What are the benefits of using Constant Elasticity of Substitution (CES) function?

CES function has been used widely in economic especially in the analysis of monopolistic competition with large number of firms and each producing differentiated products. The model dated back to Edward Chamberlin (1936) and Joan Robinson (1933) in graphical analysis. The mathematical model has been elaborated by Lancaster (1975, 1979), Spence (1976) and Dixit and Stiglitz (1977). There are two types of such models. The first type is called “ideal of variety” where many consumers differed in their preference on differentiated products. The second type is the “love of variety” where a single consumer demanding varieties of differentiated products.  In general equilibrium
analysis (GE) or computable general equilibrium (CGE) it is known as Armington
assumption, according to Armington (1969). The Armington assumption assumed that the number of varieties per countries is fixed and it is quite different from monopolistic competition where the number of varieties in each country depends on free trade (endogenously determined in the model).

The term constant elasticity of substitution is referred to the constant rate of substitution between two products or factors at constant rate with regards to the ration of their own price. That is the rate is constant and is expressed by the following expression.

Knowing the history of CES function let take a looks and its mathematical form. The benefits of CES will be summarized at the end.  Let begin with two goods case. We begin with CES production function with two factors:  Labor (L) and Capital (K).

Where δ:factor share  and σ:elasticity of substitution between factors.

It can be shown that CES is also constant return to scale (CRS) that is homogenous of degree one and it is equivalent to Cobb-Douglas function of the case constant return to scale that is 

If we assume that the factor share are equal (this is equivalent to symmetric cases among each varieties) then,

By using (2) we can re-write (1) as:

By rising both sides of (3) to the power of  we obtain:

By monotonic property of homothetic function, let;

Where   

we finally got the simplified version as:

In international trade for differentiated products such as that of Krugman (1979) is in the following form is used:

In summary the benefits of CES are:

1. It can be used for many products or factor cases where each is differentiated.
2.  It is Constant Return to Scale (CRS) function so qualified for Euler’s Theorem that is each product or factor can be paid by the rate of it marginal product. CRS will lead to zero profit and exhausted distributed of income over its factors or products
3. Easy or composite price index and the use of Shepard lemma.

The whole article is based on Robert C. Feenstra (2004),”Advanced International Trade: Theory and Evidence” and Alpha C. Chiang (1984), “Fundamental Methods of Mathematical Economics”.

ផ្ការីកក្នុងហាងកាហ្វេ

Some keywords in economics articles

Axiom: is a conventional assumption that almost generally accepted as true. For example, demand curve slopes downward, individual maximizes their utility….
Assumptions: are any set of hypothesis used to derive the claim, propositions, theorem. Usually, the assumption can be tested in emprical papers where theoritical economics base on the assumption to reach conclusion.
Claim: is a small theoritical result.
Proposition: is usual theoritical result. This mean the conclusion you conclude from the model is not very big suprising. In case, the result of your conclusion is one of the core ideas that change the views in the field it is name Theorem.
Theorem:is a big theoritical result.
Corollary: is result that can be derived from another result easily (proposition, theorem, claim)
Lemma : is result needed to help to prove another result (claim,proposition,theorem)
Remark: is the point which you should pay attention but which is not the main result for the proove of your claim, proposition or theorem.

Source: My observation on many articles

Nagoya University, School of Economics Approach 2010

There are three Cambodian students at School of Economics, Nagoya University. Listen to Cambodian student’s opinion….
Nagoya University, School of Economics Approach 2010

Visit: http://www.soec.nagoya-u.ac.jp/htm/abroad/approach/information/acceptance.html

CAPITALISM: A LOVE STORY – TRAILER

Explanation of some khmer words

stac tran territorial resposibility over many provinces.
chaovay sruk territorial resposibility over one province.
yomraj is minister of justice.
chakrei is minister of army.
kralahom is navy and foreign trade minister
veang is minster of palace.

(Source:David Chandler (2000),” A History of Cambodia”, pp.111.)

Islands in Cambodia Territory (Sea sovereignity)

Do you know how many islands located in the sea territory? Do you know how many island is inhabitated?

(http://www.kohrong-island.com/)

Zeitgeist Addendum: Just a view of radicalism against capitalism

It is just only a view by radicalism. In development economics this is classified as dual development group. In deed, market also brings efficiencet and government role is also fail not only the market. The compromise of both is best.

Waitting for Graudation Day

I am waiting for graduation day which will be on the 25th of March 2009. Another step I have done but there still a next step to go……(^.^)

Love of a life time 一生所愛(a plot in a Chinese Odyssey)

Phatcheay Bondole Jet by Sinn Sisamouth

Happy Birthday Dear!

Darling, I love you …! May all your wishes come true.

An article to understand the subprime the root of financial crisis in US

The story of financial crisis began with the two stated owned companies Fannie Mae and Freddie Mac morgage companie (housing-mogarge) which provide loan to some subprime borrower since this twin companiese depend much from government subsidy making it less cost in raisng it fund and its went beyond its role of faciliating liquidity in housing morgage to buying bond and securities (providing loan).

Also noted that the bank play role in financial credit. Since bank need money for providing loan. Where bank get deposit? Well from interbank market which include central bank as main player. Since bank borrow from other bank it has to pay for its borrow (interest). If the interest is high then when it provide loan to borrower which included companiese and household the interest rate must be higher.

First, the rates on loans paid by many consumers (adjustable-rate mortgages, for example) and companies are set with reference to the money markets. Higher rates for banks mean higher rates for everyone. Second, if the markets are blocked for more than a week some companies may find it hard to get any finance at any price. That could mean more bankruptcies and job losses. Third, more banks could go bust if the blockage continues, making investors even more risk-averse. The downward spiral would take another turn.

This is one reason for Bush government to interven with bail-out progarm to support bank credit crunch and all main companies in U.S from bankrupt. Aslo avoiding deposit queuing to withdraw their deposit- something about rebuilding belief and new expectation.

For more detail on this point I would suggest the two links:

http://www.economist.com/finance/displaystory.cfm?story_id=11751139

http://www.economist.com/finance/displaystory.cfm?story_id=12342237

 the following article explain what is “subprime” means?

Specialist lenders:Home run

Serving subprime borrowers requires specialist skills

THE word “subprime” may now send shudders down bankers’ spines. But a number of listed lenders that specialise in making loans to people with poor or no credit histories are proving that money can be made from even the riskiest customers. The way they operate may explain why mainstream lenders find it hard to descend the credit ladder.

Last month, Provident Financial, a British lender to what it calls “non-standard” borrowers, and International Personal Finance (IPF), a spin-off from Provident that operates in eastern Europe and Mexico, both issued relatively upbeat trading statements. Both reported growth in customer numbers, as other lenders have drawn in their horns. More impressively, they also said that customer arrears had remained stable.

Specialist lenders are not immune to the effects of the crisis, of course. Funding concerns have roiled the share price of Cattles, another British lender: it is seeking a banking licence so that it can gather deposits. The severity of the economic downturn will set a stern test of lenders’ credit management. But they have a number of things in their favour.

One is the frequency of their contact with customers. Both Provident Financial and IPF collect loan payments from borrowers’ homes each week, giving them instant information if a customer is struggling. Another is the incentive scheme they operate for their agents, the bulk of whose earnings is based on how much they collect. “It is better for agents to lend less and collect more than to lend more and collect less,” says Christopher Rodrigues, IPF’s chairman. IPF’s employees habitually offer less money to borrowers than the firm’s automated credit system says they can.

Mainstream lenders cannot easily follow this approach. IPF and Provident loan out smaller sums of money (the equivalent of a few hundred dollars, typically) at shorter durations and higher rates. Banks do not have teams of agents to knock on people’s doors. Specialists make a virtue of lending to people who cannot get credit elsewhere, because that means they are not loaded up with debt. But that is the point. The shift in Cattles’ business model over the past few years, to bigger loans and remote servicing, has increased its risk profile, says Robert Self, an analyst at Credit Suisse. When serving subprime borrowers, acting like a bank can be a hindrance, not a help.

Source:http://www.economist.com/finance/displaystory.cfm?story_id=12609781

Want to Learn how to Dance?

Rom Vong

Cha cha cha

Madison

For other dance follow the above link.

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…..