Understanding the Indian Economy: Large, dynamic and steadily expanding, the Indian economy is characterized by a huge workforce operating in many new sectors of opportunity.
The Indian economy is one of the fastest growing economies and is the 12th largest in terms of the market exchange rate at $1,242 billion (India GDP). In terms of purchasing power parity, the Indian economy ranks the fourth largest in the world. However, poverty still remains a major concern besides disparity in income.
The Indian economy has been propelled by the liberalization policies that have been instrumental in boosting demand as well as trade volume. The growth rate has averaged around 7% since 1997 and India was able to keep its economy growing at a healthy rate even during the 2007-2009 recession, managing a 5.355% rate in 2009 (India GDP Growth). The biggest boon to the economy has come in the shape of outsourcing. Its English speaking population has been instrumental in making India a preferred destination for information technology products as well as business process outsourcing.
The economy of India is as diverse as it is large, with a number of major sectors including manufacturing industries, agriculture, textiles and handicrafts, and services. Agriculture is a major component of the Indian economy, as over 66% of the Indian population earns its livelihood from this area.
However, the service sector is greatly expanding and has started to assume an increasingly important role. The fact that the Indian speaking population in India is growing by the day means that India has become a hub of outsourcing activities for some of the major economies of the world including the United Kingdom and the United States. Outsourcing to India has been primarily in the areas of technical support and customer services.
Other areas where India is expected to make progress include manufacturing, construction of ships, pharmaceuticals, aviation, biotechnology, tourism, nanotechnology, retailing and telecommunications. Growth rates in these sectors are expected to increase dramatically.
Despite the liberalization the economy still largely controlled by the government and the 500 major companies it owns, which together are worth around US$500 billion, or around 40% of GDP at current exchange rates. Thanks to past profligate spending, government debt is running at around 80% of GDP. Servicing the interest payments on that debt is now the single largest component of the federal budget. Fiscal discipline and deficit reduction is therefore vital for India’s future prospects.
It is also crucial to understand that India is driven primarily by domestic (consumer) consumption. This stands in marked contrast to Japan, the Asian Tigers and now China, all of whom have followed the export-oriented model.
With the massive growth of the Indian middle class, this vast country may become Asia’s first major ‘buy’ economy.
The Poverty Challenge: One of the major challenges for the Indian economy an those responsible for operating it, is to remove the economic inequalities that are still persistent in India after its independence in 1947. Poverty is still one of the major issues although these levels have dropped significantly in recent years. Over 25% of the working Indian populace is living below the poverty line (India Poverty Line and Gini Index).
Poverty is a challenge that’s becoming increasingly important in relationship to the alarming rate of new births. This implies that ever more rapid change, or birth control policies like the ‘One Child’ policy in China, are needed to reduce the numbers affected by poverty in the vast Indian economy.
The per capita income of India is 4,542 US Dollars in the context of Purchasing Power Parity. This is primarily due to the 1.1 billion population of India, the second largest in the world after China. In nominal terms, the figure comes down to 1,089 US Dollars, based on 2007 figures. According to the World Bank, India is classed as a low-income economy.
India Economic Policy: India Economic Policy plays a major role in determining various government actions on the economic field. Depending on the India economic policy, the government of India initiates various actions including preparing budget, setting interest rates etc. The economic policy also influences the national ownership, labor market, and several other economic areas where government intervention is required.
There are a number of internal factors like political beliefs and policies of the parties etc. that play pivotal roles in determining the economic policy of India. Besides these, like all other countries, Indian economic policy also gets influenced by various international institutions like the World Bank and the International Monetary Fund (IMF) etc.
The Economic Policy: The year 1991 was a significant one when it comes to Indian economic policy. The year saw a major economic policy reform, which resulted in shifting the direction of India economic policy from the post-independence era.
Indian Economic Policy Prior to 1991: Prior to 1991, the colonial experience and the Fabian-socialistic approach had a great influence over India economic policy. The policy had got inclination towards protectionism, where emphasis was given on industrialization, import substitution, business regulation, state intervention in labor and financial markets, and central planning. The India economic policy during that time had three basic features:
Autarchic trade policy
Extension of public sector
Direct, discretionary and quantitative controls on private sector
All the above three features interacted in both the institutional environment of functioning markets as well as private ownership of means of production. It generated perverse incentives, which resulted in economic growth of mere 3.5 percent per annum.
It was the first Prime Minister of India, Jawaharlal Nehru, along with noted statistician Prasanta Chandra Mahalanobis, who formulated and supervised economic policy of India after its independence. The concept of Five-Year Plans came into existence, which were influenced by the central planning in the Soviet Union. A number of industries were nationalized during the mid-1950s, which include telecommunication, mining, steel, water, machine tools, electrical plants, insurance and a few more. Setting up new businesses required elaborated licenses and regulations. ‘Red tapeism’ was also a part of it between 1947 and 1990.
The economic policy formulated by Nehru and Mahalanobis was based on direct and indirect state intervention. Though they were quite optimistic about the success of their policy, economist Milton Friedman later criticized their policy which concentrates on capital and technology-intensive heavy industry as well as subsidizing manual, low-skill cottage industry at the same time. According to Friedman, it would waste capital and labor and would slow down the growth of small manufacturers.
Indian Economic Policy After 1991: India saw an economic policy reform in 1991. During the late 80s, government of India took some bold decisions and started easing restrictions on capacity expansion, reduced corporate taxes and removed price controls etc. These led to enhancement in growth rate, which in turn led to high fiscal deficits and aggravating current account. Further, fall down of Soviet Union, which was a major trading partner of India, and the first Gulf War which caused a sharp rise in the oil prices, compelled India to face a major balance-of-payments crisis.
In this crucial juncture, the then Prime Minister Narasimha Rao and his Finance Minister Manmohan Singh initiated the economic liberalization, which changed the economic face of the country. The reforms put an end to ‘Red tapeism’ and also to several public monopolies. Foreign direct investments in a number of sectors started pouring in.
During the last few years of economic reforms, India saw some important changes in the liberalization and rationalization of:
domestic and foreign investment
import and export trade controls
public and financial activities
India GDP: Slowdown in economic growth of India has given rise to moderate expectations as far as GDP figures for India is concerned. From GDP growth rate highs of 9.4 percent in 2006 to GDP growth rate of less than 8.4 percent in 2008, Indian economy has borne adverse effects of global economic slowdown. However, a World Bank report released in early January 2008, predicted GDP growth rate to hover around 8.5 percent mark in 2009.
Reasons for India’s GDP growth rate slowdown Interest rates have reached a 6-year high, and have reduced level of consumer spending, and also investments. A global economy, which is becoming increasingly complex, has affected India’s chances for better export prospects. According to data released by India’s statistics office, year-on-year GDP growth rate stood at around 8.8 percent for first three months of 2009.
Does GDP data indicate a severe slowdown for India’s economy?
After release of statistics office data, former Finance Minister, P. Chidambaram, requested central bank policy makers not to lose focus on economic growth of India as they try to counter inflationary pressures, which incidentally has long breached 8 percent. However, these numbers cannot be taken indicative of a dramatic slowdown in Indian economy, since nation is experiencing above-average GDP growth.
Gainers and losers: Manufacturing sector growth have dropped down to about 5.8 percent in three months leading to March 31, 2008. Farm production has also been affected, registering a figure of about 2.9 percent. Gainer was construction sector, which experienced growth of nearly 12.6 percent. Construction sector grew in strength due to rapid rise in erection of new roads, airports, and power plants.
GDP Statistics (2007) As per estimates published in CIA’s World Fact book, the 2007 GDP figure stood at around $2.966 trillion. Official exchange GDP figure was nearly $1.099 trillion. Real growth rate was recorded as 9 percent. GDP per capita was around $2,600. Agriculture accounted for 17.8 percent of the total GDP. Industry contributed nearly 30 percent to India’s GDP. At 52.8 percent, services accounted for more than 52 percent of India’s gross domestic product.
India Economy History: The 12th largest economy in the world in terms of the market exchange rate, the Indian economy has come a long way to become one of the fastest growing economies. In order to have an idea of the various economic stages, one needs to make an analysis of the Indian economy history.
The pre colonial era of Indian economy: India is one of the world ‘s oldest civilizations. The main source of economy and income for the people in the ancient ages was agriculture. The fertile plains, rivers and water bodies and a favorable climate provided a wonderful scope for agricultural produce in the country. The ancient civilizations of India like Indus Valley, the Aryan civilization, Mauryan Empire, Gupta Empire and most other dynasties had a planned economic system. In some dynasties, even coins were issued. However, the chief form of trading in those times was the barter system. According to the economic rule, the farmers and villagers were required to provide a part of their crops or produce to the kings or the landlords.
Even in the Muslim rule, the economy of India was mainly based on agricultural produce. Towards the later part of the Mughal period, some trade relations were established between the Mughal Empire and the British, French and Portuguese merchants. Eventually, after the Battle of Plassey, the British East India Company eventually came into power. Thus the colonial rule in India started.
The colonial era of India is a significant part of the India Economy history. It brought a considerable change in the process of taxation from the revenue taxes to the property taxes which resulted in large scale economic breakdown. In fact a number of industries like the Indian handicrafts industry suffered huge losses. During India’s freedom struggle, the Indian Nationalists advocated for the Swadeshi Movement in which the British products were boycotted.
However, the British rule also developed the country to a great extent. The financial and banking system as well as free trade was established, a single currency system with exchange rates was brought into being, standardization of weights and measures took place and also a capital market came into existence. Stress was also given to the development of infrastructure and new telegraph lines were laid, railway lines were constructed and roads were made.
Post Independence to the 1990s: After India gained independence, stress was given to stabilize the economic system of the country. Wide scale development was made in sectors such as agriculture, village industries, mining, defense and so on. New roads were built, dams and bridges were constructed, and electricity was spread to the rural areas to improve the standard of living.
In the subsequent Five Year Plans, a number of economic reforms and policies were formulated. Public and rural sectors were developed, emphasis was given to increase the quantity and quality of the export items, making the country self sufficient and minimize imports and other related reforms. The political leaders also put stress on business regulations, central planning and nationalization of the industries in mining, electricity and infrastructure.
Another major economic reform that was initiated in the 1960s was to make India self sufficient in food grain production. In this regard, the Green Revolution
General Equilibrium Theory Get Economics Essay
General equilibrium theory has constituted an indispensible building block of neoclassical economics. This paper looks at the various components of the general equilibrium model and seeks to determine the conditions under which its assumptions hold. It also looks at the role the theory plays in economic analysis. The paper goes further to talk about the foundations on which the theory is built. Despite its sharp defence, the general equilibrium theory is still fraught with inconsistencies and its assumptions are highly implausible.
General Equilibrium Theory (GET) Analysis of equilibrium in a production-exchange economy looks at the interaction of both firms and consumers in a typical economy. Consumers seek to maximise their utility subject to a constraint while firms seek to maximise profits subject to production constraints. Thus the properties of consumer and producer behaviour are derived from simple optimization problems. These interactions help in determining the equilibrium set of prices for the goods produced in the economy. Prices depend on individual choices because in all markets demand should equal supply. But before finding these prices, one has to determine whether such equilibrium exists or not.
Starting the discussion of GET with a production-exchange economy, it is assumed that each firm is a competitive and a price-taker. Hence a firm has no influence on the prices of goods – only takes prices as given and will optimize accordingly. Assume there are k number of goods in the economy. Each firm in the economy uses inputs to produce outputs. These give each firm’s net output vector, yj, where inputs are taken as negative entries and outputs as positive entries. Firm j therefore earns revenue pyj when using the production plan yj, where p is the price vector for the goods produced. Each firm has a production possibilities set (PPS) (the set of feasible net output vectors), Yj. These are assumed to be irreversible. Thus a net output vector produced cannot be used as an input vector to produce those inputs as outputs, e.g. labour, which is used as an input, cannot be produced as an output. It is also assumed that each PPS is closed, convex and bounded below. By convexity, we mean that if two production plans, y and yi, are in the same PPS, then production plan, yii, created by taking a proportion, Î± Ïµ [0,1], of y and yi will also lie in that set. The set being closed means that if vectors close to the production plan of firm j, yj, are in the production possibilities of that firm, Yj, then yj will also be in Yj. This assumption guarantees continuity of each firm’s net supply function, so that even if an individual firm exhibits non-convexity in its technology, on aggregate, “the induced discontinuities may be smoothed out” (Varian, 1992, page 344).
The aggregate net supply function is the sum of the individual net supply functions. Thus, the aggregate PPS is the total of each firms PPS. Given that each individual firm’s production plan yj, maximises its own profits, then an aggregate production plan y, comprising of all individual production plan, will also maximise aggregate profits.
Consumers seek to maximise the utility they obtain from consumption subject to a constraint. Let c be the consumption of a good and L represents the amount of time they spend on leisure. These two factors are included in each consumer i’s demand functions, xi. The consumer has an endowment of time, which he can choose between time spent working l and time spent on leisure L so that Li= l L. Each consumer is also constrained by his earnings from providing his labour time, wl, where w is the wage rate. It is assumed that individuals’ derive their income from two sources; from firms which are owned by consumers and from their labour endowment where leisure is treated as a good sold to firms (Varian 1992, pp.342). Thus the constraints of time and the earnings from working form each consumer’s endowment, Ï‰i. Hence, the maximisation problem for the economy as a whole is represented as:
Subject to px=pÏ‰;
where Ï‰ is the total endowment of commodities and x is the collection of consumption bundles (x = (x1, x2, â€¦, xn)).
Since consumers own the firms in the economy as this is a private economy, they are entitled to the share of the firm’s profits, Tij (consumer i’s share of firm j’s profits), where = 1. Given the price vector p, each firm j chooses the production plan yj that maximizes profit pyj(p). Consumer i’s budget constraint therefore becomes:
pxi= pÏ‰i pyj
Summing all the continuous consumers’ individual demand function gives the economy’s aggregate demand function, X(p)= which is also continuous at price p. The aggregate excess demand function, z(p), is given as the difference between the aggregate demand function and the aggregate supply function. The aggregate supply function is the total of the aggregate supply function of all the consumers Ï‰ = and the aggregate net supply function Y(p). Thus, the aggregate excess demand function becomes;
z(p) = X(p) – [Y(p) Ï‰]
It is homogeneous of degree zero and will be negative when aggregate supply exceeds aggregate demand, and will be positive when aggregate demand exceeds aggregate supply.
Walras’ Law In a production economy like this, Walras’ Law states that if the above equation holds, then, for all price vectors, the value of the aggregate excess demand will be identically zero: pz(p) â‰¡ 0. i.e it is zero for all possible choices of prices, not just equilibrium prices (Varian, 2002, pp.550). If this equation pz(p)=0 holds, then demands will equal supply in all markets and we say that the system of markets is in general equilibrium.
From the Walras’ Law, it implies that the sum of price-weighted excess demands, summed over all markets, must be zero so that if one market has positive excess demand, another must have excess supply and if all but one are in balance, so is that one. Once an equilibrium has been established in one market, all other markets will also be in equilibrium. Walras’ Law therefore holds for all price vectors in and out of equilibrium since at any price, consumers’ budget constraints satisfy their net demands. Walras’ Law can therefore be used to ensure that zero excess demand for each good is sufficient to ensure that a good’s price vector contains equilibrium values, assuming prices are homogenous of degree zero. This implies, given that households have balanced budgets, the sum of excess demands across all markets must equal zero, whether or not the economy is in a GE.
Existence The question of the existence of Walrasian equilibrium looks at whether a specified model possesses a solution or not. That is, whether there is any set of prices such that demand equals supply in all markets. To ascertain this, crucial assumptions are made regarding both the technologies and consumer’s preference.
It is assumed that a) production sets Yj are closed and convex; aggregate production possibility vectors contain a positive component and are assumed to be irreversible (Varian 1992, pp.345); b) the aggregate excess demand function z(p) is not only continuous but also homogeneous of degree zero in prices. By continuous, we mean that any infinitesimal prices change should also result in infinitesimal changes in aggregate demand and that a small change in prices should not affect quantity demanded greatly; c) each consumer’s preference is closed, convex and bounded below. Thus, utility functions must be continuous, strictly increasing and concave; d) for all prices p, the value of the aggregate excess demand function be zero, i.e. pz(p)=0; and e) each consumer holds an initial endowment vector in the interior of his consumption set and that there is non-satiation. (Varian 1992, pp.344)
A Walrasian equilibrium exists and will be efficient if the above assumptions hold.
Uniqueness We now look at whether there is one price vector that clears all markets in the economy given that Walrasian equilibrium exists.
The existence problem was formally solved by Arrow and Debreu. The key axioms necessary for a unique and economically meaningful solution Blaug (1996) cited are;
Returns to scale are constant or diminishing.
Every production and consumption good can be a gross substitute.
To ensure uniqueness, goods must be gross substitutes. Two goods are gross substitutes if an increase in the price of one good say good 1 leads to an increase in the excess demand for the other good, say good 2.
Thus if all goods are gross substitutes at all prices, and if p* is an equilibrium price vector at which all markets are cleared, then p* is the unique equilibrium price vector.
Stability In the GE model, prices that prevail are those that coordinate the demands of consumers for various goods. By stability, we mean if something temporary disturbs the equilibrium, will the underlying market forces work to restore or move away from equilibrium? It is thus important to know whether, over time, a system in disequilibrium will return to equilibrium or move away from equilibrium. This analysed by price movements over time. Assume at equilibrium, the price vector of n goods is p*= (p1*, p2*,â€¦,pn*) and at time t=0, these prices are not equilibrium prices, such that p(0)â‰ p*. Then a system is said to be globally stable if the price vector at time t moves to the equilibrium price vector:
Walras called the continuous process of price adjustment as the tâtonnement process. This is used to explain the price adjustment process in a pure-exchange economy. There is mediator called the Walrasian auctioneer who announces a set of prices for goods at each instant of time. Buyers and sellers in the market make known their offers and demands for the goods at the announced prices. Trade only takes place if the price vector is an equilibrium one otherwise a new set of prices is announced until equilibrium is reached. In partial equilibrium, stability is ensured through restrictions on the shape of the excess demand curve-that it is negatively sloped (Gravelle and Rees, 2004:176-78).
An alternative to the tâtonnement process is the use of Edgeworth box and the theory of the core (Gravelle and Rees 2004). Here, a set of equilibrium price vectors are found within “the core” which gradually diminishes and moves towards the Walrasian equilibrium price vectors. It is imperative to note that this model relies on similar assumptions to those listed above, especially demand curve convexity.
First Welfare Theorem (FWT) The FWT is often perceived as the formal explanation of Adam Smith’s “invisible hand”. It basically asserts that, if markets are complete, any competitive equilibrium with transfers is Pareto optimal, thus any Walrasian equilibrium is Pareto efficient.
The FWT does not require stronger assumptions because we are in effect assuming that a GE (with convexity) already exists. Only assumption of local non-satiation of preferences is required for it to hold- that “consumers are all locally insatiable and that none of the goods is noxious, so that preferences (and the utility functions Ui) are nondecreasing. We assume that each consumer has continuous preferences.” (Kreps, 1990, pp.188)
Implications of the FWT The FWT gives a general mechanism that the competitive market can be used to ensure Pareto efficient outcome. Assume there are only two agents involved, it is easy for the two to come together and examine the possibilities for mutual trades. This also applies to markets involving many agents. Thus the FWT shows that, the particular structure of competitive markets has the desirable property of achieving a Pareto efficient allocation (Varian 2002, pp.561) and that consumers need to know only the prices of the goods in question. Therefore a competitive market will exhaust all the gains from trade.
If the behavioural assumptions of our model hold, then the market equilibrium is efficient. However, market equilibrium is not necessary “optimal” since it may not be “fair”. In an economy with externalities, for example, it is possible for equilibria to arise that are not efficient. The FWT is informative in the sense that it points to the sources of inefficiency in markets.
The Second Welfare Theorem (SWT) The SWT states that every Walrasian equilibrium is Pareto efficient. Assume x*is a Pareto efficient allocation where each agent holds a positive amount of each good. For the SWT to hold, preferences must be convex, continuous and monotonic. If these assumptions hold, then x*is a Walrasian equilibrium for the initial endowments x*for i=1,…,n.
Implications of SWT The SWT asserts that, under the conditions above, all Pareto efficient allocation is a competitive equilibrium. The SWT thus separates the problem of distribution and efficiency. The market mechanism is distributionally neutral and that competitive markets can be used to achieve balanced distributional welfare. This is done by price where it plays both the allocative role and the distributive role. The allocative role of prices indicates relative scarcity while the distributive role determines how much of different goods different agents can buy.
Criticisms of GET The main idea of the Sonnenschein-Mantel-Debreu theorem (S-M-D) was that given the highly restrictive assumptions of the GET there was no guarantee of a stable and unique equilibrium price vector because of the behaviour of the excess demand function as the aggregate excess demand function was assumed to be convex. Accinelli refers to this as ‘the most serious assumption needed to prove the existence of equilibrium’ (2002:48). The S-M-D shows that when demand functions are aggregated the resulting function actually behaves in all sorts of ways that do not ensure stability or uniqueness and that specifically, convexity cannot be maintained (Kirman 1989, pp.130-131).
S-M-D inflicted a fatal wound to the stability analysis in GET. It demonstrated that the only general properties possessed by the aggregate excess demand function were those of continuity, homogeneity of degree zero, the validity of Walras’ Law and boundary condition. The S-M-D results showed, as Tohme´ (2006, pp.214) summarized, ‘that for every given system of equilibrium prices and its associated excess demands, an arbitrary economy can be defined, exhibiting the same aggregate behaviour and the same equilibria, i.e. prices do not convey all the relevant information about the economy, since a “mock” one is able to generate the same aggregate demand.’ Kirman (2006, pp.257) also argues that, ‘the full force of the S-M-D result is often not appreciated. Without stability or uniqueness, the intrinsic interest of economic analysis based on the general equilibrium model is extremely limited.’ While this sentiment would surely have found favour with Kaldor, it arguably falls short of his fundamental call for the ‘demolition’ of GET as a major inhibition to the development of economics as a science, and certainly as an empirical science.
Kaldor (1972) sees the GET to be seriously flawed as an empirical description of real-world economies. According to Kaldor, scientific progress was not possible in economics without a major act of demolition, by which he meant the destruction of the basic conceptual framework of the theory of GE. Kaldor’s writings were to dismantle the whole edifice of GET.
Kaldor objected to the use of axiomatic assumptions in equilibrium economics. To him, unlike any scientific theory, ‘where the basic assumptions are chosen on the basis of direct observation of the phenomena’, the basic assumptions of economic theory ‘are either of a kind that are unverifiable’ – such as, consumers ‘maximize’ their utility or producers ‘maximize’ their profits – or ‘are directly contradicted by observation’ (Kaldor, 1972, pp.1238). The use of such assumptions, which were not just ‘abstract’ but ‘contrary to experience’ was in conflict with good science and thus rendered economics vacuous as an empirical science. He rejected the basic assumption of constant returns which dominated the equilibrium economics as well as the neoclassical economics. More particularly he detested the fact that ‘the general equilibrium school has always fully recognized the absence of increasing returns as one of the basic “axioms” of the system’. As a result, ‘the existence of increasing returns and its consequences for the whole framework of economic theory have been completely neglected’ (Kaldor, 1972, pp.1241-1242).
Kaldor asserts that GE is neither a description nor an explanation of actual economies, as these terms are understood by empirical scientists. Rather it is a set of theorems that are logically deducible from precisely formulated assumptions; and the purpose of the exercise is to find the minimum ‘basic assumptions’ necessary for establishing the existence of an ‘equilibrium’ set of prices (and output/input matrixes) that is (a) unique, (b) stable, (c) satisfies the conditions of Pareto optimality. (Kaldor, 1972, pp.1237). He maintains that GE as articulated by Debreu, ‘is shown to be valid only on assumptions that are manifestly unreal’ (Kaldor, 1972, pp.1240) and Kreps (1990, p. 195) sees it as a reduced form solution concept and that the Walrasian equilibrium only describes what we imagine will be the outcome of some underlying and unmodeled process.
Brief defence Critics of the GET have questioned its practicality based on the possibility of non-uniqueness of equilibria. Supporters have pointed out that this aspect is in fact a reflection of the complexity of the real world and hence an attractive realistic feature of the model. Proponents of the GET argues that even if there are multiple Walrasian equilibria for a given set of preferences and endowments, it may still be the case that each of these equilibria are all locally unique in the sense that there is no other Walrasian equilibrium price vector within a small enough range around the original equilibrium price vector. As a consequence, the set of Walrasian equilibria is finite.
Conclusion Both the GET and Welfare economics builds on the FWT and SWT and provides a very useful framework for debating the normative issues that surround the equity and efficiency aspects of public policy. Though it is built upon rotten foundations, GET gives an understanding of the whole economy using a “bottom-up” approach, starting with individual markets and agents. It is the perfect example of the instrumentalist (positive) approach to economic theory that informs all neoclassical models.