4 ms·

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 Ber

by ffn 12y ago

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.

doulomb 12y ago
I felt the same way when I saw that question and I immediately set to solving it. It was a fun question that required you to think on your feet. I think these students are just upset that they did not receive a "canned" exam, with memorization questions.
anon4 12y ago
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.
- ffn 12y ago
  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.
jules 12y ago
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.

by ffn 12y ago

doulomb 12y ago

I felt the same way when I saw that question and I immediately set to solving it. It was a fun question that required you to think on your feet. I think these students are just upset that they did not receive a "canned" exam, with memorization questions.

anon4 12y ago

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.

ffn 12y ago
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.

jules 12y ago

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.