Another Joke

Surgical preferences
Four surgeons were sitting around discussing who they like to operate on.
The first surgeon said, “I like operating on librarians. When you open them up everything is in alphabetical order”.
The second surgeon said, “I like operating on accountants. When you open them up everything is in numerical order”.
The third surgeon said, “I like operating on electricians. When you open them up everything is color coded.
The fourth surgeon said, “I like operating on lawyers”.
The other three surgeons looked at each other in disbelief. One of them asked why.
The fourth surgeon replied, “Because they are heartless, gutless, spineless, and their butts and brains are interchangeable”.

The psychiatric hotline

We’ve all had the annoying experience of calling up a hotline and waiting on the phone for eons to hear all the choices the lucky touch-tone dialers receive. Well, think how frustrating that would be if you were calling the….

PSYCHIATRIC HOTLINE

The telephone rings and an answering machine answers… “Welcome to the psychiatric hotline.” If you are obsessive compulsive, please press one repeatedly.

If you are codependent, please ask someone to press 2.

If you have multiple personalities, please press 3, 4, 5, and 6.

If you are paranoid/delusional, we know who you are, what you want, just stay on the line so that we can trace your call.

If you are a schizophrenic, listen carefully, and a little voice will tell you which number to press.

If your are manic depressive, it doesn’t matter which number you press….no one will answer anyway…..

In the land of Women

Just a movie I used to watch. The most important is if you lose u need to find the way back. (^.^)

Enjoy two Fun!

The secret of a perfect relationship

 1. It’s important to have a woman who helps at home, who cooks and cleans from time to time, and has a job.

2. It’s important to have a woman who can make you laugh.

3. It’s important to have a woman who you can trust and who doesn’t lie to you.

4. It’s important to have a woman who is good in bed and who likes to be with you.

5. It’s very, very important that these four women don’t know each other

  Expensive Barbie

A man walks into Toys-R-Us and says to the sales assistant, ‘Could you show me your Barbie dolls, please?’ ‘Certainly, sir,’ she says. ‘Here, we have Fashion Barbie at £15.95, Vacation Barbie, also £15.95, Housewife Barbie – that’s £15.95 too – and Divorcee Barbie, at £215.95.’ The man is astonished. ‘Why’s Divorcee Barbie so much?’ he asks. ‘She looks the same as the others to me.’ ‘Well, sir,’ says the assistant, ‘that’s because Divorcee Barbie comes complete with Ken’s car, Ken’s house, Ken’s furniture, Ken’s dog…’

Concave and Convex, Quasi-Concave and Quasi-Convex and Economic Optimization

One point that I myself seem to igore like most economist student is about concave and convex problem but they are quite important in building economic model of optimization. I just try to summarize and imporve my memory on these overlook points. May be it can help for my future use in research.  

Concave refer to bell-shape curve (inverse U-shape) while convex is (U-shape). Why do concave and convex is important in eonomic optimization?  The answer is simple if the carve is to be convace (strictly concave) then the opitamal point must be unique. If it happen that the curve is not strictly concave then it mean a small part of the curve will be line segment then there are possible that multiple opitmal point is feasible.

What is above quasi-concave or quasi-convex curve? Well quasi-convex or quasi-concave is similar to convex and concave case but the different is that a quasi-concave curve can include both concave and convex and likewise the quasi convex and quasi-convex case. In graphical dimension, quasi-concave is noted by some reverse curvature at the tail of the curve/ Strictly concave implies stricly quais-concave likewise the strictly convex imply stricly quasi-convex.

In any opitmization method ranging from static one such as Lagrang mutliplier method with equality constraint, Kuhn-Tucker method of inequality constraint to dynamic optimization such as Pontrygain and Bellman Equation. The curvature condition play role on uniqueness of both interior solution and corner soultion.

Mathematical Optimization Necessary and Sufficient Condition

In Economics, individuals are assumed based on rationality philosophe to making the best selection or decision for satisfying their objective function. The decision has to be made with or without constrain. For example, buyers have to balanced their budget constraint with quantiy of commodity they want to purchase to maximize their utility. Firm is willing to maximize their profit based on production cost constraint. Government has to maximize social welfare under country resource constraint.  An optimial point dose not mean it has to be the maximun, that is the largest value (in absolute term) but it is maximum in relative term to its neighbourhood avialbe selection.

In mathematical fomular to proove that a point is maximum or minimum in the case of no constraint there are condition on objective function. The necessary  condition is called first order condition  and must be staitified if the point will be selected. Mathematically, the necessary condition stated that the derevative at the maximum or minimum must be zero. (Why?) The reason is that the point must located on the peak or the buttom of the carve. Imagine the case of a ball you place  on the peak of a bell-shape it there is only the point on the peak where the ball will be stable (not move).  In multivariable funciton the first order contion (F.O.C) is the case where gradient vector is zero (gradient vector is  vector of first derivative related to each choice variabe).

However, F.O.C condition is not sufficient condition. (why?) because as the example I mentioned earlier there are case where we can place the ball on curve and still maintain stable. That is the case of inflextion point and the point is not the optimal point.  Therefore we need the sufficient condition is needed. In mathematical the secondition is the second derivaitve. If the second derivative is positive then the point is minimum and if the second derative is negative the point is maximum. (Why?) Because the seconderative tell about the shape of the curve (convex or concave) that is to say if the curve is convex (U-Shape) then there will be  minimum and the concave (inverse U-Shape) will be maxmum. In multiple variable case the second order condition hast o be check by sign differential equation or Hessian Matrix.  

But if the Second-order condition is enough to say that a point is maxium or minimum.  Not necessary. because there are case where second derivative is zero that is neither positve or negative (imposible to show curvature) but the point still maximum  or minimum.  For example, consider function y=X^4. 

The point is that Necessary condition is not enough to say that a point is optimal. It must be added by sufficient condition. Sufficent condition alone is not enough to prove optimal point.  The two must be used complemntary.