Anmol on Income and happiness

Anmol on Income and happiness


If you go to school with me, you already know what this article is about, due to our heated discussion in Eco class about it. However, if you weren’t present, this is solely about the correlation between Income and happiness, and the optimal income distribution for net happiness. Also, this article discusses the best income distribution in a society, and what government should do to achieve that distribution. Note that this assumes ceterus paribus: all other things being equal, it also assumes that income and wealth are synonyms, and interchangeable, feel free to make the formula more complex later on.

To understand the link between income and happiness, we must first accept three things. Firstly, that income isn’t the only factor, but a major factor affecting happiness. Secondly, that income has a positive correlation with happiness. Thirdly, that the relationship between income and happiness is less than linear, my assets total less than $10,000, while Warren Buffet has some $50,000,000,000, but he isn’t 5 million times happier than I am. I personally believe that there is no maximum happiness, although many people might dispute this claim.

I think the relationship between income and happiness is logarithmic, i.e. H=k*log I.
It seems to me that someone with 100 times my wealth will be as much happier than I am, as someone 100 times wealthier than him, will be happier than he is. This system seems plausible to me, though we will deal with more complex equations later. With the current formula, let’s assume that there are 2 people in the world (this can be extrapolated to much larger numbers). Their incomes are P and O, and P+O=I. Net happiness= log P+log O, Net happiness= log PO, therefore the point of maximization of PO, is the point of maximization of happiness. This is when P=O, i.e. when income are equal. Equality of income is the point at which happiness is maximized, in this situation.

Assuming you have a function for income vs happiness, to determine that the optimal distribution is when incomes are equal, we must make sure that when incomes are equal, i.e. if one person 1$, and the other person loses 1$, net happiness goes down. Change in happiness for each person ~ gradient of the curve (dy/dx). If gradient above is less than gradient below, in the happiness versus income curve, then it’s best to split wealth evenly. Therefore, the gradient should decrease as the value of x (in this case income), increases, or d^2y/dx^2 should be negative. For all less than linear equations, d^2y/dx^2 is negative, because dy/dx of x^-n, where n is a positive constant, will always be negative, and dy/dx of x^a, where a is between 0 and 1, will always result in a polynomial of the form kx^-n. Therefore, when a is between 0 and 1, when the equation is less than linear, it’s best to concentrate wealth towards the centre. When d^2y/dx^2 is 0, the distribution of wealth is irrelevant to net happiness, and when it is positive, it’s best to split the wealth unevenly.

It would be extremely unusual if net happiness could be perfectly graphed by a function. Surely, doubling one’s wealth while poor is worth significantly more than doubling it while rich. Assuming statements such as the one are true, the gradient of the curve still continues to decrease, so d^2y/dx^2 remains less than 0, and it remains better to split the wealth evenly. The gradient can only reduce, as the curve continues. Therefore, we can conclude that net happiness is maximized when income is equally distributed.


I’m sure the above statement makes me seem like a socialist. In fact, I strongly believe in communism capitalism. I wanted to make it clear that the objective of a tax is not to blindly maximize net happiness. All of us know that socialism doesn’t work, because it disinsentivizes innovation, the engine for economic growth. However, lack of economic growth is only felt in the long run, while the positive attributes of redistribution are felt immediately, which is one of the reasons why socialist revolutions started off so well, and ended, well, not so well.

The first implication of this article is that progressive taxes are fair, although the extent to which they’re in place should be debated. I believe that in the long run, an increase in net wealth, leads to a total increase in societal wealth, for all classes, regardless of how the wealth is distributed initially. Many of the richest families 2,000 years ago, are normal families now, and many of the richest families now were normal 2,000 years ago, but we’ve all benefited from long run economic growth, despite the clear economic biases towards the rich in that era (flat taxes, feudalism, selective voting rights, etc.). However, you could argue that government shouldn’t care about the long long run, which makes sense if you believe that government is there to get re-elected, or serve it’s own purpose in some other way, in which case, changes which take more than 10 years are generally ignored regardless of their benefits. The first question which needs to be answered is “how much should a government base their decisions on long term good, and how far in the long term should they look?”

The next question which needs to be answered is “how progressive should progressive taxes be?”, any measure which can be used to derive, or calculate a perfect tax plan will be helpful.

The first implication of this concept was macroeconomic. The second, has to do with microeconomics. This is a good way to measure whether or not to take certain bets. The first thing this shows is that betting on a lottery, even with no rake, is completely irrational, because losing that 1 dollar, or other small amount of money, isn’t worth a one in a million chance at a million dollars, because the satisfaction of a million dollars isn’t a million times the satisfaction of 1 dollar. The second is that when bets are a very small percentage of your net worth, what probability dictates is generally your correct decision, however, when it’s a large percentage of your wealth, it differs largely from probability. For example, if you bet half your wealth, you need at least 1.71:1. The answer is probably more than that, so the curve is probably less than a logarithmic curve. In a survey, people were asked the minimum odds they needed on a coinflip to risk $100, they said 2.1:1. This would’ve been correct if they were betting half their wealth, but the correct answer (assuming $100,000 of total wealth), was 1.001:1. Another case of people misunderstanding statistics. If we manage to link happiness to income effectively, we can understand whether or not to take bets which are a certain percentage of our wealth, or other financial risks, such as betting on the stock market. Such a formula would be very valuable for academic purposes, although it would probably be ignored in real life.

Anmol On Fiscal Policy

Anmol on Fiscal policy

Right now, the Euro Zone debt crisis, along side the American debt crisis seems extremely serious, because both economies constantly seem on the verge of default, and any such default would lead to a world wide economic collapse. That’s why the leaders of the world will do almost anything to prevent a default. Today’s article will deal mainly with how to deal with large debt burdens, calculation of debt burdens, and interest rates of bonds. Some of the answers I find will definitely surprise you and make you think.

As a response to the Italian debt crisis, Sylvio Berlusconi forced parliament to push through austerity measures, a natural reaction, also mirrored by Republicans to the American debt crisis, but how much do these measures actually help? How much of a surplus should a government actually run when they have large debt burdens? Well, lets look at the case of country X, a hypothetical country to determine the best strategy of a government

First, we must discuss the concept of the multiplier. Let’s say I gain $1, and my marginal propensity to consume (∆consumption/∆income) is 0.8, which means I’ll spend 80¢ of that dollar. The next person has 80¢ and will spend 80¢*0.8, or 64¢ of it, and so on. As you can see, this is a geometric progression, and the formula for the total amount of money in the economy is injection (of money)/1-mpc. So any injection in the economy is multiplied by 1-mpc, which is why 1-mpc is known as the multiplier.

How do you calculate the debt burden of a country? Is it the internal debt? Is it the foreign debt? Well, it’s the internal debt multiplier*internal debt+the multiplier*foreign debt.What is the internal debt multiplier? It’s the amount the economy will lose by paying off internal debt. Lets assume that government can either spend a certain amount of money, T, or return T to bond holders. If they spend T, then growth in the economy will be T*multiplier, or T/(1-mpc), whereas if they pay T to bond holders, the injection to the economy will be T(mpc)/(1-mpc), because the amount they consume will return to the economy. Therefore the debt is (T-T*mpc)/(1-mpc), or T(1-mpc)/(1-mpc) or T. The foreign debt multiplier will be 1-mpc, because the money you use to repay foreign debt automatically leaves your economy. So total debt burden= internal debt*1+foreign debt*multiplier, or internal debt+foreign debt*multiplier.

Now, we need to calculate bond yields. Assuming there is a very small chance of default, bond yields will be close to inflation. Inflation is a function of change in consumption. ∆consumption= ∆national income*mpc. To find Inflation from ∆consumption, we use the formula, ∆consumption (as % of GDP)*G(supply)/[G (supply) + G (demand)]
G being the gradient of the curve. Assuming bond yields are near inflation, as happens often in real life, bond yields are approximately ∆consumption*Gs/Gs+Gd.

Every year, your debt burden is multiplied by your bond yields, which is then added to your net budget deficit, to calculate the debt for the next year. To follow the rest of this article, you should look at a country’s debt burden as a percentage of its GDP, and not in absolute terms, as it will make more sense that way. Lets look at an example to make it easier.

Italy’s national debt is 120% of GDP, and because more reliable data isn’t available, we’ll assume that 45% of its debt is foreign, and 75% is internal. We’ll also assume that mpc=0.7, because reliable data on that too is unavailable. The total debt burden= 75%+45%/(1-0.7), or 75%+150%, or 225% of GDP. Let’s assume that despite all the calls for austerity, the Italian government decides to resist foreign pressure, and run a deficit which adds a burden= 10% of GDP. Therefore, the economy will grow by 10% of GDP to 110% of initial GDP. Assuming Gs=Gd, then Gs/Gs+Gd=1/2, and inflation will be 0.7*10*0.5=3.5%, and bond yields will be 3.5%. Just to make this example clearer, we can assume bond yields will be 4%. The new debt will be 225*1.04+10, or 244% of GDP.

The new national debt will be 244*100/110, or 222% of GDP, lower than what it was before the deficit, which is counter intuitive to what all the pro austerity economists say. What they say makes sense, if you’re in debt, spend less, pay other people back, but the math disagrees with them. Paying off a certain amount of debt will contract your economy more than it contracts your debt, therefore increasing your burden.

Of course, this only works with very large debt burdens, and beyond a point, it stops to work. This point is given by 100*(Gd+Gs)/Gs, for the economy. Note that economic growth isn’t mentioned here, because interest rates will normally be similar to economic growth, so the two tend to cancel each other out. Even unexpected growth is irrelevant, because growth is a fraction of total GDP, so the lowest debt:GDP ratio, is still the most beneficial path. Of course, after your debts reach a certain point, the point which I call “the point of madness”, it should start running surpluses to pay off the debt, that’s the point at which the debt to GDP ratio is constant regardless of deficits, or surpluses, and the deadlock can only be broken by unexpected technology growth. Of course, how economies get beyond this point is beyond me, but some of them find a way to do it. My advice to them: spend, spend, spend.

Anmol On Bailouts

Anmol On Bailouts

The Great recession which hit the US in 2007, and later spread to the rest of the world had a severe impact on the modern world. The business cycle is cruel to all those it affects, at least, when there’s a downturn. The reason for this, as usual, amongst many was due to weird financial instruments on wall street, horrible foresight, and the easy accessibility to credit. What intrigued me the most about this crisis, or at least the reaction to it, was the bailout of the banking sector. Americans realized, after the collapse of Lehman, that a collapse of one bank threatened the entire sector, and hence all large banks were now “too big to fail”. If you look at the risks that these large banks were taking, and look at the consequences of their downfall, you soon realize that the probability of a financial meltdown is much more than we think it is.

The banking crisis started in March 2008, when the New York federal reserve bailed out Bear Sterns so that it could be sold to JP Morgan Chase, to the outrage of many tax-payers. This outrage made the government reluctant to bailout the investment bank Lehman brothers when it was close to bankruptcy, and it’s collapse led to the instability of Wall Street. This of course led to TARP, the $700 Bn bailout fund for banks which was expected to cost US taxpayers $300 Bn, but ended up costing them only 19 Bn, because most of the banks who took TARP funds have already paid them back/ are on track to pay them back. $19 Bn is a very small price to pay to save the banking sector of a country as large as the US, but people still continued to oppose the bailout. This article is not going to be a summary of the great-recession, but a theoretical discussion about whether or not bailouts should be given to these institutions, and whether or not there is a way to improve the current system of bailouts.

Let’s take a brief look at the problem. In the recent Republican debate, it was brought up a few times that the biggest 6 banks in the US, accounted for 2/3rds the nations GDP. If these banks were to somehow fail simultaneously, then the US would face a crisis 3 times worse than the great depression, and the knock-on effects (small banks failing due to failure of the big banks), could make it even more significant. Now, there is no guarantee that this will happen, but if it were to happen, I can’t emphasize enough how large the crisis would be. Imagine 2012. It would be worse.

The main counter argument against bailouts, as I have learnt is that bailouts are moral hazard. If companies know that they’re going to get a bailout whenever they fail, then they need not fear failure, and can take a series of unnecessary risks. If the risks succeed, they all become billionaire’s, if they fail, then they get bailed out by the federal government. Very convenient indeed. However, we really don’t want all our large financial institutions taking unnecessary risks with our life savings, while their executives get 10’s of millions of dollars in bonuses. At the end of the day, wall street rewards risk takers. The way wall street works is that employees get a small basic salary, just enough to cover costs of living, and large bonuses based on performance. Let’s say that an employee loses a large amount of money, say $100 Mn. They still can’t take away his basic salary, so he gets paid his basic salary. Now, let’s say the employee gains $100 Mn, he’ll get a large bonus, probably in the millions of dollars. Now, if he does nothing, he’ll get a bonus, but a small one, perhaps $50,000-$100,000 at most. Looking at this from an individual point of view, why wouldn’t he take the millions or bust, and forgo the $50,000? Even if there’s only a 10% chance of him making the millions, it’s a good risk for him , but a 10% chance of gaining $100 mn, and a 90% chance of losing $100 Mn is definitely bad for your life savings. I understand that the reason why bonuses are so large relative to basic salary is to reward performance, but the problem is that there are no disincentives for making large mistakes. Even if the employee gets fired, he can easily find a job which pays close to his basic salary on Wall Street, which is what he would get despite an incorrect decision. There is effectively no downside to being wrong.

There are other hazards with the bailout package, such as the fact that the TARP loans were given out at very low interest rates, close to 0%, which was significantly lower than the free-market interest rate. As Ron Paul said “They’re borrowing money from us at 0%, and lending it back to us at 3%!” Yes, Ron Paul included the exclamation mark. This is a fairly simplistic understanding of the crisis, even though he does have a point.Companies would never take large loans, just to exploit the low interest rates, because of the various federal government restrictions placed on them if they accept TARP funds, such as a cap on executive pay at $500,000/year. To put that into perspective, a few years ago George Soros’ hedge fund paid him $2,400,000,000. No executive would willingly take a pay cut of possibly 100s of millions of dollars, just to get low yields on bonds from the federal government. However, as I said earlier, his point is still valid, if the banks were indeed as successful as they were touted to be, the government could’ve charged the market interest rate, or at least what the bank pays to its depositors.

There are other moral problems associated with Wall Street. Despite coming cap in hand to the government, begging for bailouts whenever there’s a recession, these firms strongly advocate, and lobby for de-regulation, i.e. removal of government from their markets in the boom years. As the famous saying goes, “People are capitalist during the booms, and socialist during the busts”. I can see why they act in this way, it seems to help them immensely, but this makes average citizens see corporations as evil-corporations, understandably. These firms almost seem two-faced in their agenda. So, basically the three moral problems are moral hazard, low interest rates, and the two-faced nature of large corporations. The problem with letting them fail, is financial apocalypse. Isn’t there a middle ground? The next part of this article will be about possible solutions.

Firstly, let’s assume that we let all the banks fail, just to teach the risk-taking Wall Street fat cats a lesson, and we somehow miraculously recover from the economic downturn. They have been shown by government that their risk taking will not be rewarded, and according to rational logic, the banks should then become more stable. Unfortunately, this isn’t the case. History has shown that people in positions of power, have poor knowledge of history, and occasionally come up with ridiculous assumptions. One of these situations was the options debacle, when a couple of Mathematicians came up with a perfect formula on the pricing of options, and estimated their risk of going bust at 1 in 10^24. Of course, they went bust, as was inevitable. They didn’t account for large stock market crashes, such as the one in 1987 while making their model, and one such crash made their company fail.It’s fairly ironic that both of them are Nobel laureates, but such is the field of Economics. We can only assume, that banks will act in the same way, even if we punish them once. Also, it’ll take a very long time for a country to recover from a loss of its banking system, and possibly 80%+ of its GDP.

There’s a popular theory going around nowadays which says “too big to fail, is too big”. I can’t say that I disagree with that view, but there’s a reason why big institutions exist, and why they’re efficient. Let’s say there’s a small institution, worth $1 Mn. They bet $1 Mn on a 60-40 chance, and 40% of the time they go broke, thus ruining all their investors. Now, let’s look at a large institution worth $50 Bn. Let’s say they make 500 bets of $100 Mn on a 55-45 chance. It’s highly likely that they end up ahead, because their risk is spread out, thus reducing it significantly. Although big institutions do take risks, their risks aren’t limited to one field, so one crash won’t necessarily bring them down. That’s why it is a big deal when a big institution fails, because it signals that the entire market crashed, and not just one segment. Unfortunately, the entire market crashing is not independent of one segment crashing, so there still is a lot more risk than we would like.

I feel that the people responsible for taking risks are executives, and the losers are the customers. If there’s a solution which punished executives, while protecting consumers, I feel that’s optimal. I think the banks should be bailed out, and that executives should be penalized in some way. The way to penalize them can be worked out later, but it satisfies the need for punishment of those responsible, while protecting the average citizen. Perhaps, government can limit leverage on banks which asked for TARP funds, for a fixed period of time, say, 10 years, thus making them less volatile, and less prone to swings.

There were three main reasons why the recession became as serious as it did:

1) The interconnectedness of the entire financial system. People used to give away subprime mortgages, then sell them to the a bank, which would then sell them to a larger bank. The larger bank would bundle up the mortgages, and make AIG insure them, as “securities”, which AIG would then sell to another bank, which would eventually be sold to somewhere completely random, such as a Norwegian town council. It’s almost like Chinese whispers with large amounts of money. Therefore, when the housing bubble eventually burst, all these people suffered, thus bringing down a much larger segment of the economy than it should have. Homeowners also suffered because the values of their houses dropped.

2) Banks were over leveraged, i.e. they had were risking too much money, relative to the number of assets they had. Lehman brothers was leveraged at 30:1, which meant that a 3% drop in their shares, meant that they lost 90% of their assets. Due to the volatility of markets, this eventually happened, and busted Lehman.

3) The collapse of Lehman sent ripples across the entire banking system, and made the Dow Jones Industrial Average, and various other indices crash, as people began to fear a wide banking sector collapse. This then made the banking system weaker, which people then reacted to. Sort of like a self-fulfilling prophecy. This cycle would’ve continued unless government interfered which it did.

In conclusion, I must say that government should never distort prices, as they did by reducing interest rates for sub prime mortgages (interest rates too are a price), to help every American have a home. We also need to be better at predicting these crises, as it was widely assumed that house prices would continue to rise infinitely, as gold is seen today. It would also be helpful if we found a way to control moral hazard, although risk is embedded in the psyche of all Wall Street executives. I still support the bailouts, and feel that if we come up with any method of punishment, it will increase fairness in the market.