Wednesday, September 27, 2006
Econs tml, maths on friday.. You may or may not be glad to hear that I have offered alternative explanation for the chapter on market failure: monopoly.
Some of you might undoubtedly wonder why we to achieve allocative efficiency, we require MB=MC. Here's a mathematical reason why.
Let's start by defining satisfaction, S.
S=B-C
Satisfaction of each individual in any partaking any action is calculated by taking total benefit involved and substracting from it, the total cost incurred. Remember that B and C are functions that are defined based on the variable Q, quantity. Next, we want to find the position where we get to maximise the value of S. Remember differentiation? We can find the maximum point of any curve by differentiating this function and equating the differentiated function to zero. So here goes.
d(S)/d(Q) = d(B)/d(Q) - d(C)/d(Q)
d(S)/d(Q) = 0
0= d(B)/d(Q) - d(C)/d(Q)
Therefore,
d(B)/d(Q) = d(C)/d(Q)
In econs, d(B)/d(Q) and d(C)/d(Q) are known as marginal benefit and marginal costs. See now?
Also remember that for a monopolist, his marginal revenue curve is less than the average cost curve? Yeah I now show a maths proof why.
Recall that total revenue is given by (Price)(Quantity). Also, verify that Price is a function of Quantity, yes? Here the Price referred to the by the equation is also the average cost curve. Observe that it is a straight line sloping downwards. So we can do a simple formulation:
P = -KQ ; Where P is price, K is an arbitrary constant, and Q is quantity.
Lets go back to the total revenue equation, substituting the Price equation in.
TR = -KQ^2
To find marginal revenue, we differentiate this function.
d(TR)/d(Q) = -2KQ
MR = -2KQ
Observe that the gradient of marginal revenue curve is -2K, and that the gradient of the average revenue curve is only -K. Of course, the marginal revenue curve is steeper..
Please do not be alarmed by the maths here. I used only Sec 4 A-maths and nothing more. If you are panicking over this alien maths, then do be very worried. Because its Maths exam on Friday.
Hope you have gained insight.
Jing Hao
Sunday, September 24, 2006
Lol, this is to take your mind off the usual dry mugging. Having earlier posted on the Prisoner's Dilemma, a cornerstone in game theory, lemme present another variation. It is known as the 'Chicken'. In this scenario, you and friend are driving a car on a long straight highway. Both of you are driving your car straight at each other, in a line, at high speed. Oh dear, it looks like both of you are about to crash. At the last moment, your friend decided it was too risky, and veered away, therefore avoiding a bone-crushing death. As you drive past him, you laugh at him, calling him the chicken.
In this scenario, the objective is to be the person that stays straight on course. You want to laugh at the other loser who veered away. There are only 4 possible scenarios. Either both of you refuse to give in, hence meeting your untimely deaths as both of your cars smash together. Else, one of you veer away, be it you or your friend. The person who chickened out gets laughed at. Or both of you veer away, making the same decision simultaneuously not to play this dangerous game anymore. There's no one laughing.
Of course, quite a lot of us would definitely choose to chicken out, because it guarantees at least a lifeline. So if everyone thought like this, there will only be one outcome, that is, both of you veer away. This assumes that everyone thinks rationally, and values his life more than anything else. There will of course be cases where the insane guy has nothing to lose, and prefers to see you die with him. We do not consider this sort of people in our rational behaviour analysis.
More often than not, the leader of nations are not so rational. You can see examples of Chicken being played out between nations, each taunting the other to chicken out. A good example is the Cold War between America and Russia. Both were locked in the arms race. Neither wanted to both countries to crash into each other. But at the same time, both countries hopes that the other would "chicken out" hence gaining the chance to laugh at the other nation. And so both countries continue to drive their cars straight at each other, escalating the tension. It was finally that both countries decided to back down. Else, it may have been the 2 nations go down together.
So, how would you handle this situation?
Jing Hao
Friday, September 08, 2006
Lol, here comes the ritualistic exam fever once more. People working themselves into a frenzy, be it real or fake, mugging as if their entire lives depended on it. Which is why I dont see the point in exams. Do exams breed understanding in the topic concerned? No. Are exams a true gauge of one's abilities? No. Why do we take exams? For the certificate and nothing else. What a waste of time.
People have traditionally studied for exams by pure mugging, memorising their way through that is. What an efficient method of studying. We study all the types of questions that are likely to come out for exams, memorising how to answer the questions, never once pausing the understand the mechanism working behind it. When the exam questions come up, we find that the teachers have diablolically changed the question slightly. Suddenly, it as if we have seen a whole new world. The eyes glaze over, the mouth drops. And we find that we do not know how to solve the question. Goes to show how efficient our method of studying is. Why don't we understand the mechanism behind it? It would make our job much simpler. Understanding the mechanism, means that we can solve all the variations of the same type.
People who study for sciences somehow tend to study the chapters disjointedly. We tend to think each chapter in isolation. Which is a complete mistake. Because the sciences are not meant to be studied this way. The sciences have a backbone linking all the chapters together. Hence, questions usually cross between several topics simultaneuously. For example, Kinematics, dynamics, conservation of linear momentum, energy, forces, come under a big name called mechanics. An area of the study of particles. Hence questions would ask anything under this. Under mechanics is another big sub chapter known as rotational dynamics. Here the topics are Circular motion, SHM, torque. This chapters are also the link to Wave mechanics, topics underneath are waves, light, diffraction, standing waves, resonance etc etc. So there is a sort of over arching principle that can give us leverage when solving problems. Use it.
I am not saying not to memorise anything, just that we can minimise the amount to be memorised drastically and save a lot of brain space. Which is a bonus, when you have less than 3 weeks the study 4 subjects.
I never liked the way we are examined under this system, because the system emphasises a major part on memorising and time management. I prefer to slowly think through the problem. Give a complete solution to the problem. Thats the way things should be. Not hurry your way through the paper, leaving gaping blanks; questions that are answered have tons of careless mistakes. Why not go for more creative thinking.
But perhaps there is no right way for testing knowledge..i believe no one in the world has found a correct way yet. Perhaps there might be breakthrough in times to come. Perhaps. In the meantime, more people will fall under the cutting edge of exams.
Thursday, September 07, 2006
HEY!
yes s18-ians, let's all mug really hard
and survive the promos together
which is only in abt 2 wks' time!!
whoooooo!!!!!!!
so exciting!
we aren't gonna get anymore 'U's are we???
no we aren't!
let's aim to get more 'A's instead!!
ahhhh!!
i'm hungry and starving for more 'A's!!
muggers unite~
`amelia
Monday, September 04, 2006
When I saw "let me present something to you all", I knew it's jing hao. Who else from s18 will present us with problems? lol
Anw. What I would do in such a dilemma actually depends.
I’ll spend some time to recall whatever I’ve gone thru with this accomplice and judge whether he/she is a good guy or he/she simply sucks first.
Well, if he/she sucks and I know that he never give a damn shit about others, I would rather confess and let us be in jail together for 7 years. If he happens to be nice this time, then probably, after I get out of jail, I’ll get people to bang into there to get him out haha…
If he/she has always been trustworthy, erm…then I can’t really be sure that he’s going or not going to confess. You never know. People turn evils sometimes.
But to think about it, both me and my accomplice may not be sentenced for 5years if both never confess. That was what the police officer SAID , but there is no solid evidence to put us in 5years jail.
So, I wont confess in this case. Fingers crossed for the best ,haha…Anw, actually you cant really trust the police anymore in this kindda situation, you’re a criminal! What do you expect? The police maybe trying to bluff u off…. So just try ur luck :)
-ChristinD
Sunday, September 03, 2006
TO ALL OH SIX S EIGHTEEN BEINGS.
good luck for promos! lets mug ppl!
I WANT TO MUG
WE WANT TO MUG
LETS MUG LET US ALL MUG!wahahas.
kahyan the great x)
Haha pplz, let me present something to you all, something that is well-known in game theory. Never mind that you do not know about game theory, just know that its an area of mathmatics that lays the foundation of economics theory.
This problem is known as the Prisoner's Dilemma. Some of you may have heard of it before, some of you might have not, but here is the problem anyway:
Suppose you are a criminal warlord. You and your accomplice have just been recently caught by the police for a a major crime. The police puts both of you in separate interrogating rooms. They tell each of you separately that currently they have enough evidence to sentence both of you to 5 years of jail. They just require either of you of confess to solidfy the evidence. The police tells you that if either one of you confess, the police will let the confessor go free, and sentence the other to 10 years of jail. However, if both of you confess the police will charge both of you to 7 years of jail. If neither confesses, the police will sentence of you to 5 years of jail. The police gives both of you 24 hours to think about it. Both you and your accomplice are not allowed to communicate to each other, so both of you will have to make your decision independent of the other.
While in your cell, you wonder whether you should defect( i.e. to confess and rat on your accomplice) or you should coorperate( i.e. to keep mum and not give away anything). Rational thinking may go like this: "Hmm..I should be loyal and not give away anything. However if my partner rats of me, I will go the 10 years of jail..Maybe I should just defect and leave my partner to die. But my partner may be thinking of the very same thing! If both of us defects, we would both get 7 years of jail! If only both of us can cooperate..then we would only get 5 years...Perhaps I should just save my own skin first."
What would you do if you were faced with the same dilemma?
Jing Hao
Friday, September 01, 2006
yo ppl! (:
i have created a account for us to store all our pics! (: yea so just upload all yr pics there then at the end of 2yrs we can have
MANY MANY pics! (:
1. go to
http://imagestation.com2. sign in! (:
username:
06s18password:
welove***** (same as blog password. just approach any of the wuliaos for the password! (: )
and i have uploaded an album with pics taken on wednesday at the request of our dearest jaime, so go take a look! (:
http://www.imagestation.com/mypictures/index.htmlthe rest to be uploaded after promos- im lazy (:
joli, the greatest rockker ever (:
