appendix a  solutions to the chapter questions

... = (∂1
, , ∂n
) is the gradient of
The Sobolev space H1,p(Ω) is defined to be the completion of the set {
Î C∞(Ω): ||
||1,p<∞} with respect to the norm || · ||1,p In other words, u Î H1,p(Ω) ... proof is similar to Lemma 2.2 4 The existence of solutions In this section, we introduce the main work of this paper, to prove the existence and the uniqueness of solutions to the nonhomogeneousA- ... weakly in X and the weak limit x0 is inde-pendent of the choice of the subsequence of xi Then xiconverges to x0 weakly in X Proof Suppose that xidoes not converge to x0weakly in X Then, there exist

Ngày tải lên: 20/06/2014, 22:20

... from2.26 and the condition ofTheorem 2.2that δ t ≥ 1 2−E0p−1/4 C3 1− e 1−p/4 Therefore, By virtue of the continuity of Jt and the theorem of the intermediate values, there is a constant ... where we have used2.31 and the fact that ψ1is the eigenfunction of the problem1.1–1.4, B1and B2are denoted as the expressions in the first and the second parenthesis, respectively From2.32, ... consider the following problem: ∂2u ∂t2  k ∂u a ∂u where a ≥ 0, b ≥ 0, a  b  1, and k > 0 are constants, Δ is the Laplace operator with respect to the space variables, and ∂/∂n is the outer

Ngày tải lên: 21/06/2014, 11:20

... of confining the marginal utility theory to the inves-tigation of consumption and of simple exchange, Walras went far beyond the work of its other initiators by using it to analyze the behavior ... the one presented in the edition of the Eléments that Pareto studied in the 1890s Pareto believed that the freely competitive tatonnement process featured in that model accurately described the ... “hypothesis that no scientific mind will hesitate to concede to the theoretician” (1895, p 630) After attainment of that price, the market day in his model is nevertheless in disequilibrium if the

Ngày tải lên: 06/07/2014, 02:20

... increase is given by the loss of customers to the market, not to the individual firm, since customers will return to the preferred firm when the other firms have also raised their price Thus for ... proposal “to re-write the theory of value, starting from the conception of the firm as a monopolist” (J Robinson, 1969, p 6); the aim of the book was to extend the marginal technique, enriched by the ... focus on the interdependence of firms; and (2) the assumption that the subjective demand curve, which expresses the expectations of the producers as to the relationship between the price they charge

Ngày tải lên: 06/07/2014, 02:20

... misleading to present the process as just a refinement or perfection of earlier theory To see this, consider the elements on which the price theory of the neoclassical synthesis rested: 1 The organizing ... value to take account of it Hicks and Allen saw this as their task They reformulated the theory of the consumer in terms of marginal rates of substitution and used the theory to analyze the relationship ... kept their prices constant and the other to that in which they matched any price cut made by the firm concerned (the first would be much more elastic than the second) He used this to analyze the

Ngày tải lên: 06/07/2014, 02:21

... generally, turned their attention to “generalising The General Theory to the long period.” (They were later joined by Trang 5Kaldor and then Luigi Pasinetti.) They reached back over the neoclassical ... interest, now the price that equalized the demand for and supply of money, ruled the roost; the General Theory version of the natural rate of interest, the mec (it should have been the mei), had to measure ... flexible than money wages in the long period If the economy were not saving the right amount to allow the provision of the accumulation needed to keep the economy on g n, the gap between planned investment

Ngày tải lên: 06/07/2014, 02:21

... “aspired to the name of economic theory” had to be (i) capable of giving unity to economic investigations of many different areas, (ii) relevant to the problem of control, (iii) relate to institutions ... of the application of instinct theory to the issue of labor unrest (Parker, 1920) Parker argued that the Trang 6“stabilizing of the science of psychology and the vogue among economists of the ... taken from Veblen with those from others (Rutherford, 2001) At the most basic level, the most important element in the institutionalist approach is the conception of the economic system as a set of

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... progress on the main problems set for the theory The theory had to be reinvented regularly in re-sponse to problems, and applications of the theory are often tenuous inasmuch as the theory is not ... depth The resulting dynamic is best seen historically The topic is vast In order to keep this presentation manageable, this chapter focuses on the main aspects of general equilibrium theory and the ... men’s tastes and the obstacles to satisfying them Our study includes, then, three distinct parts: 1° the study of tastes; 2° the study of obstacles; 3° the study of the way in which these two elements

Ngày tải lên: 06/07/2014, 02:21

... yet another example of an emperor who has no clothes (Kirman, 1989)? 25.6 RESPONSES TO THE FAILURE OF GE THEORY There have been a number of responses to the apparent failure of GE theory to live ... to appreciate the immensely wide range of possible applications of the idea of a Nash equilib- rium, it also freed them of the need they had previously perceived to tie down the dynamics of the ... of economic theory. 25.4 BACK TO WALRAS We have described the Arrow and Debreu paper as the capstone of the Walrasian program, but we must now try to appraise their achievement from the vantage

Ngày tải lên: 06/07/2014, 02:21

... converts to their view that monetary policy is the principal cause of cyclical fluctuations with the magisterial Monetary History of the United States (1963) The tour de force was their account of the ... technical progress (total factor productivity) His conclusion that total factor productivity was overwhelmingly the dominant factor seemed to many to be counterintuitive By the early 1960s, intellectual ... on the one side, and output and prices, on the other, became intensively methodological In the end, the war was fought to a draw in the sense that neither side won many converts Yet, under the

Ngày tải lên: 06/07/2014, 02:21

... government to watch over the expansion of the revenue of the kingdom’s property; not to put any obstacles in the way of industry; and to give the people the opportunity to spend as they choose ... produced? Is there not the earth itself, its forests and waters, and all other riches, above and below the surface? These are the inheritance of the human race, and there must be regulations for the common ... We find here no deep theory of governmental behavior and no serious analysis of the ability of government to carry out the tasks ascribed to it by these authors There is, rather, an assumed natural

Ngày tải lên: 06/07/2014, 02:21

... 2 Journal of Inequalities and Applications equations These results can be used to study the basic properties of the solutions to the nonhomogeneous A-harmonic equations Now, we first introduce ... α s,Ω,w2 3.24 Now, we have completed the proof of Theorem 3.7 Similarly, if setting w1 x following theorem w2 x w x and λ in Theorem 3.7, we obtain the Theorem 3.8 Let u ∈ D Ω, Λl be an A-harmonic ... and if Qi ∩ Qj / ∅, then there exists a cube R (this cube does not need be a member of V) in Qi ∩ Qj such that Qi ∩ Qj ⊂ NR Theorem 2.7 Let u and v be a pair of solutions to the nonhomogeneous...

Ngày tải lên: 21/06/2014, 20:20

... ate the forbidden fruit of the tree of knowledge and asserted the right to choose for themselves, they were cast out of the world of abundance into scarcity; to “eat bread in the sweat of their ... parallel with the female blame tradition of the Greek Pandora myth (Norris, 1999) The dominant thesis is, however, the challenge to divine authority by the beneficiaries of the abundance of the Garden ... in the myth, however, the system contains elements of exchange Prometheus aggregates the bones under a layer of fat in one pile, and the lean meat covered by the stomach and tripe in the other...

Ngày tải lên: 06/07/2014, 02:20

... to prove the historical continuity of economic thought and thereby refute the Schumpeterian thesis in its totality, we will also discuss the impact of the more serious challenges to the gap thesis ... Qabus Nameh: To benefit the inhabitants of the west they import the wealth of the east and for those of the east the wealth of the west, and by doing so become the instruments of the world’s civilization” ... led to rejection of the thesis These demonstrations have included the contributions of medieval Muslim scholars to the history of economics during the five centuries of the alleged Great Gap, the...

Ngày tải lên: 06/07/2014, 02:20

... unwilling to put their sole faith in the self-equilibrating forces of the marketplace in order to achieve wealth and growth On the other hand, as many argued, too much interference in the laws ... seldom these authors refer to a particular state interest when they put forward their policy recommendations Certainly, it is the aim of these writers to find means and ways to enrich the nation ... called the L G MAGNUSSON 56 theory of foreign-paid incomes,” the “labor balance of trade theory,” or the export of work theory.” Instead of holding on to the dogma that a country should strive to...

Ngày tải lên: 06/07/2014, 02:20

... order to buy food and to reconstitute their capital; the circulation process has thus allowed these two classes in the end to get what they had in the beginning What about the productive class? They ... between the landlord and the farmer, but Quesnay did not introduce any specific revenue for the farmer In his papers, farmers are supposed to pay both the taxes (whether to the state or to the Church) ... furniture, clothes, and the like Then, the sterile class spends half of the money received (150 livres) to buy food and raw materials from the productive class; the other 150 livres is used to reconstitute...

Ngày tải lên: 06/07/2014, 02:20

... aim to control the seas and to dominate the trade of the “commercial world” (essentially the sea-borne trade of Europe) Petty estimated the requirements and the costs with striking accuracy In the ... after all, the recoinage was carried out, and so on – there was no immediate stimulus to take the argument further Other, noneconomic, issues took center stage There were advances in the following ... encrease, there must arise a great superfluity from their labour beyond what suffices to maintain them They have no temptation, therefore, to encrease their skill and industry; since they cannot...

Ngày tải lên: 06/07/2014, 02:20

... activity by transmitting the total rent due to the proprietors of land for the current use of that factor The income thus provided will enable the proprietors to make the necessary purchases of ... except through the labour of the Cultivator but the cultivator has need of the Proprietor only by virtue of human conventions and the civil laws (Meek, p 128) Finally there are the artisans, ... approach to the study of political economy was through the examination of history and ethics The historical analysis is important in that he set out to explain the origins of the commercial stage The...

Ngày tải lên: 06/07/2014, 02:20

... had to be paid sufficient to prevent it being used for another crop The cost of the land did enter into the cost of production when where there were many agricultural products, rather than the ... designed his value theory to produce a theory of relative price, on the basis of adding up the per-unit costs of the labor, capital, and land inputs into production, the valuation of the inputs being ... lived in the British Isles They read the literary reviews of the day, and there was an active circulation of pamphlets They met at the Political Economy Club and in other societies such as the [Royal]...

Ngày tải lên: 06/07/2014, 02:20

... custom, and of pecuniary gain,* to tempt him to the common practice S J PEART 142 AND D M LEVY * [The law declares that the children of slaves are to follow the fortunes of the mother Hence the ... barrister Neither will the diminished profits of bricklayers, to pursue the profession of the bar, and by his competition reduce the gains of the profession to their proper level This may be the case, ... selection stops at the edge of sympathy is the beginning of the eugenics movement As Greg (1874) put it, sympathy blocked the “survival of the fittest,” and therefore these sentiments ought to be suppressed...

Ngày tải lên: 06/07/2014, 02:20