40:
1652:…market demand functions need not satisfy in any way the classical restrictions which characterize consumer demand functions… The importance of the above results is clear: strong restrictions are needed in order to justify the hypothesis that a market demand function has the characteristics of a consumer demand function. Only in special cases can an economy be expected to act as an ‘idealized consumer.’ The
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1722:, because it seems to imply that almost any observed pattern of market price and quantity data could be interpreted as being the result of individual utility-maximizing behavior. In other words, Sonnenschein–Mantel–Debreu raises questions about the degree to which general equilibrium theory can produce testable predictions about aggregate market variables. For this reason,
1845:
be zero as well. This means that there is one redundant equation and we can normalize one of the prices or a combination of all prices (in other words, only relative prices are determined; not the absolute price level). Having done this, the number of equations equals the number of unknowns and we have a determinate system. However, because the equations are
1873:, or the analysis of how the equilibrium changes when there are shocks to the economy, can still be relevant as long as the shocks are not too large. But this leaves the question of the stability of the equilibrium unanswered, since a comparative statics perspective does not tell us what happens when the market moves away from an equilibrium.
1745:. However, Abu Turab Rizvi comments that this result does not practically change the situation very much, because Brown and Matzkin's restrictions are formulated on the basis of individual-level observations about budget constraints and incomes, while general equilibrium models purport to explain changes in aggregate market-level data.
1562:
restrictions that could be placed on a market excess demand function. He conjectured that the answer was "yes," and made preliminary steps toward proving it. These results were extended by Rolf Mantel, and then by Gérard Debreu in 1974, who proved that, as long as there are at least as many agents in
1844:
In mathematical terms, the number of equations that make up a market excess demand function is equal to the number of individual excess demand functions, which in turn equals the number of prices to be solved for. By Walras's law, if all but one of the excess demands is zero then the last one has to
1918:
The literature on the
Sonnenschein–Mantel–Debreu results generally does not distinguish between the market demand curve for a single commodity, and the aggregate demand curve for an economy with many different commodities. The results have been proven to hold for any market in which there are at
1606:
that consumers assign to a commodity will always be exactly proportional to the amount of the commodity offered; for example, one million oranges would be valued exactly one million times more than one orange. Furthermore, Alan Kirman and Karl-Josef Koch proved in 1986 that the SMD theorem still
1611:
preferences, and the distribution of income is assumed to be fixed across time and independent of prices. The only income distribution that is not permissible is a uniform one where all individuals have the same income and therefore, since they have the same preferences, they are all identical.
1897:
can be understood as the fact that the excess demand only depends on the budget set itself. Hence, homogeneity is only saying that excess demand is the same if the budget sets are the same. This formulation extends to incomplete markets. So does Walras's law if seen as budget feasibility of
1691:
for the commodity, and no trades take place until equilibrium prices have been reached. This may not be realistic, but it is mathematically tractable: it makes price movements for each commodity depend only on information about that commodity. Unfortunately, as the SMD theorem shows,
990:
of an economy as a whole. This means that demand curves may take on highly irregular shapes, even if all individual agents in the market are perfectly rational. In contrast with usual assumptions, the quantity demanded of a commodity may not decrease when the price increases.
1597:
In the wake of these initial publications, several scholars have extended the initial
Sonnenschein–Mantel–Debreu results in a variety of ways. In a 1976 paper, Rolf Mantel showed that the theorem still holds even if the very strong assumption is added that all consumers have
1549:
for widely used equilibrium models, on the basis of the assumption that individuals are utility-maximizing rational agents (the "utility hypothesis"). It was already known that this assumption put certain loose restrictions on the excess demand functions for individuals
1627:
to prove that the
Sonnenschein–Mantel–Debreu results do indeed apply to the market demand curve. This means that market demand curves may take on highly irregular shapes, quite unlike textbook models, even if all individual agents in the market are perfectly rational.
1660:
In other words, it cannot be assumed that the demand curve for a single market, let alone an entire economy, must be smoothly downward-sloping simply because the demand curves of individual consumers are downward-sloping. This is an instance of the more general
1529:
is important in general equilibrium theories, because it acts as a signal for the market to adjust prices. If the value of the excess demand function is positive, then more units of a commodity are being demanded than can be supplied; there is a
1849:
there is no guarantee of a unique solution. Furthermore, even though reasonable assumptions can guarantee that the individual excess-demand functions have a unique root, these assumptions do not guarantee that the aggregate demand does as well.
1424:
1161:
1584:
These inherited properties are not sufficient to guarantee that the excess demand curve is downward-sloping, as is usually assumed. The uniqueness of the equilibrium point is also not guaranteed. There may be more than one price
1902:. Other works expanded the type of assets beyond the popular real assets structures like Chiappori and Ekland. All such results are local. In 2003 Takeshi Momi extended the approach by Bottazzi and Hens as a global result.
1538:. The assumption is that the rate of change of prices will be proportional to excess demand, so that the adjustment of prices will eventually lead to an equilibrium state in which excess demand for all commodities is zero.
2228:, pp. 105–106, "These (by now classical) results have been widely interpreted as pointing out a severe weakness of general equilibrium theory, namely its inability to generate empirically falsifiable predictions."
967:. This implies that the excess demand function does not take a well-behaved form even if each agent has a well-behaved utility function. Market processes will not necessarily reach a unique and stable
1809:
1619:
itself, and not just the excess demand curve. But in 1982 Jordi Andreu established an important preliminary result suggesting that this was the case, and in 1999 Pierre-André Chiappori and
1774:
and Alan Kirman, to abandon the project of explaining the characteristics of the market demand curve on the basis of individual rationality. Instead, these authors attempt to explain the
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1227:
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1047:
1558:), and that these restrictions were "inherited" by the market excess demand function. In a 1973 paper, Hugo Sonnenschein posed the question of whether these were the
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There are several things to be noted. First, even though there may be multiple equilibria, every equilibrium is still guaranteed, under standard assumptions, to be
1514:
1444:
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function satisfying Walras's Law can be locally seen as the aggregate market demand of some economy, even when the distribution of income is imposed a priori."
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829:
1767:. As long as a macroeconomic growth model assumes an excess demand function satisfying continuity, homogeneity, and Walras's law, it can be microfounded.
2487:
1703:' auction model requires that the price of a commodity will always rise in response to excess demand, and that it will always fall in response to an
1665:, which deals with the theoretical difficulty of modeling the behavior of large groups of individuals in the same way that an individual is modeled.
1563:
the market as there are commodities, the market excess demand function inherits only the following properties of individual excess demand functions:
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1756:
2822:
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2358:
2692:
Kirman, Alan P.; Koch, Karl-Josef (1986). "Market Excess Demand in
Exchange Economies with Identical Preferences and Collinear Endowments".
2998:
1857:. However, the different equilibria are likely to have different distributional implications and may be ranked differently by any given
2955:; Shafer, Wayne (1982). "Chapter 14 Market demand and excess demand functions". In Arrow, Kenneth J.; Intriligator, Michael D. (eds.).
2106:
1919:
least as many agents as there are commodities, so it trivially follows that they apply to any non-empty market for a single commodity.
1898:
excess-demand function. The first incomplete markets
Sonnenschein–Mantel–Debreu type of result was obtained by Jean-Marc Bottazzi and
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2640:
1831:
1426:
is a set-valued function with closed graph that satisfies Walras's law, then there exists an economy with households indexed by
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890:
2519:
Chiappori, Pierre-André; Ekeland, Ivar (1999). "Aggregation and Market Demand: An
Exterior Differential Calculus Viewpoint".
1813:
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228:
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59:
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2071:, p. 1437, "...we establish that when the number of agents is at least equal to the number of goods, then any
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at which the excess demand function is zero, which is the standard definition of equilibrium in this context.
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is a continuous function that satisfies Walras's law, then there exists an economy with households indexed by
565:
1858:
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323:
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93:
2931:(1973). "Do Walras' identity and continuity characterize the class of community excess-demand functions?".
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208:
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112:
2805:
Mas-Colell, Andreu (1988). "Four lectures on the differentiable approach to general equilibrium theory".
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1640:, Hugo Sonnenschein explained some of the implications of his theorem for general equilibrium theory:
2952:
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2888:
1419:{\displaystyle Z:\{p\in \mathbb {R} _{N}:\sum _{n}p_{n}=1,\forall n,p_{n}>0\}\to \mathbb {R} ^{N}}
1156:{\displaystyle Z:\{p\in \mathbb {R} _{N}:\sum _{n}p_{n}=1,\forall n,p_{n}>0\}\to \mathbb {R} ^{N}}
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There are several possible versions of the theorem that differ in detailed bounds and assumptions.
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in terms of the organization of society as a whole, and in particular the distribution of income.
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1534:. If excess demand is negative, then more units are being supplied than are demanded; there is a
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the number of equilibria will be finite and all of them will be locally unique. This means that
2315:
Alan Kirman (1989) The intrinsic limits of modern economic theory: The emperor has no clothes.
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2818:
2749:
2636:
2605:
Hahn, Frank (1975). "Revival of
Political Economy - The Wrong Issues and the Wrong Argument".
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Bottazzi, Jean-Marc; Hens, Thorsten (1996). "Excess-demand functions and incomplete market".
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textbook. Some economists have made attempts to address this problem, with Donald Brown and
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2406:"Still dead after all these years: interpreting the failure of general equilibrium theory"
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1687:('groping') process: the rate of change for any commodity’s price is proportional to the
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tells us nothing about market demand unless it is augmented by additional requirements.
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98:
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2721:
Kirman, Alan P. (1992). "Whom or What Does the
Representative Individual Represent?".
2992:
2944:
2797:
2784:
Mantel, Rolf (1976). "Homothetic
Preferences and Community Excess Demand Functions".
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restrictions on market variables by modeling the equilibrium state of a market as a
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2653:(2013). "Predicting the 'Global Financial Crisis': Post-Keynesian Macroeconomics".
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A possible market demand curve according to the
Sonnenschein–Mantel–Debreu results
2743:
2630:
2558:"Testable implications of general equilibrium theory: a differentiable approach"
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1679:
will not always find a unique and stable equilibrium, even in ideal conditions:
1615:
For a while it was unclear whether SMD-style results also applied to the market
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referred to the theorem as the “Anything Goes Theorem” in his graduate-level
2666:
2532:
2440:
Andreu, Jordi (1982). "Rationalization of Market Demand on Finite Domains".
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520:
451:
31:
2763:
Mantel, Rolf (1974). "On the characterization of aggregate excess-demand".
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The Sonnenschein–Mantel–Debreu results have led some economists, such as
1742:
1739:
1688:
1531:
2734:
1446:, with no producers ("pure exchange economy"), and household endowments
1183:, with no producers ("pure exchange economy"), and household endowments
2912:
2814:
2713:
2540:
2511:
1816: in this section. Unsourced material may be challenged and removed.
1653:
1603:
2965:. Handbook of Mathematical Economics. Vol. 2. pp. 671–693.
2904:
2705:
2503:
2225:
2041:
1707:. But SMD shows that this will not always be the case, because the
1642:
2834:"Excess-Demand Functions with Incomplete Markets–A Global Result"
2809:. Lecture Notes in Mathematics. Vol. 1330. pp. 19–49.
1683:
In Walrasian general equilibrium, prices are adjusted through a
2185:
2183:
1785:
2007:
2005:
2862:"The Sonnenschein-Mantel-Debreu Results after Thirty Years"
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regarded the theorem as a dangerous critique of mainstream
2134:
2132:
2130:
2022:
2020:
1950:
1948:
1492:
such that each household satisfies all assumptions in the
1277:
to a set-valued, closed graph function, we obtain another
1229:
such that each household satisfies all assumptions in the
2236:
2234:
2101:(2 ed.). Cambridge University Press. Chap 26.2.
1696:
does not reliably lead to convergence to equilibrium.
1502:
1452:
1432:
1313:
1293:
1263:
1239:
1189:
1169:
1050:
1030:
2279:"The last 50 years in growth theory and the next 10"
2052:
2050:
1980:
1978:
1965:
1963:
1014:. For the notation, see the Arrow–Debreu model page.
2488:"Testable Restrictions on the Equilibrium Manifold"
2584:Debreu, Gérard (1974). "Excess-demand functions".
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1508:
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2748:. Northampton, MA: Edward Elgar Publishing, Inc.
2189:
2068:
2319:99(395 Supplement: Conference Papers): 126-139.
1714:The theorem has also raised concerns about the
1681:
1650:
1516:is the excess demand function for the economy.
1253:is the excess demand function for the economy.
1496:except the "strict convexity" assumption, and
986:, both for individual commodities and for the
2635:. Princeton, NJ: Princeton University Press.
2357:sfn error: no target: CITEREFMas-Colell1986 (
1607:holds even if all agents are assumed to have
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8:
2632:Market Demand: Theory and Empirical Evidence
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1954:
1939:
1751:interprets the theorem as showing that, for
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1204:
1190:
1135:
1057:
2340:
2099:General Equilibrium Theory: An Introduction
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1018:
1010:The following version is formulated in the
2891:(1972). "Market excess-demand functions".
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2162:
898:
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18:
2958:Market demand and excess demand functions
2745:Post-Keynesian Economics: New Foundations
2674:
1832:Learn how and when to remove this message
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1711:need not be uniformly downward-sloping.
1932:
1911:
944:for an exchange economy populated with
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1984:
1969:
1757:dynamic stochastic general equilibrium
2556:; Polemarchakis, Herakles M. (2004).
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1996:
1675:of Sonnenschein–Mantel–Debreu that a
7:
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1889:in 1986. To do this he remarks that
1814:adding citations to reliable sources
2963:Handbook of Mathematical Economics
2619:10.1111/j.1475-4932.1975.tb00262.x
1638:Handbook of Mathematical Economics
1485:{\displaystyle \{r^{i}\}_{i\in I}}
1373:
1222:{\displaystyle \{r^{i}\}_{i\in I}}
1110:
912:Sonnenschein–Mantel–Debreu theorem
14:
2586:Journal of Mathematical Economics
2565:Journal of Mathematical Economics
940:in the 1970s. It states that the
2723:Journal of Economic Perspectives
2283:Oxford Review of Economic Policy
1790:
1763:than simpler models such as the
963:zero, and is in accordance with
865:
853:
38:
2413:Journal of Economic Methodology
1877:Extension to incomplete markets
1801:needs additional citations for
982:extended this result to market
140:Concepts, theory and techniques
2694:The Review of Economic Studies
2202:Sonnenschein & Shafer 1982
1753:modelling macroeconomic growth
1401:
1138:
1:
2971:10.1016/S1573-4382(82)02009-8
2853:10.1016/S0022-0531(03)00061-9
2577:10.1016/j.jmateco.2003.11.002
1545:worked to establish rigorous
1012:Arrow–Debreu model of economy
974:More recently, Jordi Andreu,
2945:10.1016/0022-0531(73)90066-5
2869:History of Political Economy
2860:Rizvi, S. Abu Turab (2006).
2798:10.1016/0022-0531(76)90073-9
2777:10.1016/0022-0531(74)90100-8
2598:10.1016/0304-4068(74)90032-9
2454:10.1016/0022-0531(82)90100-4
2190:Chiappori & Ekeland 1999
2069:Chiappori & Ekeland 1999
2277:Solow, R. M. (2007-03-01).
3025:
2999:General equilibrium theory
2933:Journal of Economic Theory
2841:Journal of Economic Theory
2786:Journal of Economic Theory
2765:Journal of Economic Theory
2463:Journal of Economic Theory
2442:Journal of Economic Theory
1895:homogeneity of degree zero
1720:general equilibrium theory
1573:Homogeneity of degree zero
1307:be a positive integer. If
1044:be a positive integer. If
951:can take the shape of any
914:is an important result in
2881:10.1215/00182702-2005-024
2548:Chiappori, Pierre-André;
2425:10.1080/13501780210137083
1885:was first conjectured by
2372:Bottazzi & Hens 1996
2253:Brown & Matzkin 1996
1671:points out that it is a
128:JEL classification codes
2676:10.1111/1475-4932.12016
2667:10.1111/1475-4932.12016
2533:10.1111/1468-0262.00085
2097:Starr, Ross M. (2011).
1859:social welfare function
1543:mathematical economists
314:Industrial organization
171:Computational economics
3009:Macroeconomic theories
2807:Mathematical Economics
2475:10.1006/jeth.1996.0003
2163:Kirman & Koch 1986
1709:excess demand function
1698:
1658:
1648:
1602:. This means that the
1600:homothetic preferences
1527:excess demand function
1510:
1486:
1440:
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1301:
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1247:
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1177:
1157:
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997:neoclassical economics
976:Pierre-André Chiappori
166:Experimental economics
2742:Lavoie, Marc (2014).
2226:Chiappori et al. 2004
2042:Chiappori et al. 2004
1646:
1511:
1494:"Assumptions" section
1487:
1441:
1421:
1302:
1272:
1248:
1231:"Assumptions" section
1224:
1178:
1158:
1039:
2295:10.1093/oxrep/grm004
1810:improve this article
1593:Further developments
1521:History of the proof
1500:
1450:
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1311:
1291:
1261:
1257:Similarly, changing
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1187:
1167:
1048:
1028:
938:Hugo F. Sonnenschein
393:Social choice theory
2735:10.1257/jep.6.2.117
2627:Hildenbrand, Werner
2607:The Economic Record
2267:, pp. 238–239.
2204:, pp. 671–672.
2029:, pp. 229–230.
2014:, pp. 122–123.
1871:comparative statics
1663:aggregation problem
1285: —
1022: —
942:excess demand curve
916:general equilibrium
860:Business portal
181:Operations research
161:National accounting
3004:Economics theorems
2953:Sonnenschein, Hugo
2929:Sonnenschein, Hugo
2889:Sonnenschein, Hugo
2815:10.1007/BFb0078157
2482:Brown, Donald J.;
1883:incomplete markets
1863:Hopf index theorem
1772:Werner Hildenbrand
1654:utility hypothesis
1649:
1525:The concept of an
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961:homogeneity degree
946:utility-maximizing
191:Industrial complex
186:Middle income trap
2832:Momi, T. (2003).
2824:978-3-540-50003-2
2755:978-1-84720-483-7
2141:, pp. 50–51.
1955:Sonnenschein 1973
1940:Sonnenschein 1972
1887:Andreu Mas-Colell
1881:The extension to
1867:regular economies
1861:. Second, by the
1842:
1841:
1834:
1724:Andreu Mas-Colell
1677:Walrasian auction
1636:In the 1982 book
1509:{\displaystyle Z}
1439:{\displaystyle I}
1344:
1300:{\displaystyle N}
1270:{\displaystyle Z}
1246:{\displaystyle Z}
1176:{\displaystyle I}
1081:
1037:{\displaystyle N}
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2661:(285): 228–254.
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2613:(135): 360–364.
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2571:(1–2): 105–119.
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2527:(6): 1435–1457.
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2498:(6): 1249–1262.
2484:Matzkin, Rosa L.
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2205:
2199:
2193:
2187:
2178:
2172:
2166:
2160:
2154:
2148:
2142:
2136:
2125:
2119:
2113:
2112:
2094:
2088:
2082:
2076:
2066:
2060:
2054:
2045:
2039:
2030:
2024:
2015:
2009:
2000:
1994:
1988:
1982:
1973:
1967:
1958:
1952:
1943:
1937:
1920:
1916:
1855:Pareto efficient
1837:
1830:
1826:
1823:
1817:
1794:
1786:
1765:Solow–Swan model
1547:microfoundations
1515:
1513:
1512:
1507:
1491:
1489:
1488:
1483:
1481:
1480:
1465:
1464:
1445:
1443:
1442:
1437:
1425:
1423:
1422:
1417:
1415:
1414:
1409:
1391:
1390:
1363:
1362:
1352:
1340:
1339:
1334:
1306:
1304:
1303:
1298:
1286:
1276:
1274:
1273:
1268:
1252:
1250:
1249:
1244:
1228:
1226:
1225:
1220:
1218:
1217:
1202:
1201:
1182:
1180:
1179:
1174:
1162:
1160:
1159:
1154:
1152:
1151:
1146:
1128:
1127:
1100:
1099:
1089:
1077:
1076:
1071:
1043:
1041:
1040:
1035:
1023:
1003:Formal statement
988:aggregate demand
935:
900:
893:
886:
872:Money portal
870:
869:
868:
858:
857:
354:Natural resource
146:Economic systems
42:
19:
16:Economic theorem
3024:
3023:
3019:
3018:
3017:
3015:
3014:
3013:
2989:
2988:
2987:
2981:
2951:
2927:
2905:10.2307/1913184
2887:
2864:
2859:
2836:
2831:
2825:
2804:
2783:
2762:
2756:
2741:
2720:
2706:10.2307/2297640
2691:
2655:Economic Record
2649:
2643:
2625:
2604:
2583:
2560:
2547:
2518:
2504:10.2307/2171830
2481:
2460:
2439:
2408:
2402:Ackerman, Frank
2400:
2396:
2391:
2390:
2382:
2378:
2370:
2366:
2356:
2353:Mas-Colell 1986
2351:
2347:
2339:
2335:
2327:
2323:
2314:
2310:
2276:
2275:
2271:
2263:
2259:
2251:
2247:
2239:
2232:
2224:
2220:
2212:
2208:
2200:
2196:
2188:
2181:
2173:
2169:
2161:
2157:
2149:
2145:
2137:
2128:
2120:
2116:
2109:
2096:
2095:
2091:
2083:
2079:
2067:
2063:
2055:
2048:
2040:
2033:
2025:
2018:
2010:
2003:
1995:
1991:
1983:
1976:
1968:
1961:
1953:
1946:
1938:
1934:
1929:
1924:
1923:
1917:
1913:
1908:
1879:
1838:
1827:
1821:
1818:
1807:
1795:
1784:
1634:
1625:vector calculus
1595:
1523:
1518:
1498:
1497:
1466:
1456:
1448:
1447:
1428:
1427:
1404:
1382:
1354:
1329:
1309:
1308:
1289:
1288:
1284:
1259:
1258:
1255:
1235:
1234:
1203:
1193:
1185:
1184:
1165:
1164:
1141:
1119:
1091:
1066:
1046:
1045:
1026:
1025:
1021:
1005:
949:rational agents
929:
904:
866:
864:
852:
845:
844:
815:
805:
804:
803:
802:
566:von Böhm-Bawerk
454:
443:
442:
204:
196:
195:
151:Economic growth
141:
133:
132:
74:
72:classifications
17:
12:
11:
5:
3022:
3020:
3012:
3011:
3006:
3001:
2991:
2990:
2986:
2985:
2979:
2949:
2939:(4): 345–354.
2925:
2899:(3): 549–563.
2885:
2857:
2847:(2): 240–250.
2829:
2823:
2802:
2792:(2): 197–201.
2781:
2771:(3): 348–353.
2760:
2754:
2739:
2729:(2): 117–136.
2718:
2700:(3): 457–463.
2689:
2647:
2641:
2623:
2602:
2581:
2545:
2516:
2479:
2458:
2448:(1): 201–204.
2437:
2419:(2): 119–139.
2397:
2395:
2392:
2389:
2388:
2376:
2364:
2345:
2333:
2331:, p. 231.
2321:
2308:
2269:
2257:
2245:
2243:, p. 232.
2230:
2218:
2216:, p. 231.
2206:
2194:
2179:
2177:, p. 128.
2167:
2165:, p. 460.
2155:
2143:
2126:
2124:, p. 228.
2114:
2108:978-0521533867
2107:
2089:
2087:, p. 363.
2077:
2061:
2046:
2044:, p. 106.
2031:
2016:
2001:
1999:, p. 229.
1989:
1974:
1959:
1944:
1931:
1930:
1928:
1925:
1922:
1921:
1910:
1909:
1907:
1904:
1878:
1875:
1840:
1839:
1798:
1796:
1789:
1783:
1780:
1734:deriving some
1728:microeconomics
1716:falsifiability
1669:Frank Ackerman
1633:
1630:
1594:
1591:
1582:
1581:
1576:
1570:
1541:In the 1970s,
1522:
1519:
1505:
1479:
1476:
1473:
1469:
1463:
1459:
1455:
1435:
1413:
1408:
1403:
1400:
1397:
1394:
1389:
1385:
1381:
1378:
1375:
1372:
1369:
1366:
1361:
1357:
1351:
1347:
1343:
1338:
1333:
1328:
1325:
1322:
1319:
1316:
1296:
1279:
1266:
1242:
1216:
1213:
1210:
1206:
1200:
1196:
1192:
1172:
1150:
1145:
1140:
1137:
1134:
1131:
1126:
1122:
1118:
1115:
1112:
1109:
1106:
1103:
1098:
1094:
1088:
1084:
1080:
1075:
1070:
1065:
1062:
1059:
1056:
1053:
1033:
1016:
1004:
1001:
906:
905:
903:
902:
895:
888:
880:
877:
876:
875:
874:
862:
847:
846:
843:
842:
837:
827:
822:
816:
811:
810:
807:
806:
801:
800:
793:
788:
783:
778:
773:
768:
763:
758:
753:
748:
743:
738:
733:
728:
723:
718:
713:
708:
703:
698:
693:
688:
683:
678:
673:
668:
663:
658:
653:
648:
643:
638:
633:
628:
623:
618:
613:
608:
603:
598:
593:
588:
583:
578:
573:
568:
563:
558:
553:
548:
543:
538:
533:
528:
523:
518:
513:
508:
503:
498:
493:
488:
483:
478:
473:
468:
463:
457:
456:
455:
449:
448:
445:
444:
441:
440:
435:
430:
425:
420:
415:
410:
405:
400:
395:
386:
381:
376:
371:
366:
361:
359:Organizational
356:
351:
346:
341:
336:
331:
326:
321:
316:
311:
306:
301:
296:
291:
286:
281:
276:
271:
266:
261:
256:
251:
246:
241:
236:
231:
226:
221:
216:
211:
205:
203:By application
202:
201:
198:
197:
194:
193:
188:
183:
178:
173:
168:
163:
158:
153:
148:
142:
139:
138:
135:
134:
131:
130:
125:
120:
115:
110:
105:
96:
91:
86:
81:
75:
69:
68:
65:
64:
63:
62:
57:
52:
44:
43:
35:
34:
28:
27:
15:
13:
10:
9:
6:
4:
3:
2:
3021:
3010:
3007:
3005:
3002:
3000:
2997:
2996:
2994:
2982:
2980:9780444861276
2976:
2972:
2968:
2964:
2960:
2959:
2954:
2950:
2946:
2942:
2938:
2934:
2930:
2926:
2922:
2918:
2914:
2910:
2906:
2902:
2898:
2894:
2890:
2886:
2882:
2878:
2874:
2870:
2863:
2858:
2854:
2850:
2846:
2842:
2835:
2830:
2826:
2820:
2816:
2812:
2808:
2803:
2799:
2795:
2791:
2787:
2782:
2778:
2774:
2770:
2766:
2761:
2757:
2751:
2747:
2746:
2740:
2736:
2732:
2728:
2724:
2719:
2715:
2711:
2707:
2703:
2699:
2695:
2690:
2686:
2682:
2677:
2672:
2668:
2664:
2660:
2656:
2652:
2648:
2644:
2642:0-691-03428-1
2638:
2634:
2633:
2628:
2624:
2620:
2616:
2612:
2608:
2603:
2599:
2595:
2591:
2587:
2582:
2578:
2574:
2570:
2566:
2559:
2555:
2554:Kübler, Felix
2551:
2550:Ekeland, Ivar
2546:
2542:
2538:
2534:
2530:
2526:
2522:
2517:
2513:
2509:
2505:
2501:
2497:
2493:
2489:
2485:
2480:
2476:
2472:
2468:
2464:
2459:
2455:
2451:
2447:
2443:
2438:
2434:
2430:
2426:
2422:
2418:
2414:
2407:
2403:
2399:
2398:
2393:
2385:
2380:
2377:
2373:
2368:
2365:
2360:
2354:
2349:
2346:
2343:, p. ix.
2342:
2337:
2334:
2330:
2325:
2322:
2318:
2312:
2309:
2304:
2300:
2296:
2292:
2288:
2284:
2280:
2273:
2270:
2266:
2261:
2258:
2254:
2249:
2246:
2242:
2237:
2235:
2231:
2227:
2222:
2219:
2215:
2210:
2207:
2203:
2198:
2195:
2191:
2186:
2184:
2180:
2176:
2171:
2168:
2164:
2159:
2156:
2152:
2147:
2144:
2140:
2135:
2133:
2131:
2127:
2123:
2118:
2115:
2110:
2104:
2100:
2093:
2090:
2086:
2081:
2078:
2074:
2073:smooth enough
2070:
2065:
2062:
2058:
2053:
2051:
2047:
2043:
2038:
2036:
2032:
2028:
2023:
2021:
2017:
2013:
2012:Ackerman 2002
2008:
2006:
2002:
1998:
1993:
1990:
1986:
1981:
1979:
1975:
1971:
1966:
1964:
1960:
1956:
1951:
1949:
1945:
1941:
1936:
1933:
1926:
1915:
1912:
1905:
1903:
1901:
1900:Thorsten Hens
1896:
1892:
1888:
1884:
1876:
1874:
1872:
1868:
1864:
1860:
1856:
1851:
1848:
1836:
1833:
1825:
1815:
1811:
1805:
1804:
1799:This section
1797:
1793:
1788:
1787:
1781:
1779:
1777:
1776:law of demand
1773:
1768:
1766:
1762:
1758:
1754:
1750:
1746:
1744:
1741:
1737:
1733:
1729:
1725:
1721:
1717:
1712:
1710:
1706:
1705:excess supply
1702:
1697:
1695:
1690:
1689:excess demand
1686:
1680:
1678:
1674:
1670:
1666:
1664:
1657:
1655:
1645:
1641:
1639:
1631:
1629:
1626:
1622:
1618:
1613:
1610:
1605:
1601:
1592:
1590:
1588:
1580:
1577:
1574:
1571:
1569:
1566:
1565:
1564:
1561:
1557:
1553:
1548:
1544:
1539:
1537:
1533:
1528:
1520:
1517:
1503:
1495:
1477:
1474:
1471:
1461:
1457:
1433:
1411:
1395:
1392:
1387:
1383:
1379:
1376:
1370:
1367:
1364:
1359:
1355:
1349:
1345:
1341:
1336:
1326:
1323:
1317:
1314:
1294:
1278:
1264:
1254:
1240:
1232:
1214:
1211:
1208:
1198:
1194:
1170:
1148:
1132:
1129:
1124:
1120:
1116:
1113:
1107:
1104:
1101:
1096:
1092:
1086:
1082:
1078:
1073:
1063:
1060:
1054:
1051:
1031:
1015:
1013:
1008:
1002:
1000:
998:
994:
989:
985:
984:demand curves
981:
977:
972:
970:
966:
962:
958:
954:
950:
947:
943:
939:
933:
928:
924:
923:Gérard Debreu
920:
917:
913:
901:
896:
894:
889:
887:
882:
881:
879:
878:
873:
863:
861:
856:
851:
850:
849:
848:
841:
838:
835:
831:
828:
826:
823:
821:
818:
817:
814:
809:
808:
799:
798:
794:
792:
789:
787:
784:
782:
779:
777:
774:
772:
769:
767:
764:
762:
759:
757:
754:
752:
749:
747:
744:
742:
739:
737:
734:
732:
729:
727:
724:
722:
719:
717:
714:
712:
709:
707:
704:
702:
699:
697:
694:
692:
689:
687:
684:
682:
679:
677:
674:
672:
669:
667:
664:
662:
659:
657:
654:
652:
649:
647:
644:
642:
639:
637:
634:
632:
629:
627:
624:
622:
619:
617:
614:
612:
609:
607:
604:
602:
599:
597:
594:
592:
589:
587:
584:
582:
579:
577:
574:
572:
569:
567:
564:
562:
559:
557:
554:
552:
549:
547:
544:
542:
539:
537:
534:
532:
529:
527:
524:
522:
519:
517:
514:
512:
509:
507:
504:
502:
499:
497:
494:
492:
489:
487:
484:
482:
479:
477:
474:
472:
469:
467:
464:
462:
461:de Mandeville
459:
458:
453:
447:
446:
439:
436:
434:
431:
429:
426:
424:
421:
419:
416:
414:
411:
409:
406:
404:
401:
399:
396:
394:
390:
389:Public choice
387:
385:
382:
380:
377:
375:
372:
370:
367:
365:
364:Participation
362:
360:
357:
355:
352:
350:
347:
345:
342:
340:
337:
335:
332:
330:
327:
325:
324:Institutional
322:
320:
317:
315:
312:
310:
307:
305:
302:
300:
297:
295:
292:
290:
287:
285:
282:
280:
277:
275:
274:Expeditionary
272:
270:
267:
265:
264:Environmental
262:
260:
257:
255:
252:
250:
247:
245:
242:
240:
237:
235:
232:
230:
227:
225:
222:
220:
217:
215:
212:
210:
207:
206:
200:
199:
192:
189:
187:
184:
182:
179:
177:
174:
172:
169:
167:
164:
162:
159:
157:
154:
152:
149:
147:
144:
143:
137:
136:
129:
126:
124:
121:
119:
116:
114:
111:
109:
106:
104:
100:
97:
95:
94:International
92:
90:
87:
85:
82:
80:
77:
76:
73:
70:Branches and
67:
66:
61:
58:
56:
53:
51:
48:
47:
46:
45:
41:
37:
36:
33:
29:
25:
21:
20:
2962:
2957:
2936:
2932:
2896:
2893:Econometrica
2892:
2872:
2868:
2844:
2840:
2806:
2789:
2785:
2768:
2764:
2744:
2726:
2722:
2697:
2693:
2658:
2654:
2631:
2610:
2606:
2589:
2585:
2568:
2564:
2524:
2521:Econometrica
2520:
2495:
2492:Econometrica
2491:
2466:
2462:
2445:
2441:
2416:
2412:
2394:Bibliography
2379:
2367:
2348:
2336:
2324:
2316:
2311:
2286:
2282:
2272:
2260:
2248:
2221:
2209:
2197:
2170:
2158:
2146:
2117:
2098:
2092:
2080:
2064:
1992:
1935:
1914:
1891:Walras's law
1880:
1852:
1843:
1828:
1819:
1808:Please help
1803:verification
1800:
1769:
1761:microfounded
1749:Robert Solow
1747:
1732:Rosa Matzkin
1713:
1699:
1693:
1684:
1682:
1667:
1659:
1651:
1637:
1635:
1632:Significance
1621:Ivar Ekeland
1617:demand curve
1614:
1608:
1596:
1583:
1579:Walras's law
1559:
1556:Walras's law
1540:
1524:
1280:
1256:
1017:
1009:
1006:
980:Ivar Ekeland
973:
965:Walras's law
921:, proved by
911:
909:
830:Publications
795:
418:Sociological
391: /
289:Geographical
269:Evolutionary
244:Digitization
209:Agricultural
113:Mathematical
84:Econometrics
2875:: 228–245.
2651:Keen, Steve
2289:(1): 3–14.
2175:Kirman 1992
2151:Mantel 1976
2139:Lavoie 2014
2057:Andreu 1982
1985:Debreu 1974
1970:Mantel 1974
1782:Explanation
1759:is no more
1740:topological
1701:Léon Walras
1694:tâtonnement
1685:tâtonnement
969:equilibrium
930: [
927:Rolf Mantel
666:von Neumann
319:Information
259:Engineering
239:Development
234:Demographic
176:Game theory
118:Methodology
2993:Categories
2329:Rizvi 2006
2265:Rizvi 2006
2241:Rizvi 2006
2122:Rizvi 2006
2027:Rizvi 2006
1997:Rizvi 2006
1927:References
1847:non-linear
1736:polynomial
1568:Continuity
1552:continuity
993:Frank Hahn
957:continuous
825:Economists
696:Schumacher
601:Schumpeter
571:von Wieser
491:von Thünen
452:economists
428:Statistics
423:Solidarity
344:Managerial
309:Humanistic
304:Historical
249:Ecological
214:Behavioral
108:Mainstream
2685:154247190
2592:: 15–21.
2469:: 49–63.
2433:154640384
2384:Momi 2003
2303:0266-903X
2214:Keen 2013
2085:Hahn 1975
1822:July 2019
1673:corollary
1609:identical
1475:∈
1402:→
1374:∀
1346:∑
1327:∈
1212:∈
1139:→
1111:∀
1083:∑
1064:∈
919:economics
741:Greenspan
706:Samuelson
686:Galbraith
656:Tinbergen
596:von Mises
591:Heckscher
551:Edgeworth
369:Personnel
329:Knowledge
294:Happiness
284:Financial
254:Education
229:Democracy
123:Political
89:Heterodox
32:Economics
2921:55002985
2629:(1994).
2486:(1996).
2404:(2002).
1743:manifold
1532:shortage
955:that is
953:function
834:journals
820:Glossary
771:Stiglitz
736:Rothbard
716:Buchanan
701:Friedman
691:Koopmans
681:Leontief
661:Robinson
546:Marshall
450:Notable
398:Regional
374:Planning
349:Monetary
279:Feminist
224:Cultural
219:Business
24:a series
22:Part of
2913:1913184
2714:2297640
2541:2999567
2512:2171830
1604:utility
1282:Theorem
1019:Theorem
971:point.
840:Schools
832: (
791:Piketty
786:Krugman
651:Kuznets
641:Kalecki
616:Polanyi
506:Cournot
501:Bastiat
486:Ricardo
476:Malthus
466:Quesnay
438:Welfare
408:Service
79:Applied
55:Outline
50:History
2977:
2919:
2911:
2821:
2752:
2712:
2683:
2639:
2539:
2510:
2431:
2301:
2105:
1755:, the
1587:vector
1233:, and
978:, and
959:, has
936:, and
776:Thaler
756:Ostrom
751:Becker
746:Sowell
726:Baumol
631:Myrdal
626:Sraffa
621:Frisch
611:Knight
606:Keynes
581:Fisher
576:Veblen
561:Pareto
541:Menger
536:George
531:Jevons
526:Walras
516:Gossen
384:Public
379:Policy
334:Labour
299:Health
156:Market
2917:S2CID
2909:JSTOR
2865:(PDF)
2837:(PDF)
2710:JSTOR
2681:S2CID
2561:(PDF)
2537:JSTOR
2508:JSTOR
2429:S2CID
2409:(PDF)
1906:Notes
1865:, in
1623:used
1575:, and
934:]
813:Lists
781:Hoppe
766:Lucas
731:Solow
721:Arrow
711:Simon
676:Lange
671:Hicks
646:Röpke
636:Hayek
586:Pigou
556:Clark
471:Smith
433:Urban
413:Socio
403:Rural
103:Macro
99:Micro
60:Index
2975:ISBN
2819:ISBN
2750:ISBN
2637:ISBN
2359:help
2299:ISSN
2103:ISBN
1893:and
1560:only
1554:and
1536:glut
1393:>
1287:Let
1130:>
1024:Let
910:The
797:more
521:Marx
511:Mill
496:List
2967:doi
2941:doi
2901:doi
2877:doi
2849:doi
2845:111
2811:doi
2794:doi
2773:doi
2731:doi
2702:doi
2671:hdl
2663:doi
2615:doi
2594:doi
2573:doi
2529:doi
2500:doi
2471:doi
2450:doi
2421:doi
2291:doi
1812:by
1718:of
761:Sen
481:Say
339:Law
2995::
2973:.
2961:.
2935:.
2915:.
2907:.
2897:40
2895:.
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2871:.
2867:.
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2817:.
2790:12
2788:.
2767:.
2725:.
2708:.
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2696:.
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2669:.
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2609:.
2588:.
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2567:.
2563:.
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2490:.
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2297:.
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2285:.
2281:.
2233:^
2182:^
2129:^
2049:^
2034:^
2019:^
2004:^
1977:^
1962:^
1947:^
999:.
932:es
925:,
101:/
26:on
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2600:.
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2579:.
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2514:.
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2473::
2456:.
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2423::
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2305:.
2293::
2255:.
2192:.
2153:.
2111:.
2059:.
1987:.
1972:.
1957:.
1942:.
1835:)
1829:(
1824:)
1820:(
1806:.
1550:(
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1478:I
1472:i
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1454:{
1434:I
1412:N
1407:R
1399:}
1396:0
1388:n
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1368:1
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1360:n
1356:p
1350:n
1342::
1337:N
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1315:Z
1295:N
1265:Z
1241:Z
1215:I
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1205:}
1199:i
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1191:{
1171:I
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1136:}
1133:0
1125:n
1121:p
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1105:1
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1097:n
1093:p
1087:n
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1074:N
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1058:{
1055::
1052:Z
1032:N
899:e
892:t
885:v
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