Applied general equilibrium. An introduction (Q1625202)

This textbook is the second edition of the previous version issued by Springer in 2012. General Equilibrium (GE), founded by Leon Walras in 1870-th, is the cornerstone division of neoclassical economic theory (economics), which deals an economy as a system of interacting agents with the goal to describe process of creating value and its allocation between the agents. Walras, another founder of the neoclassical economics, William Jevons, and their followers intended to create economic theory by analogy with the natural sciences which means objectivity, provable, testability and usefulness. This ambitious program of scientizating the economic theory is not fulfilled completely till now, and this circumstance imposes increased requirements to justification of theoretical apparatus and verification procedures of applied models. The most achievement of contemporary economics is considered the mathematization of the microeconomic theory respectively behavior of main economic agents that are rational and independent (on assumption) consumers and firms, and the development of Walrasian GE in reductionistic version of Kenneth Arrow and Gérard Debreu (1954), which defined mainstream of contemporary Economics; see the well-known text-books of A. Mas-Colell et al. [Microeconomic theory. New York, NY: Oxford University Press (1995; Zbl 1256.91002)]. Currently, here there is a very developed mathematical theory of individual demand, but there is no theory of market (aggregate) demand which is, as well as aggregate supply of goods owning by consumers and produced by production sector, is the main object of GE. According the reductionistic principle of methodological individualism imposed to neoclassical economics in XX-th century, market demand should be considered as the sum of demands of individuals, independently maximizing their ``utilities''. Many reputable contributors of demand theory and GE (J. Hicks and other) believed that such a sum would be also rationalized by some ``collective utility function'', but it was shown in 1953 by W. Gorman (the reference is presented in the book) and clarified by P. Samuelson [The Quart. J. Economics 70, No. 1, 1--22 (1956)] that it would be true only in the unrealistic case of identical and homogeneous individual demands. And the wide-used notion of ``representative consumer'' is correct only in this case. This circumstance turned out shattering for Arrow-Debreu version of GE, respectively properties of equilibrium set which can be unrealistically complex and artificial (theorem ``Anything goes'' by Sonnenschein-Mantel-Debreu, see Mas-Colell et al., Section 17.E, and mathematical investigation of unrealistic equilibrium singularities in recent book of Yv. Balasko [Foundations of the theory of general equilibrium. 2nd ed. Hackensack, NJ: World Scientific (2016; Zbl 1350.91004)]). Another, holistic version of Walrasian GE was proposed by Gustav Cassel (1918, presented in the references). Here the integral Walrasian presentation of production system has been preserved, but individualistic theory of consumer's demand has been rejected, and market demand was introduced as origin object via dependence of prices on aggregate consumers' demand. The Cassel's GE model was elaborated in 1930-th by Abraham Wald [Econometrica 19, 368--403 (1951; Zbl 0043.35004)] who proved the existence and uniqueness of equilibrium in the modified Cassel's economy under a condition imposed on market demand, which was later re-opened by Samuelson and was called as Weak Axiom of Revealed Preference. This result was qualified by Arrow and Debreu, as well as their followers R. Solow and others, as ``economically illegitimate'', because they understood market demand only within individualistic methodology. More critics of the contemporary Economics, in particular, equilibrium model of Arrow and Debreu, are discussed, for example, in the papers by A. Kirman [J. Economic Perspectives 6, No. 2, 117--136 (1992); CESifo Economic Studies 56, No. 4, 498--535 (2010)], by V. Polterovich [Ekonomicheskaya Nauka Sovremennoy Rossii, No. 1, 46--66 (1998)], and by V. K. Gorbunov [Ekonom. Nauka Sovrem. Rossii 4(63), 19--36 (2013; Zbl 1310.91089); Doklady Mathematics 98, No. 2, 537--539 (2018; Zbl 1419.91448)]. Thus, the theoretical basis for construction applied economic models has deep failures, and these failures should be taken into account by writers and readers of applied general equilibrium (AGE) literature. Theoretical deficiencies are being not uncommon event in investigation of reality, and successive resolution of complex problems can be obtained with help of heuristic use of theoretically non-proved but empirically plausible techniques. Concerning market demand, its successful investigation with heuristic use of models and facts of the individual demand theory was demonstrated by Richard Stone, Angus Deaton and others. The similar means are used customary in AGE models, in particular, in the reviewed book. The book consists of seven sections. The first is Introduction, and the second represents an overview of GE theory in setting of Edgeworth, Arrow and Debreu. Significantly, discussing effect of very possible non-uniqueness of equilibrium prices (without unrealistic properties of individual demands), the authors notice that ``uniqueness is the common situation in empirical analysis'' (p. 17). Correspondingly, this heuristic reassurance of equilibrium uniqueness lie in the foundation of using individual demand model for representation of collective demand of some consumers' groups, as well as the market demand, in the AGE models. Special meaning for the rest of the book has a representation the linear (Leontief type) model of an economy. Customary such a model present an economy as a whole (holistic) object, and commodities of the economy are produced by one-product industries, but the authors call the producers as ``firms'' in accordance with Arrow-Debreu equilibrium model. Third section presents a simple ``Arrow-Debreu type'' AGE model which is ``a skeleton model upon which more in depth specification will be developed later'' (p. 35). Here the only economic agents are households-consumers and firms-producers, and goods are divided on consumed ones, intermediates and factors of productions. Specificity of the model is the dependence of the household's utility functions not only on consumed goods but on factors also, and one-product firms are presented via production functions of Constant Return to Scale (CRS) type representing `value-added' of production corresponding outputs. The authors write (p. 37), in accordance with the Arrow-Debreu model: ``The economic problem of the firm is to select the profit maximizing level of output given commodity prices $p$, factor prices $\omega$ and the available technology.'' However, the problem of firm's profit maximizing hasn't solution for one-product firms with CRS property, and further the firms-producers act as cost-minimizing agents generating conditional (Hicksian) factors demand. The equilibrium in the economy is the system of three groups of equations: (i) equilibrium on all markets for goods, (ii) equilibrium on all factor markets, and (iii) zero profitability for all firms (industries). The data for this system consists of information on income and payments of agents (transactions) and it is being presented as a social accounting matrix (SAM). This model is illustrated by a simple example with two consumers, two firms, and two production factors -- labor and capital. Correspondingly, four intermediate goods arise in the economy. The Appendix 2 to the section presents the computer code of the general algebraic modeling system (GAMS) for solving the simple example. Fourth and fifth sections describe more complicate AGE models. In the former section the government sector is incorporated in three variants. First, indirect taxes on the firms' outputs are introduced into the simple model of the previous section, then factor and income taxes are being added. At last, the model incorporates household's savings, investment, and the government budget constraint. The incorporating of investment, which is a dynamic phenomenon, in the AGE model, which is static, is fulfilled as an additional production activity whose output is `capital for tomorrow'. The final equilibrium model of fourth section consists of six groups of equations. There are two numerical examples in the section, and GAMS codes for their solution. Fifth section describes the most general AGE model with external (foreign trade) sector, labor market, `consumption technology' and welfare evaluation. This model takes into account possible partly employment, non-correspondence of consumers' demand with the national economy's supply, and it allows to investigate the effects of government policies to economy and society. Sixth section represents the problem of AGE models calibration on real statistical data accumulated in a SAM. An AGE model calibrating to a given SAM means the fitting parameters of the model under condition that the equilibrium values of the model variables coincide with the corresponding data presented in the SAM. This deterministic procedure complements the more powerful method for statistical estimation of parameters when the having data insufficient for the latter. Examples of calibrating utility and production functions of CES class in the presence of taxes are presented, as well as calibration of fixed coefficients technology and tax rates. Also in the section is presented the technique of updating a SAM for the next year when the new matrix is incomplete relative to the given. Seventh section gives an overview of GE theoretical origins, arising of applied equilibrium analysis, and contemporary advances of AGE modeling in real problems. In a whole, the book presents a rather large set of ADE models with a good explanation and demonstration of their use in complex problems of economic analysis and regulation of economies. Concerning theoretical failures of neoclassical Economics and GE model of Arrow-Debreu discussed above, they are overcame with conserving the presented models and its applied potential, except welfare analysis, in frame of holistic approach to investigation of market demand and general equilibrium founded by Cassel and Wald. Firstly, this approach is natural for investigation economy as a whole object, because it's basic elements-agents, which are households and independent firms (if such exist), are not sufficiently observable, and statistics represented in SAMs are aggregate respectively households and production units, which can be very complex and highly interrelated. Secondly, the simple AGE model, which is ``a skeleton model'', naturally to consider as a holistic GE model, changing ``one-product firms'' on economy's ``industries'' (that is being done factually in real applications) and introducing explicitly collective (for consumer classes) and aggregate market demand as initial objects instead of households with unrealistic properties of rationality and independence. Examples of such approach to GE are presented in V. Gorbunov's works of 2013 and 2018, cited above. Holistic theory of market demand with the rationality property is presented in his (Russian) books, particularly in [Demand of consumers: analytical theory and applications. Ulyanovsk: UlSU Press (2015), \url{http://www.rfbr.ru/rffi/ru/books/o_1945611}], and technique of the theory verification is presented in recent paper of V. K. Gorbunov and A. G. Lvov [Zhurnal Srednevolzhskogo matematicheskogo obshchestva, 21, No. 1, 89--110 (2019) (in Russian), \url{http://journal.svmo.ru/en/archive/article?id=1645}]. This theory rehabilitates GE model of Cassel-Wald with uniqueness of equilibrium and provides its developing as AGE model.