I can remember quite a few university exams where my initial reaction was "What the ^-&%! is this?" - but you had to stay calm [1], work through it and try and actually apply the logical thinking you were supposed to be learning.
That question they have a picture of looks like something I could attempt an answer to - and I've never studied economics.
1. The actual advice I remember from my dear old mum was "keep the heid".
>That question they have a picture of looks like something I could attempt an answer to - and I've never studied economics.
My thought as well. If we assume that they have been introduced to 'coordination cost', it should be easy to answer. Non of the three sub-questions are even about calculating, they are about discussing the concepts of a very simple model.
Even if you haven't maybe it is. I might be overly cocky here but it seems obvious what kinds of costs these are and why the simple model is the way it is. Why is the exponent on N greater than 1? Because otherwise coordination costs would decrease as you add more people, right? Are their complaints basically that the exact answer to this question should have been available in the notes and that they shouldn't have to apply past knowledge and techniques to an unfamiliar problem?
"Because otherwise coordination costs would decrease as you add more people, right?"
Not so fast, or you might lose 10 points. ;-) Note that the coordination cost is given per-capita, and it is proportional to N^2. If the per-capita cost was O(N^a) for a < 1, the total cost would still be N*N^a = N^(1+a) which increases with N.
If the (per-capita) coordination cost were proportional to N, that would indicate that (e.g.) to do something, you have to contend with "N" other people (everyone else in the population), which makes sense.
The total coordination cost would be: (N people) X (per-capita cost of N) = N^2, which is familiar from various kind of networks, e.g., distributed computations in which total communication costs can rise like N^2 (where N is the number of processors).
But if the per-capita cost is proportional to N^a for some a > 1, that's even stronger. I'm not sure how you justify that. I'm sure you can, I'm just not sure how the course did it.
Maybe you say that you have to coordinate with all N other people, as well as all pairs of the N other people. The number of pairs of other people is proportional to N^2, giving you a per-capita coordination cost proportional to N^2.
Without knowing what coordination cost is, that would be my guess. I'd probably phrase it vaguely like "the cost of coordinating N people is proportional to the number of connections between those people, i.e. proportional to N^2".
But that might be less obvious to an econ student who's never studied complexity theory.
But I fear, from what you wrote, that you fell into the same trap as @gmarx above.
The claim in the exam is that the total coordination cost is above quadratic, i.e. proportional to N^b for some "b" strictly larger than 2. (Because per-capita cost is proportional to N^a for some "a" strictly larger than 1.)
This is not what is typically assumed in complexity theory.
I'm certain that when I was in secondary school most of my classmates would be able to answer (b) and (c) of that question since it's a standard 'set derivative equal to zero' question. Part (a) is indeed vague, and they want you to prove something that's incorrect, but it's not hard to see what they want to hear. Ugh, that brings back memories of answering vague questions in such a way that you know will make the teacher happy, but is actually incorrect. I remember one instance where a question on a physics exam asked us to solve a problem that did not have an unique answer (it boiled down to 3 variables and only 2 equations). So I wrote as my answer an explanation why the question could not be solved, which the teacher gave 0 points for. Later in the exam review in class I asked him what the correct answer was, and he gave incorrect reasoning. After I politely pointed out that his answer was incorrect I got 15 minutes of "public shaming" in class about how stupid I was and how dare I disagree with him. Afterwards I sent that question to a physics professor in a university, who also said that the question could not be solved. I sent that to my teacher which only made him more angry. Luckily those days are over.
Agreed, reminds me of a test I took in a stress analysis class (mechanical engineering at Arizona State University in the US). We had covered thermal expansion of unconstrained objects, as well as those held in certain dimensions by fixed walls. On the exam the professor wanted to cover both so he had the walls placed a small distance away.
Most students flipped out because they had not seen an example of that exact situation, but a moment of thinking shows that the problem should be broken into pre-contact an post-contact parts. This professor had the highest drop rate I have seen (around 30%), but his insistence on comprehension over memorization made me learn more than any other class I took.
Mobile submission, so please excuse grammar.
I'm terrible at and quite out of practice with math an have nearly no education in economics and it doesn't look that bad. I've got what I judge to be a decent guess at (a) based primarily on knowing what the word "coordination" usually means, my only hang-up with (b) is that I don't know how you get per-capita consumption from the information provided (presumably students in economics do?) and (c) looks a bit tedious but far from impossible.
This question does seem more mathy than economicsy, though, in that it looks like a math major could probably do very nearly as well at it as an econ major, if not better.
I agree with yer maw :P. I done a degree in Physics and we would get asked questions like this all the time - unseen, but with the definitions you need included mid sentence. We had our fair share of complaints about professors to make but this seems a little entitled/lazy. shrug
Aren't these students effectively claiming it's too much to expect them to know basic calculus as they're about to graduate with a degree in economics? That doesn't seem like a wholly unreasonable expectation to me and if they're unable to do so then what kinds of problems are they expecting to encounter when they get jobs?
Maybe student expectations could have been managed better but I wouldn't think you'd have to explain to economics students preparing to graduate that they should expect to utilize basic calculus during an exam.
I've been educated in and am studying in the UK at the moment, and for us exams are meant to examine how well you know the content of the course (or so we're told). If the students are correct in saying that the exam contained questions regarding things they'd never seen or had experience of before, then in my opinion the exam was unreasonable.
Throughout my entire academic career exams have worked this way, so regardless of whether they ought to know it for The Real World, if they haven't been taught it then it shouldn't have been on the exam.
My first impression looking at the questions was that they were intended to take the knowledge they had gained during the course and apply it to what may have been an unfamiliar circumstance.
Done correctly, that's a completely fair exam. I'm sort of inclined to think that if there's this much smoke, something's probably on fire though. I know my own students will complain about silly things, but if they all complain about something, invariably I end up agreeing with them.
That's an apt comparison: if no (or painfully few) students were able to give at least a reasonable answer, the problem lays in the teaching curriculum or methodology. (This may not be the course itself, it may be a broader question about hand-holding an academia or similar, but the question remains.)
I remember a particular instance in Geometry in high school. Everyone did poorly, so the teacher allowed us to work together to answer the questions again. My group was stuck on a particular question, so I asked the teacher to clarify. She refused, saying we were taught it. I retorted that since everyone was struggling, clearly the problem was on the other side of the desk. (It went over about as well as you might expect.)
Well my experience getting a degree in the UK in the 1980s was that exams would often contain questions in a different form from what you had seen before - you did know how to answer them but it definitely wasn't trivial to identify what techniques to apply to solve each question.
I get the feeling that people now expect questions to be of the form "apply technique X to data A,B,C" which is what I used to expect of secondary school level exams.
Didn't they experience exponents? Maybe multiplication should also be out of questions? Its their final year, I don't think phrases like "third question could be as well in chinese" is suited here.
I like the irony of an econ course asking students to model economic consequences in an exam, but failing to model the economic consequences of pissing off its students so much it makes the national news.
In addition, lots of topics in undergraduate econ might require require partial differentiation to derive, but not to understand, explain, or compute them.
This happened a couple of times when I was in my econ undergrad - and was done purposefully so that we would have to think way outside of the box and apply previous economic theory to "derive" new conclusions.
Nothing controversial here except for a bunch of whiny students who should know better given that it is their final year.
This happened to me once in a freshman chemistry class. The course had a few hundred students and most of them failed the first preliminary exam. The questions bore no resemblance to what we had covered in class, and one was based on a recent publication. As far as I know, the one person to do well was already a chemistry superstar prior to the course. The professor chewed us all out afterwards for not applying ourselves. I'm still angry about it to this day. None of us were dumb or not trying. Either she failed as a professor to teach us what she expected us to learn, or she was placing unreasonable expectations on us to derive new conclusions during a stressful exam. It's not wrong to expect someone to make leaps based on something they've newly learned, but there is surely a better context for that.
This is a great way to LEARN, but a terrible way to TEST.
Or more precisely, you can't lecture on facts and then test application. Learning HOW to think is as important as WHAT to think. (If the course content is centered around deriving new conclusions, then by all means, test that ability.)
I'm currently in my final year of university too (not at Sheffield) and I was amazed at how many announcements had to be made during the recent exams (2 weeks ago) to correct questions, some multiple ones per paper.
If it's only a 3-4 page exam, with only 3-5 questions in total, they should probably have been read through and attempted by a couple of lecturers beforehand.
What made it even worse was that I am at a Welsh university, so announcements have to be made both in English and in Welsh. Disrupting anybody doing a different exam and causing hassle for the students taking the incorrect one.
Disclaimer: I am attending Park University online B.S. Information Computer Science doubtful anyone on HN would even consider this as a credential or a legitimate learning experience to offer insight on econ exams.
Going against the grain here I can understand the student's frustration when tests are implemented to establish a metric that is ultimately attached to a record of sorts and in some cases can affect the psyche of the student.
My example that is somewhat related was during a "Web Programming" course we were taught basic things like DHTML, CSS, JavaScript etc. All culminating in a final project of a personal website, nothing to difficult there.However due to the nature of online courses I had to take a test at a proctored location with a computer. One week prior to the exam being sent out instructor notified us that "Administration has mandated this to be a written test." This really threw my game off. I'm not sure any developers have ever tried "writing" a full webpage including CSS and Error checks for form fields on a sheet of paper but it definitely affected my performance on the test. During the class we it was in now way imparted upon us that writing code with a pencil would be our final artifact of having learned something in the course.
As much as I and many people I have met attribute intelligence to critical and problem solving skills. The reality of "normal" institutional teaching emphasizes the ability to take tests and remember data only dumping and moving on to another subject to repeat the process. The over arching theme, in my experiences, is that remembering and regurgitating topics in the course was/is the most rewarded endeavor. For some it is very difficult to escape this conditioning of remembering and studying material in order to get the right answers on a test with critical and problem skills existing only as a side effect of "learning".
Out here in the real world, it's incredibly common for people to be thrown at a problem only slightly related to prior experience. My entire involvement with SCSI came about this way. My brother got his start in professional IT because the financial publishing company where he was a proofreader had computerized and needed someone to handle backups. This test, if fairly graded, might tell more about students' prospects for future success than a traditional test would have.
This comment is bonkers. This isn't the real world, where you can look things up on Google, or ask your economist friend, or email Brad Delong for help. This is a university exam. The whole fucking point of it is to test your understanding of the material covered in the course.
Applying the knowledge taught in the course is different from applying knowledge of something tangentially related to something taught in the course to a completely different problem, which is what seems to have happened here.
No, it's not. The whole fucking point, as you put it, is to test your ability to function in that problem domain. Testing mere regurgitation isn't that useful.
When I was in school there were plenty of tests for which the class average was under 50%. Obviously professors wouldn't try to write them this way, but writing a test that's hard but not too hard is, well, hard.
It frankly was never that big of a deal. Professors would generally curve the test and life would go on.
Certainly this doesn't merit a BBC story. If everyone bombed the test, then the professor should obviously consider giving it a healthy curve.
I had numerical analysis tests on my first year with <20% avg. on a good school. The problem here seems to be not difficulty but scope, in which case I'd say the complaints are justified. Still not warranting a BBC story.
3.a. Specialization and trade. An exponent less than one would imply that a system with more elements has a lesser coordination complexity than each element acting independently. Such would only be possible if humans became telepathic when forced into close proximity.
3.b. Consumption per person would be equal to the usable output of each person, minus overhead losses, minus stockpiling and savings. Assuming the latter to be zero, consumption is x = sigma N^0.5 - gamma N^2. To find minima and maxima, we take the first derivative with respect to N, and find where it is zero. 0.5 sigma N^-0.5 - 2 gamma N = 0. The non-imaginary solution is N=(sigma/4 gamma)^(2/3).
3.c. Plug N=2 into the above equation. To support cities of that size, gamma must be less than 9% of sigma. Sigma may be increased by gains in productivity, such as with specialization. Gamma may be reduced by lowering coordination burdens, such as by using money instead of barter, or employing merchant specialists. Changes in gamma have a greater effect on city size, so given the equal-cost choice between a universal education mandate and a guaranteed uniform currency standard, the latter is preferable, if larger cities are desired.
If student economists cannot think their way through that problem, we may assume that they will have a detrimental future effect upon both sigma and gamma, and we should therefore kill them now before they cause our cities to collapse. Judging by Detroit, we may already be too late.
Agree on both counts. This question seems to have an appropriate level of difficulty for the student rank and written in a fairly intelligible manner. Can't speak to the rest of the test, but I don't find this question off sides at all. And yes it is very likely too late.
Initially, I was on-board the whole "yeah, screw you school!" train with the students (presumably left over trauma from being intellectually sodomized by UC Berkeley's physics department), but then I read the prompt 3 in question. And I have to say, I really really like that question because it's not only testing the student on memorized economics tidbits, but also on truly applying learned theory and economics intuition to a more alive problem.
In fact, even though I'm suppose to be slaving over getting onDisconnect to clean up correctly in Emberfire for my boss before the afternoon whipping, I can't help but have fun solving this problem:
1. the gamma (coordination) term is NN because people all have their own opinions and agendas which they have to tell everyone else. In other words, if there are 3 people, person A must tell his idea to person B and person C, person B must tell his to Person A and C, etc., and in total there are 9 "tellings" (aka meetings).
2. The graph of production-v-person and cost-v-person, if plotted onto the same paper, would look like the lower case letter gamma tilted 45 degrees to the right. The most-bang-for-your-buck optimal city size would be were ( g N * N - a * sqrt N ) is largest. If I knew calculus and can do derivatives, I can get N = ( a / 4g ) ^ 2/3 as the answer.
3. A peasant city is one where (a / 4g) <= 1, that is, where talking to other people is really really hard but doing things is really easy (lol just like at my work, where we're all peasants and we slave for months only to have our projects cancelled and the blamed placed on us). "a" and "g" can change with technological improvements, for example, "g" can go up when the society discovers email, the telephone, writing, etc., and it can go down when the society discover facebook of 4chan (and then we all spend our time being holier-than-thou, insulting each others' tastes, and disparaging each others' waifus). "a" can go up with the development of productivity tools; an example of this in the javascript world where I hail from is when jashkenas discovering coffeescript, wycats + tom dale inventing ember, etc. "a" can go down when you get a legal department who insists you can't use X, can't contribute to Y, and I must watch my language F.
Your answer to 1 sounds like the answer they want to hear, but note that aN^2 is the cost per person, not of the whole city. Your explanation justifies a cost of aN per person. The question is also really vague, I hate questions where you don't find the correct answer, but rather try to infer what the teacher wants to hear. In a real city the costs per person are obviously not aN and certainly not aN^2 because the number of people that you have to meet does not scale linearly with the amount of people in the city. That would imply that if people in a village of 1000 people have a total meeting cost of $10 per person, then the people in new york have a total meeting cost of $80,000 per person. That's obviously ridiculous. Their aN^2 would imply that the total meeting cost in new york is $640,000,000 per person which is beyond ridiculous.
I can't see where we can estimate the per-capita consumption though. We know the communication cost and the per-capita production, but I don't see how I can derive total consumption from that.
Also, gamma has a loop in it and the function we're dealing with is a surjection, so its graph can't have a loop.
I was plotting 2 functions (the production function and the cost-of-production aka communication cost function) onto the same graph and looking only at the top-right part where X > 0 and Y > 0, in this case, X = number of people and Y = money (either produced or consumed). The production function, because of its sqrt(N), looks like a U flipped on its side. Meanwhile, the cost function, because of its N^2, looks like a regular U. If you have a U sitting with its butt on 0,0, and a U lying down on 0,0, and you look only at the top-right coordinate plane, it'd look kind of like the letter gamma tilted 45 degrees.
Regarding per-capita consumption and total consumption, if you have per-capita consumption, and you have N the total number of people, you can multiple per-capita consumption with the total number of people to get total consumption. If per-capita consumption varies with the number of people, then a bit of calculus is needed as you "integrate" per-capita consumption with respect to number of people to find "the area under the curve" which is your total consumption. But if the students have not yet learned calculus, I can see how it could be unfair to have them derive calculus during the test.
I've been accused of this same thing with some of the exams I have given in the past. I'll assume that most instructors probably have. Sometimes the complaints are justified, and sometimes I believe that the students have just not prepared well. Even without mass protests, I will sometimes notice that a significant fraction of students performed poorly on one or more questions/sections, and take that as an indication that I have either not covered that unit's material as well as in the past, or that I have asked the question(s) in a way that was unclear. I can't say whether or not this exam was fair, but I can say that if 90% of students make similar complaints, that I would have to take a hard look at the way I had managed the course prior to the exam.
Sorry,but I can only laugh. In Poland it was completely normal and almost expected for 100% of students to fail an Engineering or Math exam on their first try. There would be 50 people taking the exam and literally 45-50 would fail. Most people pass their exams on the 3-4th try. What adds insult to the injury is that most professors offer "0th" exam chance for those with best grades - so out of group of 50, maybe 5 would be offered to take an exam earlier than everyone else. Commonly, no one passes those exams, they are just ultra hard with super short time limits.
And then there is this question in the article - if you are studying economy you really can't answer a calculus question?
There is certainly a COllegeHumor or Onion post in there somewhere. While I agree with most people that difficult exams are par for the course, the response here will be informative for the classes following this one.
But what I found surprising from this story was that these kids are in their final year and their expectations are completely out of alignment with what the University required in the exam. It makes me wonder if the earlier years were extra easy? or this last year extra hard? And why aren't they prepared to think by the time they get to their final year?
I've never taken economics, but is it possible that this is sort of a combinatorial reason? Like, adding the N+1th person implies coordinating with N other people, so that's a quadratic growth. I'm not really sure if that's realistic though...
Try to accomplish something in a large organization and it will become intuitive. I think it was covered in "The Mythical Man Month". The more programmers you add, the worse it gets and all that.
The problem established N^2 as the given, and implied N^1 is the lower bound, by demanding an explanation for it being that way.
In a group of N people, there are N x (N-1) potential direct 1-to-1 interactions, and (N-1) x (N-2) interactions with one predetermined intermediary. Those are both N^2 terms. Per capita, it would be an N^1 term. At the human scale of around 150 personal relationships, everybody knows everybody, so the burden for anyone is knowing everyone else.
Beyond that size, you need at least one intermediary. There are N x (N-1) x (N-2) interactions between two people with an unspecified intermediary. That is an N^3 term, so N^2 per capita. The burden there is knowing at least one person that knows the person you want to deal with. At another critical size, again dependent on human social limits, you can no longer effectively use friend-of-a-friend connections.
Then you create sociological systems to take the place of personal intermediaries. These tend to scale relatively proportionally with the size of the population. A road system for a town with twice the population will be about twice as big. Miles of road per person will be similar near the median town size. The same goes for cops per person and sewer pipes per person and cash available for withdrawal from bank branches per person, and so on. For simplicity, we can just assume that all the systems of civil society scale according to N. So now all trades with two counterparties have complexity N x N x (N-1), which is again an N^3 term with an N^2 per-capita component. But the scale of the system is not necessarily N^1. We just know it's a positive number. So the per-capita coordination burden is more rightfully N^(1+something).
That "something" can be found by performing a statistical analysis of city budgets by city population. That seems like a task for someone more interested in the topic than I am.
In England University education has changed dramatically over the past few years.
Introduction of fees means that some students see an education as a product that they're buying, with that kind of "customer service" expectation tacked on.
Education is always news-worthy in England because politics.
We often see articles about exams (at all levels) going wrong - bad questions; cheating schools; bad marking; etc.
It is interesting to see this reaction. In the US we have been paying for education for quite some time and the thought that it is a product and students the purchaser and benfactor of that product does not seem to be a very important topic rather it is met with some levels of resistance and blame on the students when "we" fail or otherwise complain about our educational experiences. Lots' of walking through snow uphill both ways reactions from professors and attendees of college/university.
There's a difference between doing math proofs and solving equations, and understanding problems quantitatively (which requires some basic math competency as a prerequisite). The sample question suggests it was the latter. It's like an algorithms question where the professor tells you not to do math, just think in Big O.
> The BSc Economics course places particular emphasis on the mathematical and statistical techniques used in economic analysis. It's suitable for students with A Level Maths or equivalent. In each year you take modules to the value of 120 credits.
I remember memorizing the capitalization and white-space in answers knowing the home-brew auto-grading system would require an exact match on every answer for the final in one class... awareness of what's coming (even meta implementation details) definitely reduces the stress levels!
Same story when I was at Duke. Students can get either a BA or a BS in Econ, where the BS requires more math courses. Many BA students freaked out when there was calculus on the first exam.
An exam is supposed to test what you are taught. If 90% of the students didn't understand the exam, they weren't taught properly. That is the teacher's fault.
That question they have a picture of looks like something I could attempt an answer to - and I've never studied economics.
1. The actual advice I remember from my dear old mum was "keep the heid".