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Keynes–Ramsey Rule
In macroeconomics, the Keynes–Ramsey rule is a necessary condition for the optimality of intertemporal consumption choice. Usually it is express as a differential equation relating the rate of change of consumption with interest rates, time preference, and (intertemporal) elasticity of substitution. If derived from a basic Ramsey–Cass–Koopmans model, the Keynes–Ramsey rule may look like :\dot(t) = \frac \cdot (r - \rho) \cdot c(t) where c(t) is consumption and \dot(t) its change over time (in Newton notation), \rho \in (0,1) is the discount rate, r \in (0,1) is the real interest rate, and \sigma > 0 is the (intertemporal) elasticity of substitution. The Keynes–Ramsey rule is named after Frank P. Ramsey, who derived it in 1928, and his mentor John Maynard Keynes, who provided an economic interpretation. Mathematically, the Keynes–Ramsey rule is a necessary first-order condition for an optimal control problem, also known as an Euler–Lagrange equation. See also * Ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Macroeconomics
Macroeconomics (from the Greek prefix ''makro-'' meaning "large" + ''economics'') is a branch of economics dealing with performance, structure, behavior, and decision-making of an economy as a whole. For example, using interest rates, taxes, and government spending to regulate an economy's growth and stability. This includes regional, national, and global economies. According to a 2018 assessment by economists Emi Nakamura and Jón Steinsson, economic "evidence regarding the consequences of different macroeconomic policies is still highly imperfect and open to serious criticism." Macroeconomists study topics such as Gross domestic product, GDP (Gross Domestic Product), unemployment (including Unemployment#Measurement, unemployment rates), national income, price index, price indices, output (economics), output, Consumption (economics), consumption, inflation, saving, investment (macroeconomics), investment, Energy economics, energy, international trade, and international finance. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Interest Rate
The real interest rate is the rate of interest an investor, saver or lender receives (or expects to receive) after allowing for inflation. It can be described more formally by the Fisher equation, which states that the real interest rate is approximately the nominal interest rate minus the inflation rate. If, for example, an investor were able to lock in a 5% interest rate for the coming year and anticipated a 2% rise in prices, they would expect to earn a real interest rate of 3%. The expected real interest rate is not a single number, as different investors have different expectations of future inflation. Since the inflation rate over the course of a loan is not known initially, volatility in inflation represents a risk to both the lender and the borrower. In the case of contracts stated in terms of the nominal interest rate, the real interest rate is known only at the end of the period of the loan, based on the realized inflation rate; this is called the ex-post real interes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economic Growth
Economic growth can be defined as the increase or improvement in the inflation-adjusted market value of the goods and services produced by an economy in a financial year. Statisticians conventionally measure such growth as the percent rate of increase in the real gross domestic product, or real GDP. Growth is usually calculated in real terms – i.e., inflation-adjusted terms – to eliminate the distorting effect of inflation on the prices of goods produced. Measurement of economic growth uses national income accounting. Since economic growth is measured as the annual percent change of gross domestic product (GDP), it has all the advantages and drawbacks of that measure. The economic growth-rates of countries are commonly compared using the ratio of the GDP to population (per-capita income). The "rate of economic growth" refers to the geometric annual rate of growth in GDP between the first and the last year over a period of time. This growth rate represents the trend in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler–Lagrange Equation
In the calculus of variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. The equations were discovered in the 1750s by Swiss mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange. Because a differentiable functional is stationary at its local extrema, the Euler–Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing or maximizing it. This is analogous to Fermat's theorem in calculus, stating that at any point where a differentiable function attains a local extremum its derivative is zero. In Lagrangian mechanics, according to Hamilton's principle of stationary action, the evolution of a physical system is described by the solutions to the Euler equation for the action of the system. In this context Euler equations are usually called Lagrange ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Control
Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy. A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory. Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and Richard Bellman in the 1950s, after contributions to calc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bliss Point (economics)
In economics, the bliss point is a quantity of consumption where any further increase would make the consumer less satisfied. It is a quantity of consumption which maximizes utility in the absence of budget constraint. In other words, it refers to the amount of consumption that would be chosen by a person so rich that money imposed no constraint on his or her decisions. See also * Economic satiation * Keynes–Ramsey rule In macroeconomics, the Keynes–Ramsey rule is a necessary condition for the optimality of intertemporal consumption choice. Usually it is express as a differential equation relating the rate of change of consumption with interest rates, time prefe ... References Consumption Consumer theory {{microeconomics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Maynard Keynes
John Maynard Keynes, 1st Baron Keynes, ( ; 5 June 1883 – 21 April 1946), was an English economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. Originally trained in mathematics, he built on and greatly refined earlier work on the causes of business cycles. One of the most influential economists of the 20th century, he produced writings that are the basis for the school of thought known as Keynesian economics, and its various offshoots. His ideas, reformulated as New Keynesianism, are fundamental to mainstream macroeconomics. Keynes's intellect was evident early in life; in 1902, he gained admittance to the competitive mathematics program at King's College at the University of Cambridge. During the Great Depression of the 1930s, Keynes spearheaded a revolution in economic thinking, challenging the ideas of neoclassical economics that held that free markets would, in the short to medium term, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economic Journal
''The Economic Journal'' is a peer-reviewed academic journal of economics published on behalf of the Royal Economic Society by Oxford University Press. The journal was established in 1891 and publishes papers from all areas of economics.The editor-in-chief is Francesco Lippi (Libera Università Internazionale degli Studi Sociali Guido Carli & Einaudi Institute of Economics and Finance). According to the Journal Citation Reports, the journal has a 2020 impact factor of 3.178. History Introduction The journal was conceived in November 1890, at the inauguration of the British Economic Association (which became the Royal Economic Society in 1902). One of the central aims of the new society was to create a forum through which British economic research could be published. In a circular sent out before the inaugural meeting, Alfred Marshall, one of the founding members of the society, indicated the significant impact a new journal would have on British economic science: ''...the ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frank P
Frank or Franks may refer to: People * Frank (given name) * Frank (surname) * Franks (surname) * Franks, a medieval Germanic people * Frank, a term in the Muslim world for all western Europeans, particularly during the Crusades - see Farang Currency * Liechtenstein franc or frank, the currency of Liechtenstein since 1920 * Swiss franc or frank, the currency of Switzerland since 1850 * Westphalian frank, currency of the Kingdom of Westphalia between 1808 and 1813 * The currencies of the German-speaking cantons of Switzerland (1803–1814): ** Appenzell frank ** Argovia frank ** Basel frank ** Berne frank ** Fribourg frank ** Glarus frank ** Graubünden frank ** Luzern frank ** Schaffhausen frank ** Schwyz frank ** Solothurn frank ** St. Gallen frank ** Thurgau frank ** Unterwalden frank ** Uri frank ** Zürich frank Places * Frank, Alberta, Canada, an urban community, formerly a village * Franks, Illinois, United States, an unincorporated community * Franks, Missouri, Unit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Discounting
In economics exponential discounting is a specific form of the discount function, used in the analysis of choice over time (with or without uncertainty). Formally, exponential discounting occurs when total utility is given by :U(\_^)=\sum_^\delta^(u(c_t)), where ''c''''t'' is consumption at time ''t'', \delta is the exponential discount factor, and ''u'' is the instantaneous utility function. In continuous time, exponential discounting is given by :U(\_^)=\int_^ e^u(c(t))\,dt, Exponential discounting implies that the marginal rate of substitution between consumption at any pair of points in time depends only on how far apart those two points are. Exponential discounting is not dynamically inconsistent. A key aspect of the exponential discounting assumption is the property of dynamic consistency— preferences are constant over time. In other words, preferences do not change with the passage of time unless new information is presented. For example, consider an investment op ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Necessity And Sufficiency
In logic and mathematics, necessity and sufficiency are terms used to describe a material conditional, conditional or implicational relationship between two Statement (logic), statements. For example, in the Conditional sentence, conditional statement: "If then ", is necessary for , because the Truth value, truth of is guaranteed by the truth of (equivalently, it is impossible to have without ). Similarly, is sufficient for , because being true always implies that is true, but not being true does not always imply that is not true. In general, a necessary condition is one that must be present in order for another condition to occur, while a sufficient condition is one that produces the said condition. The assertion that a statement is a "necessary ''and'' sufficient" condition of another means that the former statement is true if and only if the latter is true. That is, the two statements must be either simultaneously true, or simultaneously false. In ordinary English (a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton Notation
In differential calculus, there is no single uniform notation for differentiation. Instead, various notations for the derivative of a function or variable have been proposed by various mathematicians. The usefulness of each notation varies with the context, and it is sometimes advantageous to use more than one notation in a given context. The most common notations for differentiation (and its opposite operation, the antidifferentiation or indefinite integration) are listed below. Leibniz's notation The original notation employed by Gottfried Leibniz is used throughout mathematics. It is particularly common when the equation is regarded as a functional relationship between dependent and independent variables and . Leibniz's notation makes this relationship explicit by writing the derivative as :\frac. Furthermore, the derivative of at is therefore written :\frac(x)\text\frac\text\frac f(x). Higher derivatives are written as :\frac, \frac, \frac, \ldots, \frac. Thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
