Q1. Define, explain and illustrate the following terms:
(i)Gross substitutes
(ii) Diagonal dominance
(iii) Local uniqueness
(iv) Global uniqueness
(v) Local stability
(vi) Global stability
(iii) Tatonnement process
Answer
(i)Gross substitutes
The gross substitute concept was first introduced by Mosak in 1944 in the context of pure trading model. Good A is a gross substitute for good B if an increase in the price of A causes an increase in demand for good B.
Goods i and j are gross substitutes at price p and income M if1
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1.http://elsa.berkeley.edu/users/webfac/dellavigna/e101a_f05/lect1005.pdf
(ii) Diagonal dominance
Diagonal dominance means in a matrix if the magnitude of the diagonal entry of a row is equal to or larger than the sum of the magnitudes of all other (non-diagonal) entries in that row. Formula for diagonal dominance is as follows:
where aij is the entry in the ith row and jth column.
If the above definition has a weak inequality ,hence it is called weak diagonal dominance ,whereas if it uses strict inequality [>] it is called strict diagonal dominance.
The above definition uses row sums it is called row diagonal dominance . If it is uses column sums it is called column diagonal dominance.
(iii) Local uniqueness
An IVP is said to have local uniqueness property if for each and for any two solutions y1 and y2 of IVP defined on intervals I1 and I2 respectively, there exists an open interval containing the point x0 such that
The local uniqueness is a result of the uniqueness of Banach fixed point
(iv) Global uniqueness
An IVP is said to have global uniqueness property if for each and for any two solutions y1 and y2 of IVP defined on intervals I1 and I2 respectively, the equality y1(x) = y2(x) holds for all
(v) Local stability
Local stability is a ability of an ecological or taxonomic unit to remain stable or unaffected by short term disturbances.
(vi) Global stability
The term stability is used for ecological stability. When an ecological or taxonomic unit is able to remain unaffected by big disturbances like habiat ,then this ability of the ecological or taxonomic unit is called Global stability.
(vii) Tatonnement process
The tatonnement process is a model for investigating stability of equilibrium. When auctions are conducted prices are announced then prices keep moving up and down as per the demand and supply on the given price. The process of finding the final equilibrium during this price movement is called tatonnement process.
Q2.: Read, summarize and think about: L. McKenzie (2008), “Gross substitutes”, (in) The New Palgrave Dictionary of Economics, 2nd Edition.
Answer : L. McKenzie (2008) used the gross substitution concept to establish the stability and uniqueness for a dynamic adjustment system of the [rices. The author also applied this concept in case of disequilibrium caused by the changes in demand. The concept of gross substitute was introduced by Mosak in 1944. But it is widely applied with the definition of Morishima (1964). The equilibrium price under uniqueness is unique up to multiplication by a positive number. The author said weak fross substitute assumed with connectedness results in uniqueness. While the weak gross substitute assumed without connectedness does not result in uniqueness.The comparison of equilibriums after changes in demand was started by Hicks in 1939. But the fact is that Hicksian theorem holds good in local stability( Local stability is a ability of an ecological or taxonomic unit to remain stable or unaffected by short term disturbances).
The global concept of comparative statics in this context was given by Marishima in 1964. Because weak gross substitute leads to local stability of the tatonnement for with or without a numeraire price adjustment models. The author says that there is an advantage of gross substitute assumptions in the local stability. The results of gross substitution assumption are useful in global stability (When an ecological or taxonomic unit is able to remain unaffected by big disturbances) only.
In tatonnement(The tatonnement process is a model for investigating stability of equilibrium. When auctions are conducted prices are announced then prices keep moving up and down as per the demand and supply on the given price. The process of finding the final equilibrium during this price movement is called tatonnement process) theory prices are revised according to the excess demand but no trading happens till the equilibrium is reached. If the trading happens at market prices then the stability of the adjustment prices exists for a pure exchange economy. The critical fact is that a trading at market price results in second order effects on excess demand. The gross substitution assumption is not appropriate for production sectors while considering the demand for factors. As the production sector consists a finite number of firms with a strictly convex production frontier. Thus this article explains the price equilibrium with the help of different concepts like gross substitution, local stability global stability and tatonnement process. It assumed gross substation effect while establishing the stability and uniqueness in price equilibrium.
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