How would a world without oil look like?

Many people think mistakenly that modern prosperity was founded on this fossil energy revolution, and that when the oil and coal is gone, it is back to the Stone Age. If we had no fossil energy, then we would be forced to rely on an essentially unlimited amount of solar power, available at five times current energy costs.

Our living standard would decline by about 11 percent.

At current rates of economic growth we would gain back the income losses from having to convert to solar power in less than six years.

This is Gregory Clark, via Economist's View.

An argument against free trade

A few posts ago, starting from the fact that non-OECD countries are for the first time in history producing more CO2 than their wealthier cousins, I wondered about the implications of global warming for free trade:

I expect another reason to be important (for the rise in CO2 emissions from non-OECD countries) and that's the migration of 'dirty industries' to the countries with the least stringent environmental standards and the lowest taxes on fossil fuels.

Can global warming in a world with widely varying taxes on CO2 emissions provide an argument against free trade? Trade is beneficial when a country has a comparative advantage in producing a certain good, but what if that advantage is borne out of differences in energy taxes? Is trade in private goods as beneficial as mainstream models suggest in the presence of global externalities?

Wikipedia has a good article, accessible to everyone, on comparative advantage. The cornerstone of trade theory and one of the most fundamental insights economics has to offer, the theory of comparative advantage powerfully demonstrates that everyone can gain from trade in the presence of different relative costs of production.

Picture a world with only two counties (let's call them USA and China) where only two goods are produced and consumed: call them 'services' and 'manufactures'. Asssume that there are no barriers to trade, so that eventually we reach an equilibrium where all gains from trade are exhausted.

Enter global warming. We now know that production of 'manufactures' also involves social costs and the free market is not efficient. The US takes immediate steps to rectify the situation and imposes a pigouvian tax on the production of manufactures. If the Chinese follow suit, the problem is solved. But what if they don't?

In the presence of taxes on US production, the relative cost of producing 'manufactures' in China goes down and production shifts away from the US to reflect the change in comparative advantage.

Under this scenario, some of the gains from trade are transferred from the US to China, as China can only emerge better off from this change in US costs of production. And the planet suffers too: with production of manufactures shifting from the US to China, the effect that a tax on the US production of manufactures has on global CO2 emissions can be as low as non-existent.

In this situation, and if the US is serious about achieving a more socially efficient outcome, it has only one option: to impose an indirect pigouvian tax on Chinese production of manufactures by introducing import duties.

In other words, to the extent that CO2 emissions are taxed at a socially inefficient level in some jurisdictions, free trade means that those that tax CO2 the least will enjoy a larger share of the gains from trade than would have been the case under a global pigouvian taxation regime. Furthermore, under a plausible set of assumptions, local taxes can be next to completely ineffective in reducing CO2 emissions, and import tarrifs and duties can lead to welfare increases in a county worried about global warming.

How long until global warming starts featuring prominently in trade negotiations?

Does private generosity harm the greater cause?

Or: Are private contributions offset by a greater decrease in public spending?

A reader asks me to place the claim I made in the concluding paragraph of my previous post in a formal setting in order to make clear what I meant (apologies to the readers who submitted requests for posts earlier - coming soon guys, promise). The paragraph in question is this:

'If the median voter knows that the higher the size of the deficit the more some citizens will voluntarily chip in, how do you think his decision on the size of the deficit will be affected? Yes, you conscientious citizens, you just made running a larger deficit the most appealing proposition.' This statement of course, depending on the extent my assumptions hold, can equally well apply to charitable giving, corporate social responsibility and the amount of household chores each of a group of housemates carry out.

While I am temporarily diverging from the customary style of this blog here, I have tried my best to keep this accessible to anyone with a year or two of economics education under their belts.

The simple (even simplistic) model below builds on standard models of public good provision. I examine what the equilibrium level of provision of the public good (call it 'clean air' if you like) is when it is provided both by government and the (perfectly competitive) private sector. Standard expositions of public good models focus on the equilibrium amount of the public good that would be provided by either voting or in a free market economy with no government under general conditions, while the aim here is to attempt to evaluate the implications of concurrent public provision and voluntary private purchases of the public good in a more restrictive setting.

I assume a closed economy with no growth. There is a finite number, n=3, of consumers/citizens. I label the three consumers as ‘left-wing’ (l), ‘median’ (m) and ‘right-wing’ (r). There are only two goods produced in this economy, a private good Yprv and a public good Ypub and there is no saving. For simplicity, I assume that there are no fixed costs of production and that the marginal cost of producing one unit of Yprv is the same as producing one unit of Ypub, with both being equal to one. This is not restrictive since the ‘units’ used are arbitrary. Also, there is perfect competition so that the price of goods equals their marginal cost.

Each individual has an endowment, Wi, and I further assume that there is perfect equality. One unit of this endowment can be used to produce either one unit of the public good or one unit of the private good.

Consumers are assigned simple Cobb-Douglas utility functions:

, i = l,m,r (1)


and I further assume that αi+bi = 1, αi, bi>0.

I define the median consumer/citizen simply to be the one that has the median α in the population of αi’s. Also, for ease of expression, I refer to the consumer/citizen that has a higher value of α, i.e a ceteris paribus higher preference for the public good, as being to ‘the left’ or being ‘left-wing’ and the consumer/citizen with the lower value of α as being to ‘the right’ or being ‘right-wing’.

The government provides Ypub with revenues obtained through taxation, and it selects the tax level in order to maximize the utility of the median voter.

Now, let’s suppose that the private sector is restricted to producing the private good only. The public good is provided solely by the government via taxation, which is required to be levied equally on every citizen. The level of tax (and thus the public good) is chosen to maximize the median voter’s utility.

All consumers (except the median voter) do not in any way choose their consumption bundle in this setup. The median voter (via the government) chooses the tax rate to maximize his own consumption and all other consumers simply contribute the amount of tax prescribed and spend the rest of their endowment on the private good.

Since this post is already unduly long, I will leave the equations determining the amount of the public good/taxation and each voter's utility as an exercise to the reader - for anyone interested, please email me and I will be happy to provide the answers.

To help get an intuitive feel for the results, the table below shows the values our variables take when we set w=100, αr=0.3, αm=0.5 and αl=0.7. The variable g refers to the amount of the public good purchased by the various individuals directly in the market (rather than provided by government via taxation), which in this case is zero for every consumer.

I will now turn to an alternative scenario, in which the private and the public good are both provided in a perfectly competitive environment, with consumers able to purchase goods at marginal cost. I model this as a sequential game of perfect information, in which the median voter selects the tax rate (which has to be equal for all citizens) and then all consumers decide the amount of the public good to purchase privately, on top of that provided via taxation.

Setting the values of the variables at the same level as in the previous example we have:








The tax rate, and the level of the public good, are now lower. The median voter and the ‘right-wing’ consumer are now better off, while the ‘left-wing’ consumer is worse off. In fact, even though we now have private contributions (by the ‘left-wing’ consumer) to the public good, the equilibrium amount of the public good is now lower than in the case with no voluntary contributions. Given our assumptions and perfect competition, introducing voluntary contributions increases the utility of the majority of the population but leads to a lower equilibrium amount of the public good.

This seemingly counterintuitive result makes perfect sense: knowing that the ‘left-wing’ consumer will find it beneficial to contribute more when the tax rate is lower, the median voter can gain by lowering the tax rate (and thus increasing his consumption of the private good and, incidentally, the ‘right-wing’ consumer’s consumption) and ‘free-riding’ on the ‘left-wing’ consumer’s contribution to the public good.

I have a hunch this may also help explain the pattern of charitable giving observed in the US: Americans have a very high level of private contributions per capita coupled with extremely lousy public funding of 'good causes' (look, for example, at donations for victims of the Tsunami). The relatively excess generosity of the private citizens is lower than the relative stinginess of the state compared to European countries, and America consistently comes out as a laggard when it comes to contributing to 'good causes'.

Tim is not a jerk

Via Mark Thoma, here's Tim Haab on his environment-ravaging weekend plans:

I'm packing up my big honkin' SUV tomorrow with my oversized family of 5 and driving 280 miles (one-way) to Lake Cumberland, Kentucky to visit with friends from Atlanta--who will be driving their oversized family of 5, 330 miles (one-way) in their big honkin' SUV. Based on the paltry gas mileage we will get--about 18 mpg--I'm figuring our family will consume about 31 gallons of gas.

At $3.50 a gallon that's $109. If we could somehow double our fuel efficiency to 36 mpg and still fit the family we would save $54 in fuel cost round trip*. For a 4.5 hour one way trip, we are paying an extra $6 per hour to drive the SUV.

So I ask myself, am I willing to pay $6 per hour to have my 3 kids separated by 2 feet each--two in the middle row, one in the back--rather than be touching each other the whole trip.

Ummm...can I get a big 'Hell Yeah'?

*For those of you wondering who will pay for the externalities I create, that's an easy one...YOU. That's why they're called externalities. Voluntarily internalizing my own externalities would ruin my faith in rationality and cause me to have to completely reinvent economics. I'm just too lazy for that right now. Yes, I'm a jerk.

First of all, a big 'Hell Yeah' for Tim. Secondly, I have to protest at his self-characterisation: he is most definitely not a jerk. You can be the most passionate advocate for the need to do more to protect the environment - Al Gore, please stand up - and still happily go on to consume ridiculous amounts of energy. (Al Gore, please refrain from sitting down)

The two are not at all inconsistent: The former is a public policy preference, while the latter relates to private preferences given public policy.

When I am asking for higher taxes on gasoline, I want them imposed on everyone, not just on me. What's the point of unilaterally deciding to cut my consumption of gas? The planet will not even notice.*

This principle is very well understood in a different, but analytically equivalent, setting: general taxation. If I am asking for higher taxes but the government instead decides to go for a tax cut, will anyone in their right mind ever blame me for not voluntarily paying more than my fair share into the public coffers? Is it hypocritical that I pay the universal 'low' rate of tax while I am the most passionate of advocates for higher rates?

* Ah, I hear you say, but what if a sizable minority of conscientious citizens (for it is a minority, otherwise it would include the all-powerful median voter) all decide to voluntarily reduce their carbon footprint? Well, that's just great: they just reduced the pressure on the not-as-conscientious median voter to do something about it by imposing a universal pigouvian tax (or other mechanism to internalise the externality).

And if that's not clear, think of my general taxation example. If the median voter knows that the higher the size of the deficit the more some citizens will voluntarily chip in, how do you think his decision on the size of the deficit will be affected? Yes, you conscientious citizens, you just made running a larger deficit the most appealing proposition.

Addendum: Again via Thoma, I have to close a linking circle and return a favour by mentioning Robert's Stochastic Thoughts:

Update II: Tim Haab (who is not a jerk) definitely gets Kevin Drum's point as he clearly understands the fundamental difference between a) advocating policy which causes people to internalize externalities and b) listening to kids in the back seat squabble for hours. Also he doesn't own any slaves which puts him a big one up on Thomas Jefferson.

Further commentary here and right here.

An interesting example of rational co-operative behavior which is not in the public interest is link begging, where bloggers attempt to reward other bloggers for links by linking back. Not as repulsive as self linking, but the first sometimes enables a rational egoist to trick Google, while the second is just pathetic.

Kevin Drum's point is this:

To consider with Drum the case of Thomas Jefferson, without anything odd (dynamic inconsistency) the position as a slave owner who advocated abolition of of slavery can be perfectly rational. The slave owner might hate slavery, but not hate the enslavement of his own slaves as much as he loves living in luxury off the sweat of their brows. His ideal outcome would be to have all slaves but his own free. A rational anti slavery slave owner knows he's not going to get away with that. Second best would be abolition of slavery -- the desire to free everyone elses slaves outweighs the desire to keep his own. Third would be continued slavery. Finally the outcome he likes least would be to free his own slaves and live in relative poverty in a slave owning country.

Before leaving this post (again), note that Drum's point is narrower that the the one made here. My argument is not only that Tim's behaviour is rational, but also that it is moral (something that cannot be said for slavery, as polution is a question of a not very well defined 'how much', while accepting slavery is a very clear 'if'). Furthermore, there is a possibility that driving a gas eating monster may actually be beneficial to the environment.

More on this counterintuitive point tomorrow, in response to a reader's request for clarification with regards to the last paragraph of my main post.

International Energy Outlook, and a scary thought

This graph is from the Energy Information Administration's International Energy Outlook for 2007 (full report, press release). World energy consumption is predicted to rise by somewhat more than half today's level by 2030 in the absence of policy and price changes.

The report also highlights 2004 as a landmark from an environmental point of view (see graph above):

From 2003 to 2004, carbon dioxide emissions from the non-OECD countries grew by almost 10 percent, while emissions in the OECD countries grew by less than 2 percent. The result of the large increase in non-OECD emissions was that 2004 marked the first time in history that emissions from the non-OECD exceeded those from the OECD countries. Further, because of the expectation that non-OECD countries will rely on fossil fuels to supply much of their future energy demand growth, carbon dioxide emissions from the non-OECD countries in 2030 are projected to exceed those from the OECD by 57 percent.

Strong economic growth in the developing world, especially China and India, is one of the main drivers of the changing geography of CO2 generation. I expect another reason to be important, however, and that's the migration of 'dirty industries' to the countries with the least stringent environmental standards and the lowest taxes on fossil fuels (here is a previous post on the Summers memo).

Can global warming in a world with widely varying taxes on C02 emissions provide an argument against free trade? Trade is beneficial when a country has a comparative advantage in producing a certain good, but what if that advantage is borne out of differences in energy taxes? Is trade in private goods as beneficial as mainstream models suggest in the presence of global externalities?

I'll try to get my thoughts together in a simple model - stay tuned, more on this coming up soon.