The economics of slave redemption

I was really disappointed when the chapter on the economics of slave redemption was dropped from more recent editions of The Economics of Public Issues (the required textbook for my ECON110 class). Slave redemption has features of unintended consequences, coupled with supply and demand, which made it a really useful application early on in the course.

To understand the problem, it is worth starting with this video, which sets the scene nicely:

Now, the problem is that these well-meaning charities, who want to reduce the number of slaves by buying them and releasing them (referred to as slave redemption), simply increase the demand for slaves. Increased demand for slaves (as shown in the diagram below from D0 to D1) increases the price of slaves (from P0 to P1), and importantly increases the quantity of slaves traded (from Q0 to Q1). So slave redemption increases the quantity of slaves traded - the opposite of what was intended.

To make matters worse, the actions of the slave redeeming charities creates some other perverse incentives. Since slavery is now more profitable than before, and we're talking about a poor country like the Sudan where per capita income in 1990 in the middle of the Second Sudanese Civil War was about US$242 (in 2000 US$), one way that non-slavers could increase their income was to pretend to be slavers. Here's how it worked: A bunch of people would gather together, and one of them would pose as a slaver and the others as slaves. Then when the well-meaning Western slave redeemers show up, the 'slaver' pockets the money, the 'slaves' are freed, and they could meet up afterwards to split the proceeds. Rinse and repeat. So, the slave redeemers might not have even be freeing 'real' slaves at all.

Anyway, MRUniversity has just released a video on Elasticity and the Economics of Slave Redemption, which extends the analysis to consider the impact of elasticity:

As Tyler Cowan notes in the video, the number of extra slaves (including 'fake' slaves) traded will depend on the price elasticity of supply of slaves, as illustrated in the diagram below (which is not drawn to scale). If supply is relatively inelastic (the supply curve is steep, like SSR), then the number of additional slaves for a given increase in demand (from D0 to D1) will be small (quantity increases from Q0 to Q1), and the price of slaves will increase greatly (from $15 to $300). In contrast, if supply is relatively elastic (the supply curve is flat, like SLR), then the number of additional slaves for the same increase in demand (from D0 to D1) will be large (quantity increases from Q0 to Q2), and the price of slaves will not increase by much (from $15 to $50).

According to this article in the Atlantic from 1999, the actions of the slave redeemers increased the price of slaves from around US$15 to US$300 (as shown in the diagram above), so it seems likely that supply was relatively inelastic (SSR) initially. However, prices fell later (to US$100 then to US$50), showing that supply is more elastic in the long run (SLR) than the short run. This is because in the long run slavers have more time to adjust to the increased demand by increasing the intensity of their slaving activity (by enslaving more people). And non-slavers take time to recognise the opportunity and gather a group of friends to take advantage of the incentives to sell 'fake' slaves.

So there you have it - the economics of slave redemption. And amazingly, despite the unintended consequences, slave redemption continues today.

Safer driving and offsetting behaviour - Golden Gate Bridge edition

Having just covered unintended consequences and offsetting behaviour in ECON110, recent changes at the Golden Gate Bridge provide us with a graphic example. As John King at the San Francisco Chronicle reports:

The California Highway Patrol announced Thursday that it is stepping up enforcement of speed limits on the Waldo Grade in Marin as well as at the bridge and toll plaza. The reason is that in the days since the more secure movable median barrier was installed, the average speed of drivers on the approach from the north has jumped even though the speed limit was lowered from 55 to 45 miles per hour.

“We’re really seeing unreasonable speeds on the bridge, much faster than before,” said Priya David Clemens, a representative for the Golden Gate Bridge District. For whatever reason, including the possibility that drivers feel safer knowing a car won’t come barreling at them from the opposite direction, “we’ve noticed speeds going up,” Clemens said. “That’s why we asked the CHP to help us.”

I've written before about safer cars and offsetting behaviour, but I will reprise some of that material here:

Rational (or quasi-rational) drivers weigh up the costs and benefits of driving faster. The benefits include less time wasted on the roads (an opportunity cost - you give up some time you could spend doing something else). Moreover, the marginal benefits probably decrease the more a driver speeds (because opportunity costs increase the more time is wasted). The costs of driving faster include an increased risk of a serious car accident - this cost is made up of two parts: (1) the probability of a serious accident occurring; and (2) the health and other costs of the accident itself. The marginal costs increase as speed increases, because the probability of an accident and its seriousness both increase.

If they are optimising, the driver will choose to drive at the speed where the marginal benefit (MB) of driving faster is exactly equal to the marginal cost (MC0). This occurs at S0 in the diagram below. At this point, driving a little bit faster entails a higher additional cost than the benefit they would receive (which is why they will drive no faster than S0).

When driving is made safer (such as by installing a median barrier on the Golden Gate Bridge), this changes the incentives that drivers face. The cost of driving fast falls (since the chance of being involved in a head-on collision on the bridge is reduced). So, in the diagram above, marginal costs of speed are lower (MC1). This increases the optimal driving speed to S1. What we would observe then is drivers driving faster because of the perceptions of greater safety, with probably an overall increased chance of being involved in accidents (but fewer head-on accidents because of the median barrier). Indeed, according to the SF Chronicle article:

An uptick in minor accidents has been seen at the toll booths, she said, though exact numbers are unavailable.

Economists term changes in behaviour like this "offsetting behaviour", because the actions of the drivers act to offset the benefits of increased safety on the bridge. It's also referred to as a Peltzman effect, after Sam Peltzman who showed in this paper (JSTOR gated) that mandatory safety devices on cars, such as seat belts, do not reduce traffic deaths, and actually increase the number of non-fatal car accidents.

[HT: Marginal Revolution]

Economics majors have the most sex!

Given the title of my blog, I couldn't really let this pass for too long without some comment. Last month, Ninja Economics pointed out this report on Students and Sex 2012 (PDF) from the UK (see Huffington Post too). According to the report's 'Inter-course League' table (no, I'm not making that up), students studying "Economics and related" courses have had on average nearly five sexual partners. Second was "Social work, community care and counselling" and third was "Marketing". "Environmental Science" and "Theology and comparative religion" are at the bottom of the table. Take from that what you will.

We've been talking about opportunity cost in ECON100 and ECON110 this week. The opportunity cost of something is defined as "its cost measured in terms of the best alternative foregone". When thinking about the best alternative foregone when attending lectures, this bit from the report becomes interesting:

Of course, that's all students not just economics students, but maybe it goes some of the way to explaining low lecture attendance at the end of O-week - is the opportunity cost of lecture attendance too high?

Apes are affected by framing too!

Classes start next week, and the first week of ECON110 covers (among other things) rationality and quasi-rationality (how human decision-makers deviate from pure rationality). One of the effects that leads to deviations from pure rationality is framing. That is, the way that different options are framed (or presented to us) can affect how we evaluate equivalent choices.

The classic example of framing is an experiment that was run in the early 1980s by Nobel prize winner Daniel Kahneman and Amos Tversky (who almost certainly would have shared the Nobel prize had he not died six years before Kahneman's success). I won't explain the experiment in detail (you can read an explanation of it here or here), but essentially the experiment demonstrates that people are more willing to choose the 'safe' (low risk) option when the options are framed positively, and more willing to choose the riskier option when the options are framed negatively. I run this experiment in my ECON110 class every year, with similar results every time.

So essentially, the particular phrasing that we use to describe a problem can affect the choices we make. Now, new research has demonstrated that chimpanzees and bonobos are also affected by framing. From Duke Today:

A Duke University study has found that positive and negative framing make a big difference for chimpanzees and bonobos too.

In experiments conducted at Tchimpounga Chimpanzee Sanctuary in the Republic of Congo and Lola ya Bonobo Sanctuary in the Democratic Republic of Congo, researchers presented 23 chimpanzees and 17 bonobos with a choice between two snacks -- a handful of nuts and some fruit.

In one series of trials, the researchers framed the fruit option positively -- by offering one piece of fruit, with a 50 percent chance of a surprise bonus piece.

In another series of trials, the researchers framed the fruit option negatively. This time they offered two pieces of fruit rather than one, but if the apes chose the fruit, half the time they were shortchanged and received only one piece instead.

Chimps and bonobos were more likely to choose the fruit over the nuts when they were offered a smaller amount of fruit but sometimes got more, versus when they were initially offered more but sometimes got less -- despite receiving equal average payoffs in both scenarios.

So, it turns out that humans aren't so special after all, and our susceptibility to framing might be hardwired into us. Interestingly, only male apes were significantly affected by framing - maybe that means that female apes are more rational than males? You can read the research paper by Christopher Krupenye (Duke), Alexandra G. Rosati (Yale), and Brian Hare (Duke) here.

[HT: Marginal Revolution]