In economics, the Golden Rule savings rate is the rate of savings which maximizes steady state growth consumption in the Solow growth model. It is a term attributed^[1] to Edmund Phelps who wrote in 1961 that the Biblical adage "do unto others as you would have them do unto you" could be applied inter-generationally inside the model to arrive at some form of "optimum". Economics (deriving from the Greek words οίκω [okos], house, and νέμω [nemo], rules hence household management) is the social science that studies the allocation of scarce resources to satisfy unlimited wants. ... In common usage, saving generally means putting money aside, for example, by putting money in the bank or investing in a pension plan. ... The steady-state is a condition of the economy in which output per worker and capital per worker do not change over time. ... In economics, the Solow growth model is a dynamic model of economic growth. ... Edmund Phelps worked in economics and was recognized for his work on economic growth at Yale’s Cowles Foundation in the 1960s. ... 1961 was a common year starting on Sunday (link will take you to calendar). ... An adage is a short, but memorable saying, which holds some important fact of experience that is considered true by many people, or it has gained some credibility through its long use. ... Wikipedia does not yet have an article with this exact name. ...

In the Solow growth model, a savings rate of 100% implies that all income is going to investment capital for future production, leading to a steady state consumption level of zero. Similarly, a savings rate of 0% implies that no new investment capital is being created, leading to all current capital depreciating without replacement and again a consumption level of zero. Somewhere in between is the "Golden Rule" level of savings, where the savings propensity is set so that per-capita consumption itself is both constant and maximized. Capital has a number of related meanings in economics, finance and accounting. ... Consumption is also an archaic name for the disease tuberculosis, presumably because, prior to the age of modern antibiotics, often it would seem that the disease was consuming patients from within as they coughed up blood. ...

Derivation of the Golden Rule savings rate

If the other parameters of the Solow model are taken as 'given' (beyond the policy-maker's control), but the savings rate can be set exogenously to maximize steady state consumption the solution can be derived from the steady state equations. Exogenous (or exogeneous) (from the Greek words exo and gen, meaning outside and production) refers to an action or object coming from outside a system. ... The steady-state is a condition of the economy in which output per worker and capital per worker do not change over time. ...

Per capita consumption (c) is the difference between output per capita (y) and savings per capita:

c(k) = y(k)[1 − s]

where s is the propensity to save, c = per-capita consumption and k = the captial/labour ratio (i.e. capital per capita). In the steady state: In classical economics and all micro-economics labour is one of four factors of production, the others being land, capital and enterprise. ... Capital has a number of related meanings in economics, finance and accounting. ...

Therefore:

Where n is the constant exogenous growth rate, and y* is the steady state output per worker at the golden rule savings rate.

Measuring the Golden Rule savings rate

Since the Golden Rule represents the optimal savings rate to maximize consumption in the economy, an important question for policy-makers is whether the economy is saving too much or too little.

Policy that can change the savings rate

Various economic policies can have an effect on the savings rate and, given data about whether an economy is saving too much or too little, can in turn be used to approach the Golden Rule level of savings. Consumption taxes, for example, may reduce the level of consumption and increase the savings rate, whereas capital gains taxes may reduce the savings rate. These policies are often known as savings incentives in the west, where it is felt that that the prevailing savings rate is "too low" (below the Golden Rule rate), and consumption incentives in countries like Japan where demand is widely considered to be too weak because the savings rate is "too high" (above the Golden Rule)^[2]. A sales tax is a tax on consumption. ... In many jurisdictions, including the United States and the United Kingdom, a capital gains tax or CGT is charged on capital gains, that is the profit realised on the sale of an asset that was previously purchased at a lower price. ... The term Western world can have multiple meanings depending on its context. ... The supply and demand model describes how prices vary as a result of a balance between product availability at each price (supply) and the desires of those with purchasing power at each price (demand). ...

Private and public saving

Japan's high rate of private saving is offset by its high public debt. A simple approximation of this is that the government has borrowed 100% of GDP from its own citizens backed only with the promise to pay from future taxation. This does not necessarily lead to capital formation through investment (if the revenue from bond sales is spent on present government consumption rather than infrastructure development, say). Investment is a term with several closely-related meanings in finance and economics. ... Dutch East India Company bond, issued in 1623. ...

Golden rule taxes within economic models

If consumption tax rates are expected to be permanent then it is hard to reconcile the common hypothesis that rising rates discourage consumption with rational expectations (since the ultimate purpose of saving is consumption^[3]). However, consumption taxes tend to vary (e.g. with changes in government or movement between countries), and so currently high consumption taxes may be expected to go away at some point in the future, creating an increased incentive for saving. The efficient level of capital income tax in the steady state has been studied in the context of a general equilibrium model and Judd (1985) has shown that the optimal tax rate is zero.^[4]. However, Chamley (1986) says that in reaching the steady state (in the short run) a high capital income tax is an efficient revenue source.^[5] expectation in the context of probability theory and statistics, see expected value. ... Rational expectations is a theory in economics used to model the determination of expectations of future events by economic actors, originally proposed by John F. Muth (1961). ... General Equilbrium (linear) supply and demand curves. ... 1985 is a common year starting on Tuesday of the Gregorian calendar. ... 1986 is a common year starting on Wednesday of the Gregorian calendar. ...

Notes

^  Origin of the term described at newschool.edu

^  Since the golden rule applies only in the steady state an economy not in that state "should not" aspire to the golden rule savings rate, even if the precepts of neo-classical economics growth theory is accepted. For example, the Soviet Union had a famously high savings rate policy in an attempt to "catch up" to the West, the fact that this lowered present consumption below the golden rule rate was justified with the argument that capital accumulation was necessary to reach the world level of industrialization, but that this was a short-term policy of capital deepening. Normative economics is the branch of economics that incorporates value judgements about what the economy should be like or what particular policy actions should be recommended to achieve a desirable goal. ... Neoclassical economics is the grouping of a number of schools of thought in economics. ... General In economics, accounting and political economy, capital accumulation is often equated with investment. ... Capital deepening is a term used in economics to describe an economy where capital per worker is increasing, it is an increase in the capital intensity. ...

^  Frankel, D.M (1998), Transitional Dynamics of Optimal Capital Taxation Macroeconomic Dynamics, 2, page 493. (David Frankel writes that a wage tax is the "perfect tool" for influencing the quantity of leisure consumption. Page 495 describes the problem of failing to make government commitment to a tax rate credible). 1998 is a common year starting on Thursday of the Gregorian calendar, and was designated the International Year of the Ocean. ... For the album by Blur, see Leisure (album). ... Game theory is a branch of applied mathematics that uses models to study interactions with formalised incentive structures (games). It has applications in a variety of fields, including economics, international relations, evolutionary biology, political science, and military strategy. ...

^  Chamley, C. (1986), Optimal taxation of capital income in general equilibrium with infinite lives. Econometrica 54. Chamley writes that before reaching the golden rule steady state capital income taxes are efficient in the sense that they do not promote deadweight loss through intertemporal consumption substitution. 1986 is a common year starting on Wednesday of the Gregorian calendar. ... In economics, a deadweight loss is a permanent loss of well being to society that can occur when equilibrium for a good or service is not Pareto optimal, (that at least one individual could be made better off without others being made worse off). ...

^  Judd, K.L. (1985), Redistributive taxation in a simple perfect foresight model. Journal of Public Economics 28, page 59. 1985 is a common year starting on Tuesday of the Gregorian calendar. ...