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On the importance of sunk costs

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.)

Teaching EC102 – Economics B

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. 🙂