OT:Any economics experts ?

[dennis]

But the lecturers are so much better these days and they only let the best do the courses. 8-|

[stuart noble]

The best payers you mean :-)

[Charles Bryant]

In article , Jethro_uk wrote: }

} }Just had a gander at the question which has caused all the fuss, and is }it just me, or is it quite doable ? True I know **** all about "peasant }economies" or "1-person-cities", and I am making an educated guess at }"output" and "co-ordination costs", but overall it seems a }straightforward mathematical proposition - certainly not out of place in }a degree. } }Or am I missing something ?

Well, I would be able to provide answers, but I suspect they would not be what was expected. I'll reproduce the question (replacing sigma/gamma with s/g) with my answers:

! Consider a country with many cities and assume that there are N>0 ! people in each city. Output per person is sN**0.5 and there is a ! coordination cost per person of gN**2. Assume that s > 0 and g > 0. ! ! (a) What sort of things does the coordinaton cost term gN**2 repesent?

It could be anything, or nothing, since this is just an arbitrary term in an invented example that has nothing to do with reality.

Since this might be a surprising assertion, I'll explain it. Coordination needs at least two parties - you don't coordinate with yourself. So for N=1 this term must be zero. We know it is intended to apply to the case where N=1 as that case is mentioned explicitly in part (c), but gN**2 is g when N=1, and we're told to assume g > 0, so the term must be bogus.

There is a second reason why it must be bogus even if we ignore the anomaly for N=1 and just let it be g. It is reasonable for a city to have 1,000,000 people, but in this city the coordination costs rise to 1,000,000,000,000g. Even if g is one penny, for a city of a million people, the coordination costs are 10 billion pounds. If the city has a GDP analogous to London, that's a cost of 18% of the city's GDP. And remember that's per person! The total coordination cost expended in this city is a quadrillion pounds. That's roughly twenty times the GDP of the whole world currently. There is no possible way that this could be modelling any real-world quantity.

! Why does it make sense that the exponent on N is greater than 1?

It doesn't. If costs grew exponentially the world would be a far different place. Instead of having economies of scale, we would have economies of smallness.

! (b) Draw a graph of per-capita consumption as a function of N and ! derive the optimal city size N. How does it depend on the parameters s ! and g? Provide intuition for your answers.

No figures were provided as a basis to compute consumption. Output is given, and coordination costs are given, but there are two problems with merely using them to calculate consumption. Firstly, there may be other costs not covered, and secondly, not everything produced need be consumed. For example, start with a traditional joke about setting up two shoe factories where one makes all the left shoes and one all the right. Between them, they produce a certain level of output. Now assume that one stops producing (e.g. due to a strike, fire, etc). The aggregate output of the factories has halved, yet the consumption has fallen to nearly zero.

However, if we ignore that problem and simply try to graph the equation p = sN**0.5 - gN**2 we find a different problem. Any paper supplied is lacking in sufficient dimensions. There are four variables: p, s, g, and N, so we would need four-dimensional paper. If the quantities were meaningful, it might be possible to draw a representative selection of lines (i.e. each showing p vs N for fixed s & g), or to draw perspective 3D plots with one fixed variable though realistically even that would require something like gnuplot.

! (c) Describe which combinations of s and g generate a peasant economy, ! meaning an economy with no cities (or 1-person cities). Why might the ! values of the parameters s and g have changed over time? What do these ! changes imply in terms of the optimal city size?

Despite a few criticisms of this part, it's quite easy. Taking the bogus formula we used in (b) and differentiating with respect to N, we get N=(s/g/4)**(2/3) and setting N=1 we get s = 4g.

However, a peasant economy is not one where N=1. Such an economy is one of loners (like Alexander Selkirk).

While g is nonsensical, and therefore its changes cannot specifically be explained, but in general transaction costs will fall with the advance of technology.

s is more reasonable. Setting N=1 we find that s is the measure of the productivity of one person alone. This will change mainly through technological development. For example, consider the difference between Mozart and Michael Jackson. Due to technological developments, performances by Mozart could only be heard by those actually attending them, while vastly more people could hear performances by Michael Jackson both because of the ability to broadcast live to a larger audience and the ability to make recordings for future listening.

Both s and g might be affected by external events. For example, extended bad weather might interrupt communications, increasing coordination costs, and might reduce production of some goods (e.g. farm produce).

Obviously, the "optimal" city size is N=1 for s/g = 4. As s/g increases, this optimal size increases. Since this increases, it would suggest that this model predicts that cities would get bigger with advancing technology. Since the model is complete nonsense, this suggests that it was constructed with this in mind.

Finally, the use of the term "optimal" deserves criticism. Anyone who works in a real science or engineering field knows to be very wary of it. Optimality is always with respect to some particular criterion. A device might be optimised for reliability, power consumption, weight, robustness, price, or many other criteria. It is important to state the criterion explicitly. Otherwise it encourages two different errors: that different people will understand it to be with respect to different criteria; or that people will forget that there are different criteria.