretty much those who speak loudest about this who are most against fixing the rotten system. Rotten? Read on.

Kristof

The hospital arranged a conference call with a social worker, who outlined how the dementia and its financial toll on the family would progress, and then added, out of the blue: “Maybe you should divorce.”

“I was blown away,” M. told me. But, she said, the hospital staff members explained that they had seen it all before, many times. If M.’s husband required long-term care, the costs would be catastrophic even for a middle-class family with savings.

Eventually, after the expenses whittled away their combined assets, her husband could go on Medicaid — but by then their children’s nest egg would be gone, along with her 401(k) plan. She would face a bleak retirement with neither her husband nor her savings.

A complicating factor was that this was a second marriage. M.’s first husband had died, leaving an inheritance that he had intended for their children. She and her second husband had a prenuptial agreement, but that would not protect her assets from his medical expenses.

The hospital told M. not to waste time in dissolving the marriage. For five years after any divorce, her assets could be seized — precisely because the government knows that people sometimes divorce husbands or wives to escape their medical bills.

“How could I divorce him? I loved him,” she told me.

“I explored a lot of options with an attorney here in town,” she added. “The attorney said, ‘I don’t see any other options for you.’ It took about a year for me to do the divorce, it was so hard.”

sylvarose on dailykos

"Rep. Hill you said this fight for health care has been going on a long time. Twenty some years ago my family did everything right. My father had a job. My mother was self employed. We had insurance. My parents had bought their own home. Then my mother's MS had become too bad where she needed 24 hour care. My father went to three different lawyers who all told them the same thing, 'Sir you have a choice. Divorce your wife, abandon her, or lose everything you have now and everything you will have and your ability to help your kids.' My brother was already starting college and I was in high school. My parents' divorce was finalized on my 17th birthday. My family was shattered so that my Mom could get on medicaid which provided her care for the next 17 years of her life.

Contrast that to my sister-in-law who is from Spain. When her family member with three young kids was diagnosed terminal they died in peace knowing their family was together. They didn't lose their home and the family wasn't burdened with health care bills. How in this country can we let this happen where a man has to divorce his wife of 15 years..the mother of his two children just so she can get the care she needs? Go ahead and boo me if you want..that's Ok. I've already lived through the pain."

Where I was booed at the beginning by those against health care..those for it stood up and clapped. I sat down and my hands were shaking.