Thursday 22 January 2015

General Equilibrium - Illustration (Cobb-Douglas)

By Aleesha Mary Joseph

Let's begin with an easy one to understand the concept of General Equilibrium.

Suppose, U1(X11 , X12 ) = X11 X12 and U2(X21 , X22 ) = X21 X22 .

Let (e11 , e12 ) = (10,0) & (e21 , e22 ) = (0,10).

Normalize P2 to be equal to 1.

Then note that individual 1’s income M1 = 10*P1 + 0*1 = 10P1.
Similarly individual 2’s income M2 = 0*P1 +1 0*1 = 10.

Since the utility functions are cobb douglas, demand functions can be derived by equating MRS with P1/P2 and substituting the relevant expression in the budget constraint.

The demand functions so derived will be as follows:
X11 = M1 /2P1 = 10P1/2P1 = 5

X12 = M1 /2P2 = 10P1/2P2 = 5P1 (Because P2 is normalized to 1)

X21 = M2 /2P1 = 10/2P1 = 5/P1

X22 = M2 /2P2 = 10/2P2 = 5 (Because P2 is normalized to 1)

The Market clearing condition says

X11 + X21 = e11 + e21

5 + 5/P1 = 10. 

On solving this we get P1 = 1. Hence the competitive equilibrium price ratio P1/P2 = 1

Convince yourself that the same price ratio will clear the market clearing equation for good 2 as well ie X12+ X22 = e12 + e22 .

Substituting P1 =1 in the demand functions, we get the competitive equilibrium allocation
As (X11 , X12 ) = (5,5)
     (X21 , X22 ) = (5,5)

With competitive equilibrium price P1/P2 as 1.

The articles to follow will cover min/max utility functions and lexicographic preferences. Stay tuned.

(Aleesha Mary Joseph graduated from St. Stephen's College in 2013. She is currently pursuing MA in Economics at Delhi School of Economics)

Sunday 18 January 2015

General Equilibrium

By Aleesha Mary Joseph

Hi friends,

This blog is already rich with advice for cracking DSE entrance. I would just like to emphasize on one thing i.e, doubt clearance. Because it is disheartening to see a question in the examination which you had marked as doubt in your preparatory material. It can even cost you a place in DSE.

No doubt is silly. If you find it hard to ask your teacher, then 

1)  Ask your friends or classmates. 

2)  Mail it to anyone who you think would know the answer. Doesn't matter even if the person is someone whom you have never met {may be you can message current DSE students (list available on DSE’s website) via Facebook}. 

3)  Post your questions on groups meant for economics entrance preparations. Even if you think your questions are very trivial, just post it, because there will definitely be many other students with the same doubt but are just shying away from posting the same. One such group can be found at http://economicsentrance.in/ (Group by Amit Goyal)

 Whatever the way is just make it a point to clear all your doubts before the D-day!!

For many students the general equilibrium(GE) section is scary and that is mostly because of their lack of knowledge on how to approach the GE problems. Trust me once you look at the technique GE becomes your cup of tea! 

I believe the following material on GE problems may be of some help to students who don’t attend coaching classes. I have skipped many steps. But feel free to ask for any further explanations. The material was made assuming that you already have some basic knowledge about GE set up. Please refer Nicholson & Snyder for conceptual clarity. The best way to master GE problems is by making your own problems with all sorts of utility functions and trying out in square and rectangular edgeworth box. If you go through the past year question papers you will get an idea of the various kinds of utility functions that the DSE faculty like. Most questions can be answered once you find the contract curve and competitive equilibrium allocation. So try to find the same for all sorts of weird looking combinations of utility functions and endowments: P Enjoy practicing and GE problems will be a cakewalk for you in the exam. Few questions can be found at http://econdse.org/pghosh-001/  :) 

General Set Up

Suppose individual 1’s utility function is represented by U1 (X11 , X12 ) and for individual 2 it is U2 (X21 , X22 ). 

Let the endowment for individual 1 be (e11 , e12) and for individual 2 it is (e21 , e22).
To find the competitive equilibrium allocation following steps are recommended:

1)  Find individual demands for good 1 and 2. ie X11 , X12  , X21 and  X22 . These quantities will be a functions of P1 / P2 . (or will be functions of P1 alone if we normalize P2 to be 1)

2)  Then equate X11 + X21 = e11 + e21 for this is the market clearing condition for good 1. i.e the total quantity of good 1 being demanded by individuals 1 & 2 should be equal to the total supply of good 1 available in the economy.

3)  On solving the above equation we will get the competitive equilibrium price ratio P1 / P2 .

4)  By Walras’s law the equilibrium price ratio obtained above will clear the market for good 2 as well.

General Equilibrium problems with step by step solutions will be covered in the articles to follow. Stay tuned.

(Aleesha Mary Joseph graduated from St. Stephen's College in 2013. She is currently pursuing MA in Economics at Delhi School of Economics)

Monday 5 January 2015

Let's bell the CAT

By Suhani Popli

It was nearly a year and a half ago, when I was one of those many final year kids, juggling with the different ‘options’ that would help them build a future – that I decided to pursue the MBA degree. A dilemma that exists in most of our minds is that between a management degree from abroad versus that from within India. There is no end to this debate, but since I belong to the latter group, I would describe the process of getting through that in this piece of writing.

There are different exams held for the admission to a management institute in India, the popular ones being the CAT, the XAT, the NMAT, IIFT, exams specific to colleges, and so on. A gateway to the premier Business Schools of the country, the CAT, as an exam, does not really need an introduction, so I’ll skip that part. I’d rather use this space telling you what the different phases in the process of doing this exam are.

      1.  The Initial Phase

As one would expect, there are different ways to go about this. People can choose to do absolutely nothing, or study on their own selves, or join a coaching institute. If in the second category, I would suggest an aspirant to pick up study material from online/reliable offline sources. Trust me there is no dearth of either. However (and this opinion is strictly personal), I have always felt that the CAT requires not only a basic and complete knowledge of the relevant material for quantitative, logical and verbal ability, but also a grasp on the tips & tricks that could help accelerate one’s speed to solve.

My guides, both in terms of the preparation material and the teachers, came from the coaching institute I was enrolled in. And I genuinely believe that someone teaching me a particular concept would make it clearer to me, as compared to my reading it from a book. However, one is his/her own judge of what works best for the purpose of learning. Hence, the most important part in this phase is for an aspirant to pick the category that suits best.

Incase one does plan to join a coaching institute – honestly, there isn’t much of a difference between the names that exist in the market today. All of them have material and test series which are comprehensive. Thus, I would suggest to the aspirants to take advice from their seniors who must have attended such classes. Based on what they say (take views of students from at least two different places), make the final decision.

      2.  The Preparation Phase

Personally, my preparation was at the coaching institute I joined. However, for almost everyone I know, it is actually during the summer vacations when people put in their best effort to study. Personally, if I look back, I see that those two months were quite intense, and it was my coaching faculty who guided me through most of what I did. What is important in this phase is to identify the areas where one needs work and hence polish those well. There is no key to this, but to practise – regularly and efficiently.

As the end approaches, it becomes extremely significant to practise as many mock tests as possible. Also, practicing the CAT papers of the past five to ten years can be extremely useful. This serves a dual purpose – one of making the aspirants familiar to the exam pattern and the other of helping them learn how to manage time. Taking a step forward, it is more important for one to analyze mistakes post a mock test. Though this part is more time consuming than taking the exam itself, it ensures the avoidance of the same mistakes in future.

      3.  The D-Day

First, different myths float when one tries to choose a date – of the exam being easier on weekdays than on weekends, of taking the exam on a particular day, etc. – all of this, yes, ALL of it is absolute crap. Nothing such is true. The exam is such that there is a large common pool of questions designed each year, and questions are pulled out from this pool everyday in random combinations to form a question paper. Hence, one can never predict the difficulty level of any particular day or time slot.

Second, aspirants should make sure they look at all the 30 questions in each section. At various instances, the questions in the beginning tend to be difficult compared to the ones later in sequence. Thus getting stuck at initial questions can lead to very negative outcomes.

Third, keep calm and get done with the exam.

      4.  After the declaration of the results

Once the results are declared, successful aspirants get calls from the different business schools. The last step in the process entails preparation for the GD/WAT processes and the PI – i.e. the Group Discussion, the Written Ability Test and the Personal Interview rounds. The key to succeeding here would be to know two things well – one’s own resume and the current affairs. Infact, reading the newspaper is a habit that one should try and pick up early – since it also is helpful in the preparation of the verbal section of the CAT.

Like conventional CAT preparation pieces, I don’t want to end this article by stating a list of which business schools are the best in the country. One can easily Google and find that out. Rather, I would like to put forth the idea that it is important to think through the direction in which life is taking one. And whether it is a job, a master’s degree or an MBA – make an informed choice, one that you really want to do! All the best :)

Suhani Popli graduated from St. Stephen's College in 2013. She scored 98.2 percentile in CAT 2012 and is currently a student at IIM Kozhikode.