Diminishing returns in a project #
I've been thinking about why people should ever change projects. The longer they're on the project, the more familiar they are with it, and the more effective they are. We might draw this on a graph, with productivity increasing over time:
Labels: economics
Setting the Carbon Tax #
The carbon tax is a tax on CO2 emissions. It aligns incentives of business (profit) and society (stable climate) by giving businesses an opportunity to make more money if they find ways to reduce their CO2 emissions.
One open question with the carbon tax is how to choose the tax rate. Several countries already have a carbon tax, but they seem to set it at a fixed rate, or increase it by a fixed amount each year. Even the Carbon Tax Center says, “There is no magic formula or right number”. I think they're approaching it wrong. Carbon taxes are essentially prices on carbon emissions. Governments shouldn't set prices, and they shouldn't set carbon tax rates either. The market should do it, with a little help from the government.
First, we should decide what level of CO2 emissions are “sustainable”. You can think of this as the “supply” of available emissions. There is no need to go below this level, although doing so will not be harmful. We should be able to continue emitting at the sustainable level for thousands of years. This level is then set as the eventual sustainable target.
Our current emissions are rather high. We can think of this as “demand”. Since demand is higher than supply, we need to raise prices (the carbon tax rate, currently 0% in the U.S.). We need to decide when we want to reach the sustainable level, and then interpolate target levels from the current level to the sustainable target. This might be a straight line for simplicity, but could also be an S-curve or exponential decay.
For example, let's say that the current CO2 emissions are 6 billion metric tons, and we decide that 1 billion metric tons, combined with more forests, is sustainable. Let's further suppose that we want to reach this target in 10 years. That means we need to reduce emissions by 0.5 billion metric tons each year, so we set our target for 2009 to 5.5, 2010 to 5.0, 2011 to 4.5, etc., until 2018, at 1.0 billion metric tons.
Each year (or perhaps every month), we look at the current level of emissions and the target level, and increase or decrease the carbon tax rate. If we're emitting more than the target, we'll increase the tax rate. If we're emitting less (which may happen in a few years, if all the businesses are competing to increase profits by reducing emissions), then we decrease the tax rate. By altering the tax rate in this way, we can stay close to the target.
The problem on the business side is that if the tax rates change every month, there's a lot of uncertainty (just as for any prices that change suddenly every month), and it's hard to change plans that quickly. What will likely develop is an insurance market. Insurers will sell insurance that the tax rate won't go up much, and businesses will buy the insurance to hedge against sudden increases. Does this eliminate the incentives for businesses? No! They're now paying insurance and taxes. The cost of insurance is set by the likelihood at the tax rates will go up. The insurance industry is in the best position to guess this, because they'll be visiting the businesses to determine how quickly emission reductions are going into place. The insurance companies will then be able to predict the future emissions, and set insurance rates based on that. Since they're the ones making payouts when businesses (collectively) don't reduce emissions, the insurance companies will then have an incentive to push businesses to act sooner. They also have the incentive to share techniques across businesses. They make more money when businesses collectively reduce emissions.
Most carbon tax proposals use a fixed price and hope that the output will decline. Most cap-and-trade proposals use a hard limit on emissions, and a variable, potentially volatile price. The variable carbon tax rate proposal combines aspects of both approaches. It uses variable prices, but they're varying less often; it uses a target instead of a hard cap, which allows businesses to buy more time; and it generates revenue for society. With a market based scheme, incentive are aligned. Society will want reduced emissions, businesses will want to reduce tax rates (by reducing emissions), and insurance companies will want to reduce payouts (by convincing businesses to reduce emissions). If businesses fail to reduce emissions, they pay an ever increasing compensation to society for the delay. Furthermore, the open question of what to set the tax to, which is open to lobbying, is replaced by the question of how much to change the tax, which I think is harder to game. This scheme also tells you when we've achieved our goal: emissions are at the sustainable target level. Even at this level, we continue the carbon tax to prevent emissions from going up, and we continue to take in revenue from those businesses that produce emissions. This will keep our emissions near the sustainable level.
Labels: economics, environment, future
Economics of giving to charities #
It's that time of year when lots of people are giving to various charities, and I've been thinking about, if I decided to give, how I would decide. My mental economic model for businesses is that businesses engage in trade. Trade is the exchange of one thing for a more valuable thing. On both sides. From that I've tried to build a model for charities and philanthropy.
Economics of trade
Suppose you (running a business) have a sandwich that you're selling for $2. It's very likely that the sandwich is worth less than $2 to you. If it was worth more than $2, you'd rather keep the sandwich, so you wouldn't be selling it. So let's say it's worth $1 to you. Now suppose I have $2 and decide to buy a sandwich from you. It's very likely that the sandwich is worth more than $2 to me. If it was worth less than $2, I'd rather keep $2 than buy the sandwich. So let's say it's worth $3 to me. Both of us have chosen to trade something less valuable for something more valuable. Before the trade, the sum total of what we had was $1 (your sandwich) + $2 (my money) = $3. After the trade, we have $2 (your money) + $3 (my sandwich) = $5. Trades generate value out of thin air. The world is now $2 richer because of this trade. Free markets make for wealthy countries because people aren't prevented from trading.
Model for Gifts
If you think about trades, they work because both sides have the right incentives. When they both choose to trade, the world is better off. When either chooses not to trade, there's no harm done. Yes, there are some cases where the world is better off if they trade, but they don't both choose to trade, but in those situations a change in price will enable the trade, and both will end up benefiting.
With giving gifts, not only charities but also Christmas gifts, birthday gifts, etc., the person paying and the person receiving the sandwich are not the same. It's much harder to ensure that the trade is actually increasing wealth in the world. Suppose I buy you a sandwich, and I paid $2 for it. I don't know how much it's worth to you. You could say that it's worth $5 to you, but since it's not your money on the line, there's no incentive for you to say the true value. Suppose it's worth nothing to you. So before the trade, the seller has $1 (sandwich), I have $2 (money), and you have $0, a total of $3. After the trade, the seller has $2 (money), I have $0, and you have $0 (sandwich), a total of $2.
Gift giving opens up the possibility that a trade makes the world worse off economically. There are other reasons to give gifts of course, but just keep in mind that economically they're not so good.
Christmas and Birthday gifts are rare; the most common source of economic loss from giving is kids (and to a lesser extent, spouses). Kids might say they really want the $150 pair of shoes, but since they're not the ones working 20 extra hours to buy those shoes, they have no incentive not to make the trade. They make that sad face, or whine, or tell you that all their friends have those shoes, or nag you a great deal. They know how to manipulate parents. Lots and lots of inefficient trades are made by or for kids, causing parents to struggle to make ends meet.
These inefficient trades also can occur with charities. If you're giving to a charity and they “do good” with that money, you don't know whether what they did was worth more than what you gave. You end up judging based on how good it makes you feel, which means charities have an incentive to make you feel good, through special events (seeing lots of people involved in a “special event” makes you much more likely to give money), pictures of needy people (seeing a few people makes that emotional connection that you don't get if you read about helping millions), and other tactics. My view of charities, until recently, has been that there's a high potential for inefficiency and emotional manipulation, just as with kids. I've been trying to form a model that would help me make decisions about whether to give, and to whom, that isn't just to make me feel good, but something that will actually do good.
Externalities
There's something I left out of the model of trades. There's more than just the two parties involved. Maybe the business polluted to make that sandwich. Maybe I littered instead of throwing the sandwich wrapper away. The trade didn't take into account these “externalities” — effects on the rest f the world outside the seller and the buyer.
The standard solution to this is to estimate those effects and charge people for them. Let's take an extreme example, with $5 of pollution for a sandwich. (I think this is extreme for sandwiches but there are probably other industries for which it's reasonable to say the damage to the environment is higher than the value of the product.) Before the trade, there was $1 (your sandwich) + $2 (my money) + $5 (rest of world) = $8, and after the trade there was $2 (your money) + $3 (my sandwich) + $0 (rest of world) = $5. Although the seller and buyer are better off, the trade made the world worse. If we could charge the seller $5 for polluting, the price of the sandwich would be $7 instead of $2. And at $7, I wouldn't buy the sandwich, since it's only worth $3 to me. The trade would be stopped, which is just what we wanted here. To make money, the business needs to figure out how to reduce pollution.
I like the charging-for-pollution solution better than laws against pollution, or trade-and-cap systems (I'll have to make another post about that). With a law, the business's incentive is to fight the law, doing as little as possible, because they still make more money if they pollute. Whereas with charging, the businesses makes more money by not pollution. Since profit motivates business, I want the system to give more profit when the business pollutes less. However it's often impractical to measure the impact of pollution, and that's why we have simplistic black-and-white laws in place.
Model for Philanthropy
We have this artificial line between business and charity. We even call the charities “non-profits”, to distinguish them from businesses (even though some businesses don't make a profit). And there's the sense that charities do good for the world and businesses are bad. I think the world is more complicated than that. There's a whole set of potential projects that have both business and philanthropic aspects. For example, microfinance can generate profits and help lots of people at the same time. Tesla Motors might not ever make money, but it could jump-start the market for cleaner cars. Neither counts as a charity; you're not just handing out money. But there's the potential for it to do more good than a charity. The tax laws in the U.S. encourage giving to charity over investing in a “socially reponsible” business that does good things for the world.
If I'm going to do something with money that I don't need, I want to put it into a place that gives the highest return on investment. But in the case of philanthropy, in that return I need to consider not only what I get back, but also what good it does for the world. Externalities are a way of looking at this. Normally an externality is something negative. But there are also positive externalities. If I invested in a business that makes less profit than other businesses, but generates a lot of good in the world, that's a positive externality. The return on investment for me might be low, but the return to the world could be high. Whether it's classified as an investment or a charity isn't relevant (except there are tax implications that affect the return on investment); I want to find things that have a high rate of return. There's also regular shopping. Just as I might avoid “sweatshop“ products, I might favor products that have positive externalities.
Giving
Unfortunately, I haven't found much that can guide me to high-return philanthropy. Businesses report cost and revenue but not externalities. Charities report costs and donations but not the effects they have. I started following GiveWell a while ago because they seemed to be the only ones that came even close to what I was looking for. I was pleased to see they got mainstream press recently. They tend to pick things that are more tangible, and they seem to consider “saving lives” separately from economic benefit, but in general I like what they're saying and doing. I like that they focus on benefits more than cost efficiency, and they're trying to compare different approaches to see what's most effective. I'm also following Acumen Fund, which tries to help people through investments rather than charity.
Businesses looking for customers use emotions, marketing, sales tactics, and they come to you. When they get investors they use numbers, and you tend to go to them. I want to see the numbers side of philanthropic organizations. I don't want them contacting me to tell me how they're “doing good”. I assume almost all of them are doing good. What I'm really trying to decide, by building an economic model, is where to invest. It may be giving to a charity; it may be investing in a business; it may be buying products. It'll probably be all three. The main problem I see is that there isn't enough information, for businesses or charities, and that there's this artificial line drawn between the two. There should be a unified way of thinking about business and charity that finds the best of both, and allows for new types of organizations that don't fit into the current system. Good information about externalities would change the world.
The Price of Gas #
Prices are typically driven by supply and demand. I was curious about the price of gasoline. When I buy a gallon of gasoline, I pay for it, but others pay for it too. My purchase increases the aggregate demand. Higher demand means higher prices. Higher prices means other people pay more for gas.
How much more do others have to pay?
I can't calculate exactly but with some simplifying assumptions I can make an estimate:
- Limit this calculation to the United States. There are complex issues that influence gas prices around the world, some economic and some political, and it's much simpler to make this estimate with just one country. This would ordinarily not work, except the next assumption makes it possible:
- Gasoline supply in the U.S. is limited by refining capacity in the U.S. With “maintenance”, “shutdowns”, “inspections”, fires, and other capacity issues, I believe it's reasonable to say the supply — at least in the short term — is fixed, and that everything that is produced is consumed.
In other words, if I buy one extra gallon of gas, other Americans need to buy one less gallon. What would it take to make them buy less? Raise the price. By how much?
Let's call the total quantity consumed by everyone else Q. Let's call the current price P. We want to know how much the price has to go up to make Q go down by 1. If everyone else (collectively) buys 1 gallon les, then I can buy that gallon. The key to the relationship between P and Q is the price elasticity of demand:
e = %ΔQ / %ΔP = (ΔQ/Q)/(ΔP/P)
What I really want to know is when I spend $D on gas, how much more do other Americans have to spend? Spending $D means ΔQ = D/P, which can also be written as D = ΔQ×P. What everyone else has to spend is Q×ΔP. So let's compute Q×ΔP. First, let's rearrange e:
e = (ΔQ/Q)/(ΔP/P) = (ΔQ×P) / (Q×ΔP)
So Q×ΔP = (ΔQ×P)/e = D/e.
When I spend an extra $D on gas, others have to spend an extra $D/e on gas. That's the answer I was looking for.
Except … what's the value of e?
There are various estimates: 0.2, 0.01, 0.1, 0.034 to 0.077 in 2001-2006, and 0.26. When I spend an extra $40 on gas, other Americans have to spend between $153 and $4000. I'm not sure which to believe, but I'm going to guess it's around 0.1, which means others have to spend an extra $400 on gas. Where does that money go? To the oil companies.
Let's look at it in reverse: if you found a way to spend $40 less on gas (maybe carpooling, planning errands better, or driving less aggressively), not only would you save that $40, the oil companies would miss out on $400 (maybe as much as $4000), because you'd be helping other Americans spend less on gas.
I'm not even going to try estimating how much more everyone pays when someone drives a big SUV instead of a fuel efficient car…
Labels: economics
Paradox of Choice #
I've been reading The Paradox of Choice, a book about more choices not always being better. There's also a one hour talk by the author. It made me think about how we might model choices, either for understanding our own behavior or for writing simulation games. The author of the book argues that at an abstract level people understand the benefit of additional choices but ignore their costs, whereas in practice people are affected by those costs, albeit not always in a rational way.
To model the benefit of choice, I'm going to say that if there are N-1 choices, and you are presented with 1 additional choice, your benefit has increased. By how much? It's only a benefit if the new choice was better. Since there are now N choices, let's say the probability the new one is better is 1/N. If it is better, by how much is it better? I think you can build an expectation function based on the distribution (for example, a gaussian distribution), but I'm going to be simplistic and say the benefit is constant. The new item is always 1 unit of value better than the old one. In practice I think the benefit decreases as the number of choices goes up, so I'm being generous here. So the added benefit of the Nth choice is the probability it's better multiplied by the amount it's better: 1/N * 1. To determine the total benefit, we have to sum from choice 1 to choice N, and we end up with something approximately equal to the logarithm: ln(N).
To model the cost of choice, I'm going to say that you have to make the comparison between the new item and the old items, even if the new item isn't better. You might compare to each of the old items, giving a cost of N, or maybe you only compare to the best of the previous items, giving a cost of 1. I'm going to be generous here and say the added cost is just 1. The total cost then is 1 for each new item, or a total of N.
So now we have a model in which both the benefits and costs go up as the number of choices increases. Each additional choice brings smaller and smaller benefits but larger and larger costs. Here's a plot of what this might look like:
Initially having choices greatly adds to your well-being. However, the rising costs eventually overtake the diminishing benefits, and the total value of having choices goes down. This seems to be the main message of the book: that additional choices do not always make us better off.
When I defined the model, I decided to be generous. The incremental benefit is 1 in my model, but it's probably decreasing as the number of choices goes up. This means the total benefit is lower than in my model. The incremental cost is 1 in my model, but it's probably increasing as the number of choices goes up, because people at some level will compare to all the alternatives, not just one. This means the total cost is higher than in my model. So the graph above is optimistic; in reality it probably drops even faster.
Note that the graph has no scale. That's because I think the costs and benefits will depend a great deal on the situation. When buying toothpaste, the benefit of more choices is pretty limited. But when choosing a job or spouse, it makes a much larger impact on your life. The main point is that additional choices will eventually not be worth the cost of evaluating them, so at some point you should just make your decision and not worry about it anymore.
Labels: economics