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On the importance of sunk costs

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John Barrdear
on 1 December 2008
in Economics and Teaching
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This is mostly for my students in EC102.  There’s a concept in economics called sunk costs.  A sunk cost is one that is spent and unrecoverable:  it’s gone and you can’t get it back.  Since you cannot get them back, you should ignore sunk costs when deciding what to do in the future.  To illustrate the importance of that dictum, consider the following:

You are a software company.  Your business model involves a large, upfront expenditure as you develop and write your program, followed by extremely low variable costs when selling it (the marginal cost of producing another DVD is very low).  Since you’ll be the only company selling this particular piece of software, you will have pricing power as a (near) monopolist. Before you start, you can estimate the demand curve you’ll face and from that estimate what your total revenue will be (remember, MR = MC will give you the (Q,P) pair).  If your expected revenue is larger than your estimate of the total cost of developing and selling the software, you should go ahead.

For simplicity, we’ll assume that the marginal cost of producing a new DVD is zero. That means that your Variable Cost is zero and Total Cost = Fixed Cost.  For any uber-nerds in the audience, we’ll also assume risk-neutrality (so that we only need to look at expected values) and a rate of time preference equal to zero (so that we can compare future money to today’s money without discounting).

Here’s the situation we start with:

Month Fixed Cost (actual) Fixed Cost (future, estimated) Fixed Cost (total, estimated) Total Revenue (estimated)
January 0 100 100 120

In January, since you expect your revenue to exceed your costs, you decide to go ahead.  But in February, after spending 50, you realise that it’s going to take more work than you first thought to write the software.  In fact, you still need to spend another 80 to get it ready for sale.  You’re now facing this situation:

Month Fixed Cost (actual) Fixed Cost (future, estimated) Fixed Cost (total, estimated) Total Revenue (future, estimated)
January 0 100 100 120
February 50 80 130 120

Should you still keep going?

The answer is yes!  The reason is that, in February, the 50 you spent in January is a sunk cost.  You cannot get it back and so should ignore it in your calculations.  In February you compare a future cost of 80 and a future revenue of 120 and decide to go ahead.  The 40 you will make will offset your sunk costs for a total profit of -10.  If you stopped, your total profit would have been -50.

This sort of situation is depressingly common in the IT industry.  You can even get awful situations like this:

Month Fixed Cost (actual) Fixed Cost (future, estimated) Fixed Cost (total, estimated) Total Revenue (future, estimated)
January 0 100 100 120
February 50 80 130 120
… … … … …
October 140 10 150 80

By October, you’ve already spent 140 - more than you ever thought you might make as revenue - and you still aren’t finished.  Thankfully, you think you’ve only got to spend 10 more to finish it, but you’ve also now realised that the demand isn’t so good after all (maybe you’ve had to cut back on the features of your product so not as many people will want it), so your estimated future revenue is only 80.

Even then you’re better off ploughing ahead, since you’re choosing between a loss of 140 and a loss 70.

For extra credit:  Imagine that you’re the bank lending money to this software company.  In January you lent them 100, in February an extra 30.  In October, knowing that the company is going to go bankrupt, would you lend them the last 10 as well?  (Yes, I realise that I’m ignoring the cost to the IT company of interest repayments.)

Could you do first-year economics?

Published
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John Barrdear
on 10 November 2008
in Economics and Teaching
. 0 Comments

Once again, I’m teaching EC102, a mathematics-oriented introduction to economics for first-year undergraduate students at the London School of Economics.  The following is a question from one of the students’ weekly quizzes:

A population consists of two types, “friendlies” (Fs) and “aggressives” (As). Each individual interacts with a randomly chosen member of the population. When two Fs interact, they each earn 3 units. When two As interact, they each earn 0. When an F and an A interact the former gets 1 unit and the latter 5 units. The growth rate of each type is proportional to their average payoff. What will be the equilibrium population share of Fs?

There are some hints over the fold …
Continue reading ‘Could you do first-year economics?’

VW: Supply, Demand and Elasticity

Published
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John Barrdear
on 29 October 2008
in Economics, Finance and Teaching
. 1 Comment

Something very interesting happened to the share price of Volkswagen this week.  The FT has the story:

Volkswagen’s shares more than doubled on Monday after Porsche moved to cement its control of Europe’s biggest carmaker and hedge funds, rushing to cover short positions, were forced to buy stock from a shrinking pool of shares in free float.

VW shares rose 147 per cent after Porsche unexpectedly disclosed that through the use of derivatives it had increased its stake in VW from 35 to 74.1 per cent.
…
[T]he sudden disclosure meant there was a free float of only 5.8 per cent – the state of Lower Saxony owns 20.1 per cent – sparking panic among hedge funds. Many had bet on VW’s share price falling and the rise on Monday led to estimated losses among them of €10bn-€15bn ($12.5bn-$18.8bn).

For my students in EC102, this is interesting because of the shifts in Supply and Demand and the elasticity of those curves.  The buying and selling of shares in companies is a market just like any other.  Here’s an idea of what the Supply and Demand curves for shares in Volkswagen were originally:

Shares in Volkswagen (original)

The quantity is measured as a percentage because you can only ever buy up to 100% of a company.  Notice that the supply curve suddenly rockets upwards at around 45%.  That’s because originally, 55% of the shares of Volkswagen weren’t available for sale.  20% was owned by the state of Lower Saxony and 35% by Porsche, and they weren’t willing to sell at any price [In reality, if you were to offer them enough money, they might have been willing to sell some of their shares, but the point is that it would have had to have been a lot].  We say that for quantities above 45%, the supply of shares was highly, even perfectly, inelastic.

Notice, too, that the demand curve is also extremely inelastic at quite low quantities.  That is because a lot of hedge funds had shorted the VW stock.  Shorting (sometimes called “short selling” or “going short”) is when the investor borrows shares they don’t own in order to sell them at today’s price.  When it comes time to return them, they will buy them on the open market and give them back.  If the price falls over that time, they make money, pocketing the difference between the price they sold at originally and the price they bought at eventually.  A lot of hedge funds were in that in-between time.  They had borrowed and sold the shares, and were then hoping that the price would fall.  The demand at very low quantities was inelastic because they had to buy shares to pay back whoever they’d borrowed them from, no matter which way the price moved or how far.

On Monday, Porsche surprised everybody by announcing that they had (through the use of derivatives like warrants and call options), increased their not-for-sale stake from 35% to a little over 74%.  This meant that instead of 45% of the shares being available for sale on the open market, only 6% were.  It was a shift in the supply curve, like this:

Shares in Volkswagen (new)

Because at such low quantities both supply and demand were very inelastic, the price jumped enormously.  Last week, the price finished on Friday at roughly €211 per share.  By the close of trading on Monday, it had reached €520 per share.  At the close of trading on Tuesday, it was €945 per share.  In fact, during the day on Tuesday it at one point reached €1005 per share, temporarily making it the largest company in the world by market capitalisation!

Who said that first-year economics classes aren’t fun?

Australia, you’re not as rich as you think you are

Published
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John Barrdear
on 18 January 2008
in Australia, Economics and Teaching
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We’re covering this in my EC102 classes this week and I thought it interesting enough to share with a wider audience:

Looking at what goes into GDP is usually a pretty tedious affair, but the simplest way to think of it is like this: GDP is meant to represent the total value added. It is new work done; new stuff produced.

One upshot of this is that new houses are counted in GDP, while sales of existing houses are not. This is because sales of existing houses are just value transferred - an exchange of assets - and so don’t represent new effort. That’s not quite true. The real-estate agent fees and legal fees associated with the sale count, since they are new work done: they add new value by facilitating the trade.

Here’s a trick in looking at value added: we only need to look at the prices of final goods. This is because the price of the final good will represent the total value added along the entire production chain. The typical example of this used in introductory textbooks is bread:

Who Sells Price Value added
Farmer Wheat $0.10 $0.10
Miller Flour $0.20 $0.10
Baker Bread $0.45 $0.15
Supermarket Packaged and convenient bread $1.00 $0.55


The price of the final good - packaged, convenient bread - is $1.00, which exactly equal to the sum of all the value added. So when the statisticians want to calculate a country’s GDP, they can ignore all the intermediate levels and just add up all the final goods that were produced.So what counts as a final good? Anything that gets sold to someone for consumption or investment. That might be to an individual, or to a private firm, or the government, or someone overseas. (Of course, since I buy both bread and flour from my supermarket, flour is sometimes an intermediate good and sometimes a final good; but it’s easy to tell which is which - flour sold by the supermarket is final, while flour sold by the miller is intermediate.)

Now consider a country that has a large natural resource sector. Australia is a great example. So are all the oil exporting countries. We’ll pick the mining of iron ore in Australia as an example. Just like with the wheat above, there is a whole range of production possibilities based on the iron ore. However, when it’s exported, the final good that gets counted from the point of view of the Australian economy is the iron ore in the ship as it sails off to another country.The mining companies are definitely adding value. They’ve got to find the stuff in the first place, dig it up, clean it a bit to get rid of the dirt, transport it to the coast and then ship it overseas. They’ve also got to maintain all their equipment and allow for the fact that they wear out over time. All of that is new effort. But the price that India or China pays for the ore is more than cost of doing all of that. A large fraction of the price they pay represents the market value of the underlying asset - the ore - itself. But since the mining company didn’t actually produce the ore, that part of the price shouldn’t really count in GDP, for the same reason that when existing houses are sold, only the agent and legal fees are counted. None of this is really news.

When natural-resource-based industries are only a small part of a country’s economy, there’s not too much distortion, so we tend not to worry about it. But when those industries represent a large share of the national income, then the overestimates can be significant. In Australia, mining represents about 6.7% of the national economy. A fair chunk of that will be “true” value added, but a large share of it is really just the transfer of assets. How much? Well, BHP currently has a Return on Equity of 49%, while the long-run, risk-free return on capital is more like 8-10%. So as a very rough guess, assuming that BHP is representative of the mining industry as a whole and that the mining industry is competitive, we might suggest that Australia’s “true” GDP is at least 39% * 6.7% = 2.6% smaller than we think it is.

Some people might at this point wonder about the farmer back in the bread example. What if the farmer who, like BHP, is taking something from the land, is actually only adding 60% of the value that we think she is? The answer lies in the fact that there is a large production chain that builds up from the farmer’s wheat. Even if we remove a large fraction of the farmer’s value-added, that is only a small share of the total value added that we see in the final good’s price. So we would expect this overestimate to be very small overall. The point about mining is that we are only adding a small amount of value relative to that of the asset we are trading away, so as a percentage of the final good, the asset itself is quite large.

Teaching EC102 - Economics B

Published
by
John Barrdear
on 1 October 2007
in Economics and Teaching
. 1 Comment

Apologies for the hiatus. I’ve been moving house, dealing with a broken computer, finishing up a job and stuff like that.

It turns out that I will be a class teacher (a “T.A.” for any Americans in the audience, a “tutor” for any Australians) this year for EC102. It is the largest course offered by LSE, with something like 700 students. It’s meant to be a year-long introduction to economics for the more mathematically-inclined students that intend to continue studying the topic in the rest of their degree. I’ll be looking after five classes, with 15 or so eager young minds in each. Joy. :-)