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)