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General equilibrium theory
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In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an overall general equilibrium. General equilibrium theory contrasts to the theory of partial equilibrium, which only analyzes single markets.
General equilibrium theory both studies economies using the model of equilibrium pricing and seeks to determine in which circumstances the assumptions of general equilibrium will hold. The theory dates to the 1870s, particularly the work of French economist Léon Walras in his pioneering 1874 work Elements of Pure Economics.[1]
Contents
[hide]
1 Overview
2 Modern concept of general equilibrium in economics
3 Properties and characterization of general equilibrium
3.1 First Fundamental Theorem of Welfare Economics
3.2 Second Fundamental Theorem of Welfare Economics
3.3 Existence
3.3.1 Nonconvexities in large economies
3.4 Uniqueness
3.5 Determinacy
3.6 Stability
4 Unresolved problems in general equilibrium
5 Computing general equilibrium
6 Other schools
6.1 Keynesian and Post-Keynesian
6.2 New classical macroeconomics
6.3 Socialist economics
7 See also
8 Notes
9 References
10 External links
Overview[edit]
It is often assumed that agents are price takers, and under that assumption two common notions of equilibrium exist: Walrasian, or competitive equilibrium, and its generalization: a price equilibrium with transfers.
Broadly speaking, general equilibrium tries to give an understanding of the whole economy using a "bottom-up" approach, starting with individual markets and agents. (Macroeconomics, as developed by the Keynesian economists, focused on a "top-down" approach, where the analysis starts with larger aggregates, the "big picture".) Therefore, general equilibrium theory has traditionally been classified as part of microeconomics.
The difference is not as clear as it used to be, since much of modern macroeconomics has emphasized microeconomic foundations, and has constructed general equilibrium models of macroeconomic fluctuations. General equilibrium macroeconomic models usually have a simplified structure that only incorporates a few markets, like a "goods market" and a "financial market". In contrast, general equilibrium models in the microeconomic tradition typically involve a multitude of different goods markets. They are usually complex and require computers to help with numerical solutions.
In a market system the prices and production of all goods, including the price of money and interest, are interrelated. A change in the price of one good, say bread, may affect another price, such as bakers' wages. If bakers don't differ in tastes from others, the demand for bread might be affected by a change in bakers' wages, with a consequent effect on the price of bread. Calculating the equilibrium price of just one good, in theory, requires an analysis that accounts for all of the millions of different goods that are available.
The first attempt in neoclassical economics to model prices for a whole economy was made by Léon Walras. Walras' Elements of Pure Economics provides a succession of models, each taking into account more aspects of a real economy (two commodities, many commodities, production, growth, money). Some think Walras was unsuccessful and that the later models in this series are inconsistent.[2][3]
In particular, Walras's model was a long-run model in which prices of capital goods are the same whether they appear as inputs or outputs and in which the same rate of profits is earned in all lines of industry. This is inconsistent with the quantities of capital goods being taken as data. But when Walras introduced capital goods in his later models, he took their quantities as given, in arbitrary ratios. (In contrast, Kenneth Arrow and Gérard Debreu continued to take the initial quantities of capital goods as given, but adopted a short run model in which the prices of capital goods vary with time and the own rate of interest varies across capital goods.)
Walras was the first to lay down a research program much followed by 20th-century economists. In particular, the Walrasian agenda included the investigation of when equilibria are unique and stable.(Walras' Lesson 7 shows neither uniqueness, nor stability, nor even existence of an equilibrium is guaranteed.)
Walras also proposed a dynamic process by which general equilibrium might be reached, that of the tâtonnement or groping process.
The tâtonnement process is a model for investigating stability of equilibria. Prices are announced (perhaps by an "auctioneer"), and agents state how much of each good they would like to offer (supply) or purchase (demand). No transactions and no production take place at disequilibrium prices. Instead, prices are lowered for goods with positive prices and excess supply. Prices are raised for goods with excess demand. The question for the mathematician is under what conditions such a process will terminate in equilibrium where demand equates to supply for goods with positive prices and demand does not exceed supply for goods with a price of zero. Walras was not able to provide a definitive answer to this question (see Unresolved Problems in General Equilibrium below).
In partial equilibrium analysis, the determination of the price of a good is simplified by just looking at the price of one good, and assuming that the prices of all other goods remain constant. The Marshallian theory of supply and demand is an example of partial equilibrium analysis. Partial equilibrium analysis is adequate when the first-order effects of a shift in the demand curve do not shift the supply curve. Anglo-American economists became more interested in general equilibrium in the late 1920s and 1930s after Piero Sraffa's demonstration that Marshallian economists cannot account for the forces thought to account for the upward-slope of the supply curve for a consumer good.
If an industry uses little of a factor of production, a small increase in the output of that industry will not bid the price of that factor up. To a first-order approximation, firms in the industry will experience constant costs, and the industry supply curves will not slope up. If an industry uses an appreciable amount of that factor of production, an increase in the output of that industry will exhibit increasing costs. But such a factor is likely to be used in substitutes for the industry's product, and an increased price of that factor will have effects on the supply of those substitutes. Consequently, Sraffa argued, the first-order effects of a shift in the demand curve of the original industry under these assumptions includes a shift in the supply curve of substitutes for that industry's product, and consequent shifts in the original industry's supply curve. General equilibrium is designed to investigate such interactions between markets.
Continental European economists made important advances in the 1930s. Walras' proofs of the existence of general equilibrium often were based on the counting of equations and variables. Such arguments are inadequate for non-linear systems of equations and do not imply that equilibrium prices and quantities cannot be negative, a meaningless solution for his models. The replacement of certain equations by inequalities and the use of more rigorous mathematics improved general equilibrium modeling.
Modern concept of general equilibrium in economics[edit]
The modern conception of general equilibrium is provided by a model developed jointly by Kenneth Arrow, Gérard Debreu, and Lionel W. McKenzie in the 1950s.[4][5] Debreu presents this model in Theory of Value (1959) as an axiomatic model, following the style of mathematics promoted by Nicolas Bourbaki. In such an approach, the interpretation of the terms in the theory (e.g., goods, prices) are not fixed by the axioms.
Three important interpretations of the terms of the theory have been often cited. First, suppose commodities are distinguished by the location where they are delivered. Then the Arrow-Debreu model is a spatial model of, for example, international trade.
Second, suppose commodities are distinguished by when they are delivered. That is, suppose all markets equilibrate at some initial instant of time. Agents in the model purchase and sell contracts, where a contract specifies, for example, a good to be delivered and the date at which it is to be delivered. The Arrow–Debreu model of intertemporal equilibrium contains forward markets for all goods at all dates. No markets exist at any future dates.
Third, suppose contracts specify states of nature which affect whether a commodity is to be delivered: "A contract for the transfer of a commodity now specifies, in addition to its physical properties, its location and its date, an event on the occurrence of which the transfer is conditional. This new definition of a commodity allows one to obtain a theory of [risk] free from any probability concept..."[6]
These interpretations can be combined. So the complete Arrow–Debreu model can be said to apply when goods are identified by when they are to be delivered, where they are to be delivered and under what circumstances they are to be delivered, as well as their intrinsic nature. So there would be a complete set of prices for contracts such as "1 ton of Winter red wheat, delivered on 3rd of January in Minneapolis, if there is a hurricane in Florida during December". A general equilibrium model with complete markets of this sort seems to be a long way from describing the workings of real economies, however its proponents argue that it is still useful as a simplified guide as to how real economies function.
Some of the recent work in general equilibrium has in fact explored the implications of incomplete markets, which is to say an intertemporal economy with uncertainty, where there do not exist sufficiently detailed contracts that would allow agents to fully allocate their consumption and resources through time. While it has been shown that such economies will generally still have an equilibrium, the outcome may no longer be Pareto optimal. The basic intuition for this result is that if consumers lack adequate means to transfer their wealth from one time period to another and the future is risky, there is nothing to necessarily tie any price ratio down to the relevant marginal rate of substitution, which is the standard requirement for Pareto optimality. Under some conditions the economy may still be constrained Pareto optimal, meaning that a central authority limited to the same type and number of contracts as the individual agents may not be able to improve upon the outcome, what is needed is the introduction of a full set of possible contracts. Hence, one implication of the theory of incomplete markets is that inefficiency may be a result of underdeveloped financial institutions or credit constraints faced by some members of the public. Research still continues in this area.
Properties and characterization of general equilibrium[edit]
See also: Fundamental theorems of welfare economics
Basic questions in general equilibrium analysis are concerned with the conditions under which an equilibrium will be efficient, which efficient equilibria can be achieved, when an equilibrium is guaranteed to exist and when the equilibrium will be unique and stable.
First Fundamental Theorem of Welfare Economics[edit]
The First Fundamental Welfare Theorem asserts that market equilibria are Pareto efficient. In a pure exchange economy, a sufficient condition for the first welfare theorem to hold is that preferences be locally nonsatiated. The first welfare theorem also holds for economies with production regardless of the properties of the production function. Implicitly, the theorem assumes complete markets and perfect information. In an economy with externalities, for example, it is possible for equilibria to arise that are not efficient.
The first welfare theorem is informative in the sense that it points to the sources of inefficiency in markets. Under the assumptions above, any market equilibrium is tautologically efficient. Therefore, when equilibria arise that are not efficient, the market system itself is not to blame, but rather some sort of market failure.
Second Fundamental Theorem of Welfare Economics[edit]
Even if every equilibrium is efficient, it may not be that every efficient allocation of resources can be part of an equilibrium. However, the second theorem states that every Pareto efficient allocation can be supported as an equilibrium by some set of prices. In other words, all that is required to reach a particular Pareto efficient outcome is a redistribution of initial endowments of the agents after which the market can be left alone to do its work. This suggests that the issues of efficiency and equity can be separated and need not involve a trade-off. The conditions for the second theorem are stronger than those for the first, as consumers' preferences and production sets now need to be convex (convexity roughly corresponds to the idea of diminishing marginal rates of substitution i.e. "the average of two equally good bundles is better than either of the two bundles").
Existence[edit]
Even though every equilibrium is efficient, neither of the above two theorems say anything about the equilibrium existing in the first place. To guarantee that an equilibrium exists, it suffices that consumer preferences be strictly convex. With enough consumers, the convexity assumption can be relaxed both for existence and the second welfare theorem. Similarly, but less plausibly, convex feasible production sets suffice for existence; convexity excludes economies of scale.
Proofs of the existence of equilibrium traditionally rely on fixed-point theorems such as Brouwer fixed-point theorem for functions (or, more generally, the Kakutani fixed-point theorem for set-valued functions). See Competitive equilibrium#Existence of a competitive equilibrium. The proof was first due to Lionel McKenzie,[7] and Kenneth Arrow and Gérard Debreu.[8] In fact, the converse also holds, according to Uzawa's derivation of Brouwer's fixed point theorem from Walras's law.[9] Following Uzawa's theorem, many mathematical economists consider proving existence a deeper result than proving the two Fundamental Theorems.
Another method of proof of existence, global analysis, uses Sard's lemma and the Baire category theorem; this method was pioneered by Gérard Debreu and Stephen Smale.
Nonconvexities in large economies[edit]
Main article: Shapley–Folkman lemma
Starr (1969) applied the Shapley–Folkman–Starr theorem to prove that even without convex preferences there exists an approximate equilibrium. The Shapley–Folkman–Starr results bound the distance from an "approximate" economic equilibrium to an equilibrium of a "convexified" economy, when the number of agents exceeds the dimension of the goods.[10] Following Starr's paper, the Shapley–Folkman–Starr results were "much exploited in the theoretical literature", according to Guesnerie,[11]:112 who wrote the following:
some key results obtained under the convexity assumption remain (approximately) relevant in circumstances where convexity fails. For example, in economies with a large consumption side, nonconvexities in preferences do not destroy the standard results of, say Debreu's theory of value. In the same way, if indivisibilities in the production sector are small with respect to the size of the economy, [ . . . ] then standard results are affected in only a minor way.[11]:99
To this text, Guesnerie appended the following footnote:
The derivation of these results in general form has been one of the major achievements of postwar economic theory.[11]:138
In particular, the Shapley-Folkman-Starr results were incorporated in the theory of general economic equilibria[12][13][14] and in the theory of market failures[15] and of public economics.[16]
Uniqueness[edit]
See also: Sonnenschein–Mantel–Debreu theorem
Although generally (assuming convexity) an equilibrium will exist and will be efficient, the conditions under which it will be unique are much stronger. While the issues are fairly technical the basic intuition is that the presence of wealth effects (which is the feature that most clearly delineates general equilibrium analysis from partial equilibrium) generates the possibility of multiple equilibria. When a price of a particular good changes there are two effects. First, the relative attractiveness of various commodities changes; and second, the wealth distribution of individual agents is altered. These two effects can offset or reinforce each other in ways that make it possible for more than one set of prices to constitute an equilibrium.
A result known as the Sonnenschein–Mantel–Debreu theorem states that the aggregate excess demand function inherits only certain properties of individual's demand functions, and that these (Continuity, Homogeneity of degree zero, Walras' law and boundary behavior when prices are near zero) are the only real restriction one can expect from an aggregate excess demand function: any such function can be rationalized as the excess demand of an economy. In particular uniqueness of equilibrium should not be expected.
There has been much research on conditions when the equilibrium will be unique, or which at least will limit the number of equilibria. One result states that under mild assumptions the number of equilibria will be finite (see regular economy) and odd (see index theorem). Furthermore, if an economy as a whole, as characterized by an aggregate excess demand function, has the revealed preference property (which is a much stronger condition than revealed preferences for a single individual) or the gross substitute property then likewise the equilibrium will be unique. All methods of establishing uniqueness can be thought of as establishing that each equilibrium has the same positive local index, in which case by the index theorem there can be but one such equilibrium.
Determinacy[edit]
Given that equilibria may not be unique, it is of some interest to ask whether any particular equilibrium is at least locally unique. If so, then comparative statics can be applied as long as the shocks to the system are not too large. As stated above, in a regular economy equilibria will be finite, hence locally unique. One reassuring result, due to Debreu, is that "most" economies are regular.
Work by Michael Mandler (1999) has challenged this claim.[17] The Arrow–Debreu–McKenzie model is neutral between models of production functions as continuously differentiable and as formed from (linear combinations of) fixed coefficient processes. Mandler accepts that, under either model of production, the initial endowments will not be consistent with a continuum of equilibria, except for a set of Lebesgue measure zero. However, endowments change with time in the model and this evolution of endowments is determined by the decisions of agents (e.g., firms) in the model. Agents in the model have an interest in equilibria being indeterminate:
Indeterminacy, moreover, is not just a technical nuisance; it undermines the price-taking assumption of competitive models. Since arbitrary small manipulations of factor supplies can dramatically increase a factor's price, factor owners will not take prices to be parametric.[17]:17
When technology is modeled by (linear combinations) of fixed coefficient processes, optimizing agents will drive endowments to be such that a continuum of equilibria exist:
The endowments where indeterminacy occurs systematically arise through time and therefore cannot be dismissed; the Arrow-Debreu-McKenzie model is thus fully subject to the dilemmas of factor price theory.[17]:19
Some have questioned the practical applicability of the general equilibrium approach based on the possibility of non-uniqueness of equilibria.
Stability[edit]
In a typical general equilibrium model the prices that prevail "when the dust settles" are simply those that coordinate the demands of various consumers for various goods. But this raises the question of how these prices and allocations have been arrived at, and whether any (temporary) shock to the economy will cause it to converge back to the same outcome that prevailed before the shock. This is the question of stability of the equilibrium, and it can be readily seen that it is related to the question of uniqueness. If there are multiple equilibria, then some of them will be unstable. Then, if an equilibrium is unstable and there is a shock, the economy will wind up at a different set of allocations and prices once the convergence process terminates. However stability depends not only on the number of equilibria but also on the type of the process that guides price changes (for a specific type of price adjustment process see Walrasian auction). Consequently, some researchers have focused on plausible adjustment processes that guarantee system stability, i.e., that guarantee convergence of prices and allocations to some equilibrium. When more than one stable equilibrium exists, where one ends up will depend on where one begins.
Unresolved problems in general equilibrium[edit]
Research building on the Arrow–Debreu–McKenzie model has revealed some problems with the model. The Sonnenschein–Mantel–Debreu results show that, essentially, any restrictions on the shape of excess demand functions are stringent. Some[18] think this implies that the Arrow–Debreu model lacks empirical content. At any rate, Arrow–Debreu–McKenzie equilibria cannot be expected to be unique, or stable.
A model organized around the tâtonnement process has been said to be a model of a centrally planned economy, not a decentralized market economy. Some research has tried to develop general equilibrium models with other processes. In particular, some economists have developed models in which agents can trade at out-of-equilibrium prices and such trades can affect the equilibria to which the economy tends. Particularly noteworthy are the Hahn process, the Edgeworth process and the Fisher process.
The data determining Arrow-Debreu equilibria include initial endowments of capital goods. If production and trade occur out of equilibrium, these endowments will be changed further complicating the picture.
In a real economy, however, trading, as well as production and consumption, goes on out of equilibrium. It follows that, in the course of convergence to equilibrium (assuming that occurs), endowments change. In turn this changes the set of equilibria. Put more succinctly, the set of equilibria is path dependent... [This path dependence] makes the calculation of equilibria corresponding to the initial state of the system essentially irrelevant. What matters is the equilibrium that the economy will reach from given initial endowments, not the equilibrium that it would have been in, given initial endowments, had prices happened to be just right
(Franklin Fisher).[19]
The Arrow–Debreu model in which all trade occurs in futures contracts at time zero requires a very large number of markets to exist. It is equivalent under complete markets to a sequential equilibrium concept in which spot markets for goods and assets open at each date-state event (they are not equivalent under incomplete markets); market clearing then requires that the entire sequence of prices clears all markets at all times. A generalization of the sequential market arrangement is the temporary equilibrium structure, where market clearing at a point in time is conditional on expectations of future prices which need not be market clearing ones.
Although the Arrow–Debreu–McKenzie model is set out in terms of some arbitrary numéraire, the model does not encompass money. Frank Hahn, for example, has investigated whether general equilibrium models can be developed in which money enters in some essential way. One of the essential questions he introduces, often referred to as the Hahn's problem is : "Can one construct an equilibrium where money has value?" The goal is to find models in which existence of money can alter the equilibrium solutions, perhaps because the initial position of agents depends on monetary prices.
Some critics of general equilibrium modeling contend that much research in these models constitutes exercises in pure mathematics with no connection to actual economies. In a 1979 article, Nicholas Georgescu-Roegen complains: "There are endeavors that now pass for the most desirable kind of economic contributions although they are just plain mathematical exercises, not only without any economic substance but also without any mathematical value."[20] He cites as an example a paper that assumes more traders in existence than there are points in the set of real numbers.
Although modern models in general equilibrium theory demonstrate that under certain circumstances prices will indeed converge to equilibria, critics hold that the assumptions necessary for these results are extremely strong. As well as stringent restrictions on excess demand functions, the necessary assumptions include perfect rationality of individuals; complete information about all prices both now and in the future; and the conditions necessary for perfect competition. However some results from experimental economics suggest that even in circumstances where there are few, imperfectly informed agents, the resulting prices and allocations may wind up resembling those of a perfectly competitive market (although certainly not a stable general equilibrium in all markets).[citation needed]
Frank Hahn defends general equilibrium modeling on the grounds that it provides a negative function. General equilibrium models show what the economy would have to be like for an unregulated economy to be Pareto efficient.[citation needed]
Computing general equilibrium[edit]
Main articles: Applied general equilibrium and Computable general equilibrium
Until the 1970s general equilibrium analysis remained theoretical. With advances in computing power and the development of input–output tables, it became possible to model national economies, or even the world economy, and attempts were made to solve for general equilibrium prices and quantities empirically.
Applied general equilibrium (AGE) models were pioneered by Herbert Scarf in 1967, and offered a method for solving the Arrow–Debreu General Equilibrium system in a numerical fashion. This was first implemented by John Shoven and John Whalley (students of Scarf at Yale) in 1972 and 1973, and were a popular method up through the 1970s.[21][22] In the 1980s however, AGE models faded from popularity due to their inability to provide a precise solution and its high cost of computation.
Computable general equilibrium (CGE) models surpassed and replaced AGE models in the mid-1980s, as the CGE model was able to provide relatively quick and large computable models for a whole economy, and was the preferred method of governments and the World Bank. CGE models are heavily used today, and while 'AGE' and 'CGE' is used inter-changeably in the literature, Scarf-type AGE models have not been constructed since the mid-1980s, and the CGE literature at current is not based on Arrow-Debreu and General Equilibrium Theory as discussed in this article. CGE models, and what is today referred to as AGE models, are based on static, simultaneously solved, macro balancing equations (from the standard Keynesian macro model), giving a precise and explicitly computable result.[23]
Other schools[edit]
General equilibrium theory is a central point of contention and influence between the neoclassical school and other schools of economic thought, and different schools have varied views on general equilibrium theory. Some, such as the Keynesian and Post-Keynesian schools, strongly reject general equilibrium theory as "misleading" and "useless". Other schools, such as new classical macroeconomics, developed from general equilibrium theory.
Keynesian and Post-Keynesian[edit]
Keynesian and Post-Keynesian economists, and their underconsumptionist predecessors criticize general equilibrium theory specifically, and as part of criticisms of neoclassical economics generally. Specifically, they argue that general equilibrium theory is neither accurate nor useful, that economies are not in equilibrium, that equilibrium may be slow and painful to achieve, and that modeling by equilibrium is "misleading", and that the resulting theory is not a useful guide, particularly for understanding of economic crises.[24][25]
Let us beware of this dangerous theory of equilibrium which is supposed to be automatically established. A certain kind of equilibrium, it is true, is reestablished in the long run, but it is after a frightful amount of suffering.
—  Simonde de Sismondi, New Principles of Political Economy, vol. 1, 1819, pp. 20-21.
The long run is a misleading guide to current affairs. In the long run we are all dead. Economists set themselves too easy, too useless a task if in tempestuous seasons they can only tell us that when the storm is past the ocean is flat again.
—  John Maynard Keynes, A Tract on Monetary Reform, 1923, ch. 3
It is as absurd to assume that, for any long period of time, the variables in the economic organization, or any part of them, will "stay put," in perfect equilibrium, as to assume that the Atlantic Ocean can ever be without a wave.
—  Irving Fisher, The Debt-Deflation Theory of Great Depressions, 1933, p. 339
Robert Clower and others have argued for a reformulation of theory toward disequilibrium analysis to incorporate how monetary exchange fundamentally alters the representation of an economy as though a barter system.[26]
New classical macroeconomics[edit]
While general equilibrium theory and neoclassical economics generally were originally microeconomic theories, new classical macroeconomics builds a macroeconomic theory on these bases. In new classical models, the macroeconomy is assumed to be at its unique equilibrium, with full employment and potential output, and that this equilibrium is assumed to always have been achieved via price and wage adjustment (market clearing). The best-known such model is Real Business Cycle Theory, in which business cycles are considered to be largely due to changes in the real economy, unemployment is not due to the failure of the market to achieve potential output, but due to equilibrium potential output having fallen and equilibrium unemployment having risen.
Socialist economics[edit]
Within socialist economics, a sustained critique of general equilibrium theory (and neoclassical economics generally) is given in Anti-Equilibrium,[27] based on the experiences of János Kornai with the failures of Communist central planning, although Michael Albert and Robin Hahnel later based their Parecon model on the same theory[28].
See also[edit]
General equilibrium theorists (category)
Cobweb model
Decision theory
Game theory
Mechanism design theory
Notes[edit]
Jump up ^ Walras, Léon (1954) [1877]. Elements of Pure Economics. Irwin. ISBN 0-678-06028-2. Scroll to chapter-preview links.
Jump up ^ Eatwell, John (1987). "Walras's Theory of Capital". In Eatwell, J.; Milgate, M.; Newman, P. The New Palgrave: A Dictionary of Economics. London: Macmillan.
Jump up ^ Jaffe, William (1953). "Walras's Theory of Capital Formation in the Framework of his Theory of General Equilibrium". Economie Appliquée. 6: 289–317.
Jump up ^ Arrow, K. J.; Debreu, G. (1954). "The Existence of an Equilibrium for a Competitive Economy". Econometrica. 22 (3): 265–290. doi:10.2307/1907353. JSTOR 1907353.
Jump up ^ McKenzie, Lionel W. (1959). "On the Existence of General Equilibrium for a Competitive Economy". Econometrica. 27 (1): 54–71. doi:10.2307/1907777. JSTOR 1907777.
Jump up ^ Debreu, G. (1959). Theory of Value. New York: Wiley. p. 98.
Jump up ^ McKenzie, Lionel W. (1954). "On Equilibrium in Graham's Model of World Trade and Other Competitive Systems". Econometrica. 22 (2): 147–161. doi:10.2307/1907539. JSTOR 1907539.
Jump up ^ Arrow, K. J.; Debreu, G. (1954). "Existence of an equilibrium for a competitive economy". Econometrica. 22 (3): 265–290. doi:10.2307/1907353.
Jump up ^ Uzawa, Hirofumi (1962). "Walras' Existence Theorem and Brouwer's Fixed-Point Theorem". Economic Studies Quarterly. 13 (1): 59–62. doi:10.11398/economics1950.13.1_59.
Jump up ^ Starr, Ross M. (1969). "Quasi-equilibria in markets with non-convex preferences" (PDF). Econometrica. 37 (1): 25–38. doi:10.2307/1909201. JSTOR 1909201.
^ Jump up to: a b c Guesnerie, Roger (1989). "First-best allocation of resources with nonconvexities in production". In Bernard Cornet and Henry Tulkens. Contributions to Operations Research and Economics: The twentieth anniversary of CORE (Papers from the symposium held in Louvain-la-Neuve, January 1987). Cambridge, MA: MIT Press. pp. 99–143. ISBN 0-262-03149-3. MR 1104662.
Jump up ^ See pages 392–399 for the Shapley-Folkman-Starr results and see page 188 for applications in Arrow & Hahn: Arrow, Kenneth J.; Hahn, Frank H. (1971). "Appendix B: Convex and related sets". General Competitive Analysis. Mathematical economics texts [Advanced textbooks in economics]. San Francisco, CA: Holden-Day, Inc. [North-Holland]. pp. 375–401. ISBN 0-444-85497-5. MR 0439057.
Jump up ^ Pages 52–55 with applications on pages 145–146, 152–153, and 274–275 in Mas-Colell, Andreu (1985). "1.L Averages of sets". The Theory of General Economic Equilibrium: A Differentiable Approach. Econometric Society Monographs. Cambridge UP. ISBN 0-521-26514-2. MR 1113262.
Jump up ^ Hildenbrand, Werner (1974). Core and Equilibria of a Large Economy. Princeton Studies in Mathematical Economics. Princeton, N.J.: Princeton University Press. pp. viii+251. ISBN 978-0-691-04189-6. MR 0389160.
Jump up ^ See section 7.2 Convexification by numbers in Salanié: Salanié, Bernard (2000). "7 Nonconvexities". Microeconomics of market failures (English translation of the (1998) French Microéconomie: Les défaillances du marché (Economica, Paris) ed.). Cambridge, MA: MIT Press. pp. 107–125. ISBN 0-262-19443-0.
Jump up ^ An "informal" presentation appears in pages 63–65 of Laffont: Laffont, Jean-Jacques (1988). "3 Nonconvexities". Fundamentals of Public Economics. MIT. ISBN 0-585-13445-6.
^ Jump up to: a b c Mandler, Michael (1999). Dilemmas in Economic Theory: Persisting Foundational Problems of Microeconomics. Oxford: Oxford University Press. ISBN 0-19-510087-5.
Jump up ^ Turab Rizvi, S. Abu (2006). "The Sonnenschein-Mantel-Debreu Results after Thirty Years". History of Political Economy. 38 (Suppl. 1): 228–245.
Jump up ^ As quoted by Petri, Fabio (2004). General Equilibrium, Capital, and Macroeconomics: A Key to Recent Controversies in Equilibrium Theory. Cheltenham, UK: Edward Elgar. ISBN 1-84376-829-1.
Jump up ^ Georgescu-Roegen, Nicholas (1979). "Methods in Economic Science". Journal of Economic Issues. 13 (2): 317–328. JSTOR 4224809.
Jump up ^ Shoven, J. B.; Whalley, J. (1972). "A General Equilibrium Calculation of the Effects of Differential Taxation of Income from Capital in the U.S.". Journal of Public Economics. 1 (3–4): 281–321. doi:10.1016/0047-2727(72)90009-6.
Jump up ^ Shoven, J. B.; Whalley, J. (1973). "General Equilibrium with Taxes: A Computational Procedure and an Existence Proof". The Review of Economic Studies. 40 (4): 475–489. JSTOR 2296582.
Jump up ^ Mitra-Kahn, Benjamin H. (2008). "Debunking the Myths of Computable General Equilibrium Models" (PDF). Schwarz Center for Economic Policy Analysis Working Paper 01-2008.
Jump up ^ Keen, Steve (May 4, 2009). "Debtwatch No 34: The Confidence Trick".
Jump up ^ Keen, Steve (November 30, 2008). "DebtWatch No 29 December 2008".
Jump up ^ • Robert W. Clower (1965). "The Keynesian Counter-Revolution: A Theoretical Appraisal," in F.H. Hahn and F.P.R. Brechling, ed., The Theory of Interest Rates. Macmillan. Reprinted in Clower (1987), Money and Markets. Cambridge. Description and preview via scroll down. pp. 34-58.
• _____ (1967). "A Reconsideration of the Microfoundations of Monetary Theory," Western Economic Journal, 6(1), pp. 1–8[permanent dead link] (press +).
• _____ and Peter W. Howitt (1996). "Taking Markets Seriously: Groundwork for a Post-Walrasian Macroeconomics", in David Colander, ed., Beyond Microfoundations, pp. 21–37.
• Herschel I. Grossman (1971). "Money, Interest, and Prices in Market Disequilibrium," Journal of Political Economy,79(5), p p. 943–961.
• Jean-Pascal Bénassy (1990). "Non-Walrasian Equilibria, Money, and Macroeconomics," Handbook of Monetary Economics, v. 1, ch. 4, pp. 103-169. Table of contents.
• _____ (1993). "Nonclearing Markets: Microeconomic Concepts and Macroeconomic Applications," Journal of Economic Literature, 31(2), pp. 732–761 (press +).
• _____ (2008). "non-clearing markets in general equilibrium," in The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.
Jump up ^ Kornai, János (1971). Anti-Equilibrium: On Economic Systems Theory and the Tasks of Research. Amsterdam: North-Holland. ISBN 0-7204-3055-0.
Jump up ^ Albert, Michael; Hahnel, Robin (1991). AThe Political Economy of Participatory Economics. Princeton: Princeton University Press. p. 7.
References[edit]
Arrow, K. J.; Hahn, F. H. (1971). General Competitive Analysis. San Francisco: Holden-Day. ISBN 0-8162-0275-3.
Black, Fischer (1995). Exploring General Equilibrium. Cambridge, MA: MIT Press. ISBN 0-262-02382-2.
Eaton, B. Curtis; Eaton, Diane F.; Allen, Douglas W. (2009). "Competitive General Equilibrium". Microeconomics: Theory with Applications (Seventh ed.). Toronto: Pearson Prentice Hall. ISBN 978-0-13-206424-8.
Geanakoplos, John (1987). "Arrow-Debreu model of general equilibrium". The New Palgrave: A Dictionary of Economics. 1. pp. 116–124.
Grandmont, J. M. (1977). "Temporary General Equilibrium Theory". Econometrica. 45 (3): 535–572. doi:10.2307/1911674. JSTOR 1911674.
Hicks, John R. (1946) [1939]. Value and Capital (Second ed.). Oxford: Clarendon Press.
Kubler, Felix (2008). "Computation of general equilibria (new developments)". The New Palgrave Dictionary of Economics (Second ed.).
Mas-Colell, A.; Whinston, M.; Green, J. (1995). Microeconomic Theory. New York: Oxford University Press. ISBN 0-19-507340-1.
McKenzie, Lionel W. (1981). "The Classical Theorem on Existence of Competitive Equilibrium". Econometrica. 49 (4): 819–841. doi:10.2307/1912505. JSTOR 1912505.
_____ (1983). "Turnpike Theory". Journal of Economic Theory. 30 (2): 330–352. doi:10.1016/0022-0531(83)90111-4.
_____ (1987). "General equilibrium". The New Palgrave: A Dictionary of Economics. 2. pp. 498–512.
_____ (1987). "Turnpike theory". The New Palgrave: A Dictionary of Economics. 4. pp. 712–720.
_____ (1999). "Equilibrium, Trade, and Capital Accumulation". Japanese Economic Review. 50 (4): 371–397. doi:10.1111/1468-5876.00128.
Samuelson, Paul A. (1941). "The Stability of Equilibrium: Comparative Statics and Dynamics". Econometrica. 9 (2): 97–120. doi:10.2307/1906872. JSTOR 1906872.
_____ (1983) [1947]. Foundations of Economic Analysis (Enlarged ed.). Harvard University Press. ISBN 0-674-31301-1.
Scarf, Herbert E. (2008). "Computation of general equilibria". The New Palgrave Dictionary of Economics (Second ed.).
Schumpeter, Joseph A. (1954). History of Economic Analysis. Oxford University Press.
External links[edit]
Selected entries on general equilibrium theory from The New Palgrave Dictionary of Economics, 2nd Edition, 2008 with Abstract links:
"Arrow–Debreu model of general equilibrium" by John Geanakoplos.
"general equilibrium" by Lionel W. McKenzie.
"general equilibrium (new developments" by William Zame.
"non-clearing markets in general equilibrium" by Jean-Pascal Bénassy.
overlapping generations model of general equilibrium" by John Geanakoplos.
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It's Raining, It's Pouring
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"It's Raining, It's Pouring"
Nursery rhyme
Recorded
1939
Songwriter(s)
Unknown
Children's literature portal
"It's Raining, It's Pouring" is an English language nursery rhyme and children's song. It has a Roud Folk Song Index number of 16814.
Lyrics[edit]
It's raining; it's pouring.
The old man is snoring.
He bumped his head and went to bed,
And wouldn’t get up in the morning.
Origins and interpretation[edit]
The first two lines of this rhyme can be found in The Little Mother Goose, published in the US in 1912.[1] The melody most often associated with it is the same as "A Tisket, A Tasket", which is in the public domain. The earliest known audio recording of the song was made in 1939 in New York by anthropologist and folklorist Herbert Halpert and is held in the Library of Congress.[2] It was noted in 1939 in New York by Charles Ives (1874–1954) and a version of it was copyrighted in 1944 by Freda Selicoff.[3]
It has been suggested that the verse is a "classic description" of a head injury ("bumped his head"), followed by a lucid interval and an inability to resume normal activity ("couldn't get up in the morning"). However, it has also been suggested that, in regards to the first verse at least, that the rhyme is an interpretation of an accidental death ("didn't get up in the morning; indicating that no attempt or ability to get up made).[4]
References[edit]
Jump up ^ Anon, The Little Mother Goose (1912, Dodd, Mead & Company, 3rd edn., 1918), p. 169.
Jump up ^ "Audio Recordings It's raining, it's pouring", Library of Congress, retrieved 16 June 2015.
Jump up ^ C. W. Henderson, The Charles Ives Tunebook (Indiana University Press, 2008), p. 141; Library of Congress Copyright Office, Catalog of copyright entries (Library of Congress, Copyright Office, 1944), p. 1362.
Jump up ^ A. H. Kaye, "Essential Neurosurgery" 3rd Ed., (Blackwell Publishing, 2004), p. 57
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"A-Tisket, A-Tasket"
"Aiken Drum"
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"Did You Ever See a Lassie?"
"Hey Diddle Diddle"
"Hickory Dickory Dock"
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"I'm a Little Teapot"
"It's Raining, It's Pouring"
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"Three Little Kittens"
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"A Sailor Went to Sea"
"Down Down Baby"
"Mary Mack"
"Miss Susie"
"Miss Lucy"
"Pat-a-cake"
"Pease Porridge Hot"
"Pretty Little Dutch Girl"
"Stella Ella Ola"
Counting
"Duck, duck, goose"
"Eeny, meeny, miny, moe"
"One, Two, Buckle My Shoe"
"One, Two, Three, Four, Five"
"This Old Man"
"Tinker, Tailor"
Finger-
plays
"Five Little Ducks"
"Five Little Monkeys"
"Five Little Speckled Frogs"
"Itsy Bitsy Spider"
"Little Robin Redbreast"
"Round and Round the Garden"
"This Little Piggy"
"Two Little Dickie Birds"
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"London Bridge"
"The Muffin Man"
"Mulberry Bush"
"Oranges and Lemons"
"Ring a Ring o' Roses"
"The Farmer in the Dell"
Riddle
"As I was going to St Ives"
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"Hush, Little Baby"
"Rock-a-bye Baby"
Rounds
"Ding Dong Bell"
"Frère Jacques"
"Kookaburra"
"Row, Row, Row Your Boat"
"Scotland's Burning"
"Three Blind Mice"
Retrieved from "https://en.wikipedia.org/w/index.php?title=It%27s_Raining,_It%27s_Pouring&oldid=852528270"
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text:
Humko Deewana Kar Gaye
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Humko Deewana Kar Gaye
Directed by
Raj Kanwar
Produced by
Raj Kanwar
Bhushan Kumar
Krishan Kumar Dua
Written by
Abbas Tyrewala
Vipul Amrutlal Shah
Richard Curtis
Starring
Akshay Kumar
Bipasha Basu
Katrina Kaif
Anil Kapoor
Music by
Anu Malik
Himesh Reshammiya
Background score=Raju Rao
Cinematography
Vikas Sivaraman
Edited by
Kuldip K. Mehan
Production
company
Inderjit Films Combine
Distributed by
T-Series
Release date
14 April 2006
Running time
152 mins
Country
India
Language
Hindi
Humko Deewana Kar Gaye (translation: You Made Me Crazy) is a 2006 Indian Hindi romantic drama film directed by Raj Kanwar, produced by Raj Kanwar, Bhushan Kumar & Krishan Kumar and starring Akshay Kumar and Katrina Kaif, Bipasha Basu, Anil Kapoor and Manoj Joshi also star in the movie in supporting roles. The film is inspired by British romantic movie Notting Hill.[1] The film is produced by the Indian music company, T-Series and Inderjit Films Combine. The movie's score and soundtrack is composed by Anu Malik with lyrics by Sameer. Himesh Reshammiya rendered a special song for the film which became extremely popular. The film released on 14 April 2006. The music of the film released on 2 February 2006.
Contents
[hide]
1 Plot
2 Cast and Crew
2.1 Cast
2.2 Crew
3 Box office and reception
4 Soundtrack
5 References
6 External links
Plot[edit]
Aditya (Akshay Kumar), an automobile engineer, is passionate about cars. Not only is he an engineer, he is also a test driver for the company. He is engaged to marry Sonia (Bipasha Basu), a budding fashion designer. Aditya and Sonia are not on the same wavelength; while he is a traditionalist, she is an ultra-modern woman for whom career comes first. Much as Aditya tries to overlook these facts, they keep coming in the way of their relationship. Nevertheless, their wedding date is fixed and their families are preparing for the event.
Meanwhile, Aditya is sent by his employer to Canada to learn about a new car model to be launched in India. Sonia also leaves at the same time for Paris in connection with a fashion show. Aditya arrives in Canada and is received by his sister Simran (Bhagyashree), her husband Robby (Mahesh Thakur) and their son, who all live in Canada. Destiny makes Aditya continually bump into Jia (Katrina Kaif), daughter of business tycoon Yashwardhan Birla, and fiancée of the business magnate Karan Oberoi (Anil Kapoor). She has come to Canada all by herself to shop for her wedding. Despite her family's great wealth, she is a simple girl with a thirst for true love. She had everything she could ask for in her childhood but never time from her ever-so-busy father. Now, the man her father has chosen for her hardly has any time for her either. She finds a friend in Aditya, and as the two spend time together, their friendship grows.
Aditya gets a chance from the company to participate in a car rally. He persuades Jia to participate with him and they win. On returning from the rally, their car gets stuck in the snow and they have to spend the night together. They share intimate moments, which makes them forget that they are engaged to other people. Soon, they realize they are falling in love. When Jia tells Aditya that she believes her father is responsible for her mother's death, Aditya tells this to his best friend and roommate, Nawab. On a drunken night, Nawab tells his other friend, who is a reporter. The reporter then publishes this in the newspaper. Jia is extremely hurt, and returns to India to marry Karan. Aditya also returns to India to get married to Sonia, and does not attempt to meet Jia.
Sonia turns out to be the designer for Jia's wedding. Mr Oberoi invites Sonia (as the wedding designer) and Aditya (as her fiancé) to attend his wedding, and Sonia persuades a reluctant Aditya to attend. Jia's friend and Karan's secretary, Jenny, bumps into Nawab, who reveals that it was his fault that Jia's secret suspicion was published in the papers. But it is too late — the wedding ceremony is over and Jia and Karan are married. Jia then goes to meet Aditya to apolgize. They confess their love for each other, but agree never to meet again. However, Karan catches them talking, and questions Jia. She claims that she truly loves Karan and that Aditya is just a good friend.
When Aditya leaves the wedding, he finds an upside-down car on the road, and it turns out that Jia has had an accident and is trapped under the car. As petrol leaks, Aditya goes into the car to help Jia. The car catches fire, just as Aditya manages to free her. He helps her out of the car, while the press and public gather around. He accompanies Jia to Karan, telling him that Jia only belongs to him. However, Karan has a change of heart and pulls Jia's mangalsutra off, telling her to marry Aditya. Aditya's engagement with Sonia is also broken, and he and Jia hug, finally united.
Cast and Crew[edit]
Cast[edit]
Akshay Kumar as Aditya Malhotra
Bipasha Basu as Sonia Berry
Katrina Kaif as Jia A. Yashvardhan (Mona Ghosh Shetty as the dubbing voice)
Anil Kapoor as Karan Oberoi
Mahesh Thakur as Robby Kohli
Bhagyashree as Simran Kohli (Special Appearance)
Delnaaz Paul as Tanya Berry
Manoj Joshi as Rasikbhai Galgalia
Shernaz Patel as Jennifer
Gurpreet Ghuggi as Gurpreet Guggi
Vivek Shauq as Nawab Sharif
Ranjeet as Harpreet Malhotra
Puneet Issar as Yuvraj Berry
Helen as Kitty Kohli
Master Abhay Kanwar as Dumpty Kohli
Himesh Reshammiya as himself - Special Appearance
Crew[edit]
Director: Raj Kanwar
Story: Raj Kanwar
Dialogue: Sudhanshu Dube, Anurag Singh
Producer: Raj Kanwar, Gulshan Kumar, Kishan Kumar & Bhushan Kumar
Music: Anu Malik and Himesh Reshammiya
Cinematography: Vikas Sivaraman
Choreography: Ganesh Acharya
Lyrics: Sameer
Box office and reception[edit]
[2][3] The movie received mixed reviews from the critics, however it managed on boxoffice to be average though the audiences overwhelmed the movie till date.
Soundtrack[edit]
The Soundtrack of the movie was composed by Anu Malik and Himesh Reshammiya, and the lyrics were authored by Sameer. The Soundtrack was well received, and amongst the best of the year. It contains 8 songs, alongside its 5 variants and 3 remixes. According to the Indian trade website Box Office India, with around 12,00,000 units sold, this film's soundtrack album was the year's tenth highest-selling.[4]
Song
Singer(s)
Composer
"Humko Deewana Kar Gaye" Sonu Nigam & Tulsi Kumar Anu Malik
"Humko Deewana Kar Gaye-II" Sonu Nigam Anu Malik
"Humko Deewana Kar Gaye-Sad" Sonu Nigam Anu Malik
"Humko Deewana Kar Gaye-Sad II" Tulsi Kumar Anu Malik
"Tum Sansoon Main" Himesh Reshammiya & Tulsi Kumar Himesh Reshammiya
"Tum Sansoon Main-Remix" Himesh Reshammiya & Tulsi Kumar Himesh Reshammiya
"Tum Sansoon Main-Unplugged" Himesh Reshammiya & Tulsi Kumar Himesh Reshammiya
"Rockstar" Abhijeet Bhattacharya, Anu Malik & Sunidhi Chauhan Anu Malik
"Dekhte Dekhte" Abhijeet Bhattacharya & Alka Yagnik Anu Malik
"Mere Saath Chalte Chalte" Shaan, Sunidhi Chauhan, Krishna Beura Anu Malik
"For Your Eyes Only" Sonu Nigam, & Nandini Srikar Anu Malik
"For Your Eyes Only-Remix" Sonu Nigam, & Nandini Srikar Anu Malik, remixed by Jatin Sharma
"Bhula Denge Tum Ko Sanam" Sonu Nigam Anu Malik
"Bhula Denge Tum Ko Sanam-Remix" Sonu Nigam Anu Malik, remixed by Jatin Sharma
"Fanah" K.K. & Anu Malik Anu Malik
"Fanah-Remix" K.K. Anu Malik, remixed by Akbar Sami & Anu Malik
References[edit]
Jump up ^ http://anantsworld.tripod.com/remakes.html
Jump up ^ http://ww.smashits.com/katrina-akshay-pair-fails-to-lift-the-love-spirit/movie-review-5379.html
Jump up ^ http://www.bollywoodhungama.com/movies/review/12476/index.html
Jump up ^ "Music Hits 2000–2009 (Figures in Units)". Box Office India. Archived from the original on 24 June 2010.
External links[edit]
Humko Deewana Kar Gaye on IMDb
Retrieved from "https://en.wikipedia.org/w/index.php?title=Humko_Deewana_Kar_Gaye&oldid=814747013"
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Death in Heaven
From Wikipedia, the free encyclopedia
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252b – "Death in Heaven"
Doctor Who episode
Promotional image for the episode
Cast
Doctor
Peter Capaldi (Twelfth Doctor)
Companion
Jenna Coleman (Clara Oswald)
Others
Samuel Anderson – Danny Pink
Michelle Gomez – Missy
Chris Addison – Seb
Ingrid Oliver – Osgood
Jemma Redgrave – Kate Stewart
Sanjeev Bhaskar – Colonel Ahmed
James Pearse – Graham
Antonio Bourouphael – Boy
Shane Keogh-Grenade – Teenage boy
Katie Bignell – Teenage girl
Jeremiah Krage – Cyberman
Nicholas Briggs – Voice of the Cybermen
Nick Frost – Santa Claus
Production
Directed by
Rachel Talalay
Written by
Steven Moffat
Script editor
David P Davis
Produced by
Peter Bennett
Executive producer(s)
Steven Moffat
Brian Minchin
Incidental music composer
Murray Gold
Series
Series 8
Length
2nd of 2-part story, 60 minutes
Originally broadcast
8 November 2014
Chronology
← Preceded by Followed by →
"Dark Water" "Last Christmas"
List of Doctor Who serials
"Death in Heaven" is the twelfth and final episode of the eighth series of the British science fiction television programme Doctor Who. It is the second episode of a two-part story involving the return of the Cybermen and the Master in the form of 'Missy', the first part being "Dark Water", written by Steven Moffat and directed by Rachel Talalay. The episode stars Peter Capaldi, Jenna Coleman, Samuel Anderson, Michelle Gomez, Chris Addison, Jemma Redgrave, and Ingrid Oliver.
The episode received mostly positive reviews, with critics praising its writing, direction, and acting. With Peter Capaldi, Jenna Coleman, Samuel Anderson, and Michelle Gomez receiving widespread acclaim for their performances, Gomez was consistently highly praised in reviews, with many calling her a highlight of the eighth series.[1][2][3][4]
Contents
[hide]
1 Plot
1.1 Continuity
2 Production
3 Reception
4 Notes
5 References
6 External links
Plot[edit]
Continuing from "Dark Water", Clara Oswald is trapped with a Cyberman in the headquarters of 3W in St Paul's Cathedral and manages to stop it from killing her by stating that she is really the Doctor.[nb 1]
Outside, the Doctor reels from the revelation that Missy, the woman controlling the Cybermen, is a female incarnation of the Master. The public appears unconcerned by the arrival of the Cybermen, but UNIT, led by Kate Lethbridge-Stewart, turn up and surround the Doctor, Missy, and her group of Cybermen. The Cybermen take to the air using built-in leg jets and scatter over the British Isles. Missy reveals that 91 Cybermen – one for every major population area in the United Kingdom – have been released from St Paul's to explode over graveyards in each populated area, releasing 'Cyberpollen' that will resurrect the dead as Cybermen. Similar events occur all over the world. UNIT renders both Missy and the Doctor unconscious and takes them into custody.
In the Nethersphere, the dimension where Missy has trapped the souls of the dead, Danny Pink has chosen not to "delete" his emotions (having been given the choice in the prior episode). He sees the Nethersphere environment going dark and asks the virtual assistant Seb what is happening. Seb reveals that the "cloud" that is the Nethersphere is dispersing, and the souls are being released back to their bodies via rainclouds. Meanwhile, Clara tries to use her knowledge of the Doctor to authenticate her claim, but fails to convince the Cybermen in 3W that she truly is the Doctor. She is saved by Danny, who is now a Cyberman but has retained his personality.
Aboard a protected UNIT aircraft, Kate reveals to the Doctor that, per United Nations emergency protocols, he has been designated "President of Earth" with full control of the planet's armies. Cyberpollen is reconstituting the dead as Cybermen, but the Doctor is unable to get anything further from Missy about her plans for the Cybermen. He tells Kate and other officials on board that there is nothing they can do for Earth now. In the meantime, Clara awakens at a graveyard where Danny reveals himself to her. Danny asks her to activate his cyber-body's emotion inhibitor, as he cannot stand the physical and emotional pain he now suffers.
Missy escapes her captors and kills UNIT scientist Osgood. The Doctor faces her as a horde of flying Cybermen attack the plane. Clara calls the Doctor on the TARDIS's phone. Missy admits she is the one who gave Clara that phone number ("The Bells of Saint John") to bring her and the Doctor together. Clara asks for his help to stop Danny's torment, but the Doctor, fearing that Danny would then kill Clara, refuses. Missy then blasts open one of the plane's cargo doors, sending Kate and the Doctor plummeting towards the ground to their deaths while she teleports to safety. The Doctor narrowly escapes by calling the TARDIS to catch him and break his fall, and he joins Clara at the graveyard. The Doctor still refuses to help Danny for moral reasons. He asks Danny about Missy's plans, but Danny tells him that the Cyberhive cannot be fully accessed without the inhibitor. As the Doctor is hesitant, Clara insists that she be the one to do it. The Doctor reluctantly gives her his sonic screwdriver to turn the inhibitor on. Danny then reveals that a second rainfall is coming, one which will convert living humans into Cybermen.
Missy teleports to join them and gives the Doctor control of the Cyberarmy, as a birthday present. She explains that he can lead his own personal Cyberman army as a conquering force to save the universe from tyranny, such as that of the Daleks, as he has always wanted. The Doctor protests that no one should have such power. Missy taunts that he does not trust himself, and she wants to prove to him that they are fundamentally the same. The Doctor ultimately rejects the gift, accepting that he is not a "good man", and passes the control bracelet to Danny, who is revealed to have kept hold of his personality through his love for Clara. Danny leads the Cyberarmy into the sky, where he and they explode, incinerating all the Cyberpollen clouds across the world, thus stopping the second rainfall and saving humankind.
Although disappointed that her plan has been ruined, Missy suggests that she and the Doctor can still become friends again and return to Gallifrey, which she claims has now returned to its original location. Furious over what has happened, Clara instead prepares to kill Missy with her own weapon. The Doctor, however, insists on committing the deed himself to keep Clara's hands clean. He acknowledges to Missy that she wins. But, before he can fire, a solitary Cyberman vaporises Missy and gestures towards an unconscious, but still living, Kate Lethbridge-Stewart. The Doctor realises that this Cyberman is her father, the late Brigadier Lethbridge-Stewart, also with his humanity intact. The Doctor salutes his old friend (something Kate remarked earlier that her father always wanted from the Doctor), and Lethbridge-Stewart fires his leg jets and flies away.
Two weeks later, Danny contacts Clara from the Nethersphere as it begins to shut down. Explaining that there is only enough power in Missy's control bracelet to bring one person back to life, Danny uses it to resurrect the boy he had accidentally killed while serving in the army. He asks Clara to return the boy to his parents. In the interim, the Doctor travels to the spatial coordinates given by Missy, only to find nothing there; Gallifrey remains lost. Some time later, Clara meets with the Doctor to tell him about Danny's fate. Assuming Danny is alive again, the Doctor interrupts her with the news that he found Gallifrey and plans to return home, wanting to spare Clara's feelings. Clara, in turn, says that she and Danny are going to settle down and resume their relationship. They bid each other goodbye.
Continuity[edit]
As the first full episode since The End of Time to feature the Master with her true identity revealed, "Death in Heaven" features various references to previous episodes featuring the Master. Osgood refers to previous incidents on Earth featuring the Master, including his tenure as Prime Minister in "The Sound of Drums". When boarding the airbase, the Doctor believes that he is going to the Valiant, an airborne aircraft carrier partially designed by the Master in "The Sound of Drums". Missy uses the phrase "Oh, my giddy aunt", an expression associated with the Second Doctor.[5]
The Cyberman head that Kate reveals is from the 1968 episode The Invasion, which also featured Cybermen invading near St. Paul's Cathedral.[5]
The scene in which Missy is tied to a chair on board the plane was written as a parallel to the Master tying the Doctor to a chair in The End of Time.[6]
The location of the planet Gallifrey—"in the constellation of Kasterborous" at galactic coordinates 10-0-11-00:02—was first mentioned in the Fourth Doctor story Pyramids of Mars.[5]
The episode ends with Santa Claus (Nick Frost) entering the TARDIS and asking the Doctor what he would like for Christmas, leading into the Christmas special "Last Christmas".
Production[edit]
The read through for "Death in Heaven" took place on 12 June 2014. Production of the episode overlapped with "Dark Water"; the opening scene involving UNIT was filmed prior to the final scene in the previous episode. Principal photography for the episode concluded on 21 July 2014.[5]
Reception[edit]
Overnight ratings estimate that the episode was watched by 5.45 million viewers. The finale was watched by a total of 7.60 million viewers. The episode received an AI score of 83. This was a lower score than the first part of the story received.[7]
The episode received mostly positive reviews. Dan Martin writing for The Guardian praised Michelle Gomez's performance, noting that she "preens with a perfect combination of madness and malevolence that is just so Master". He also notes that her demise is a nod to the Roger Delgado era of the Master. He summed up the final as "Action-packed, uncompromising, filled with genuine emotion".[1] While writing for The Daily Telegraph, Michael Hogan noted that Danny Pink got a "stupendous send-off" and that it would be a shame if Missy did not reappear in the future. Hogan also loved the two nods to Nicholas Courtney who played Brigadier Lethbridge-Stewart. He gave the episode four stars out of five.[8] Dave Golder, writing for SFX, gave the episode four stars out of five. He criticised some parts of the episode, including Danny's final moments in the graveyard, and he felt the episode was "less chilling than Dark Water". Overall, he stated "[it] was an immensely enjoyable series finale".[9]
Writing for IGN, Matt Risley, gave the episode an "Amazing" 9.1, calling it "a powerful and emotional finale to Capaldi's masterful first season." He also praised Michelle Gomez for her performance, but criticised the use of the Cybermen and plot holes.[4] On the AV Club, writer Alasdair Wilkins gave the episode A-, calling it a "bittersweet ending for the season". When commenting on the season as a whole, he said "we are left to ponder one of Doctor Who's most complex, emotionally rich seasons".[10]
Simon Brew of Den of Geek gave a mixed to positive review. He praised Michelle Gomez's, Capaldi's and Coleman's performances, but was critical of the Cybermen, believing them to be the weakest of the three cliffhanger threads from the previous week. He was also critical of the pacing and some plot holes and threads that were slightly unbelievable, citing the falling Doctor homing into the TARDIS as the main culprit. He was disappointed with Bhaskar's limited role in the episode and lack of resolutions to certain plot points. Overall though, he believed it to be one of the better finales since the show returned in 2005.[11]
The Register gave a generally negative review, with writer Brid-Aine Parnell saying "This finale couldn't lift itself up from the messy morass of the rest of the season… it didn't make sense, it was ridiculous and contrived and just not engaging." She was critical of plot holes in the episode and the fact no explanation was given for how the Master returned. She was however pleased with Gomez' performance believing it to be the best part of the episode, calling her "fantastic". Gavin Clarke said of the Doctor's "meltdown" in the Tardis: "This was a [sic] unexpected moment, his console trashing made more powerful for its silence over swelling music" and of it overall "Did Death in Heaven succeed? Mostly 'yes', some grumbling 'no's' and a bit of breathing deeply and just letting it go". His colleague, Jennifer Baker, said "The rationale for clouds and rain and pollination was confused, but zombie Cybermen climbing out of graves was worth it!"[2] Dan Wilson of Metro also gave a negative review, citing that it "left far too many threads hanging," but he too was positive about Michelle Gomez as the Master.[3]
Notes[edit]
Jump up ^ In the credits sequence that follows, the credits for Jenna Coleman and Peter Capaldi are reversed (with Coleman's appearing first), and an image of Coleman's eyes replaces Capaldi's. This gives the appearance that Clara is indeed the Doctor, though this is later shown to be untrue.
References[edit]
^ Jump up to: a b "Doctor Who recap series 34 episode 12: Death in Heaven", The Guardian, 8 November 2014 .
^ Jump up to: a b Gavin Clarke (8 Nov 2014). "Doctor Who trashing the TARDIS, Clara alone, useless UNIT – Death in Heaven". The Register. Retrieved 15 February 2015.
^ Jump up to: a b "Doctor Who series 8 finale: Death in Heaven left far too many threads hanging - Metro News". Metro.
^ Jump up to: a b "Doctor Who Death in Heaven review", IGN, UK, 8 November 2014 .
^ Jump up to: a b c d "Doctor Who, Series 8, Death in Heaven - Death in Heaven: Fact File". Doctor Who. BBC. 8 November 2014. Retrieved 9 November 2014.
Jump up ^ "Doctor Who: Steven Moffat on series 8, Missy, lies and leaks". Den of Geek.
Jump up ^ Series 8 ratings accumulator, UK: Doctor Who TV .
Jump up ^ "Doctor Who review: Death in Heaven, Peter Capaldi", The Telegraph, UK .
Jump up ^ Golder, Dave (8 November 2014), "Doctor Who 8, 12 Death in Heaven", SFX, UK .
Jump up ^ Wilkins, Alaisdair, "Doctor Who Death in Heaven", TV club, The AV Club .
Jump up ^ "Doctor Who series 8: Death in Heaven review", TV, Den of geek .
External links[edit]
Wikiquote has quotations related to: Twelfth Doctor
"Death in Heaven" at the BBC Doctor Who homepage
"Death in Heaven" on Tardis Data Core, an external wiki
"Dark Water / Death In Heaven" at Doctor Who: A Brief History of Time (Travel)
"Death in Heaven" on IMDb
[show]
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Colony in Space
The Dæmons
The Sea Devils
The Time Monster
Frontier in Space
Fourth Doctor
The Deadly Assassin
The Keeper of Traken
Logopolis
Fifth Doctor
Castrovalva
Time-Flight
The King's Demons
The Five Doctors
Planet of Fire
The Caves of Androzani
Sixth Doctor
The Mark of the Rani
The Ultimate Foe
Seventh Doctor
Survival
Eighth Doctor
Doctor Who
Tenth Doctor
"Utopia" / "The Sound of Drums" / "Last of the Time Lords"
The End of Time
Twelfth Doctor
"Deep Breath"
"Into the Dalek"
"The Caretaker"
"Flatline"
"In the Forest of the Night"
"Dark Water" / "Death in Heaven"
"The Magician's Apprentice" / "The Witch's Familiar"
"Extremis"
"The Lie of the Land"
"Empress of Mars"
"The Eaters of Light"
"World Enough and Time" / "The Doctor Falls"
See also
Destiny of the Doctors
Doctor Who: The Curse of Fatal Death
Scream of the Shalka
[show]
v
t
e
Doctor Who: Cybermen stories
First Doctor
The Tenth Planet
Second Doctor
The Moonbase
The Tomb of the Cybermen
The Wheel in Space
The Invasion
Fourth Doctor
Revenge of the Cybermen
Fifth Doctor
Earthshock
The Five Doctors
Sixth Doctor
Attack of the Cybermen
Seventh Doctor
Silver Nemesis
Tenth Doctor
"Rise of the Cybermen" / "The Age of Steel"
"Army of Ghosts" / "Doomsday"
"The Next Doctor"
Eleventh Doctor
"The Pandorica Opens"
"Closing Time"
"Nightmare in Silver"
"The Time of the Doctor"
Twelfth Doctor
"Dark Water" / "Death in Heaven"
"World Enough and Time" / "The Doctor Falls"
Torchwood
"Cyberwoman"
Minor appearances
The War Games
The Mind of Evil
Carnival of Monsters
Logopolis
Mawdryn Undead
Dimensions in Time
"Dalek"
"Human Nature"
"A Good Man Goes to War"
"The Day of the Doctor"
"Face the Raven"
"Hell Bent"
[show]
v
t
e
Doctor Who: UNIT television stories
Second Doctor
The Invasion
Third Doctor
Spearhead from Space
Doctor Who and the Silurians
The Ambassadors of Death
Inferno
Terror of the Autons
The Mind of Evil
The Claws of Axos
The Dæmons
Day of the Daleks
The Time Monster
The Three Doctors
The Green Death
Invasion of the Dinosaurs
Planet of the Spiders
Fourth Doctor
Robot
Terror of the Zygons
The Android Invasion
The Seeds of Doom
Seventh Doctor
Battlefield
Tenth Doctor
"The Christmas Invasion"
"The Sound of Drums" / "Last of the Time Lords"
"The Sontaran Stratagem" / "The Poison Sky"
"Turn Left"
"The Stolen Earth"
"Planet of the Dead"
Eleventh Doctor
"The Power of Three"
"The Day of the Doctor"
Twelfth Doctor
"Death in Heaven"
"The Magician's Apprentice"
"The Zygon Invasion" / "The Zygon Inversion"
Torchwood
"Fragments"
Children of Earth
The Sarah Jane Adventures
Enemy of the Bane
Death of the Doctor
Minor appearances
Colony in Space
The Mutants
The Time Warrior
The Five Doctors
"Aliens of London" / "World War Three"
"Journey's End"
The End of Time
"The Bells of Saint John"
"The Return of Doctor Mysterio"
See also
The Web of Fear
Mawdryn Undead
Dimensions in Time
Scream of the Shalka
Wartime
Downtime
Auton trilogy
History of UNIT
List of UNIT personnel
Retrieved from "https://en.wikipedia.org/w/index.php?title=Death_in_Heaven&oldid=801263460"
Categories:
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