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Exponential growth is a process that increases quantity over time at an ever-increasing rate. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time ...
RGR is a concept relevant in cases where the increase in a state variable over time is proportional to the value of that state variable at the beginning of a time period. In terms of differential equations, if is the current size, and its growth rate, then relative growth rate is. If the RGR is constant, i.e., a solution to this equation is.
For example, a growth rate of 2.5% per annum leads to a doubling of the GDP within 28.8 years, whilst a growth rate of 8% per year leads to a doubling of GDP within nine years. Thus, a small difference in economic growth rates between countries can result in very different standards of living for their populations if this small difference ...
In economics, the Golden Rule savings rate is the rate of savings which maximizes steady state level of the growth of consumption, [1] as for example in the Solow–Swan model. Although the concept can be found earlier in the work of John von Neumann and Maurice Allais, the term is generally attributed to Edmund Phelps who wrote in 1961 that ...
For example, with an annual growth rate of 4.8% the doubling time is 14.78 years, and a doubling time of 10 years corresponds to a growth rate between 7% and 7.5% (actually about 7.18%). When applied to the constant growth in consumption of a resource, the total amount consumed in one doubling period equals the total amount consumed in all ...
Growth accounting. Growth accounting is a procedure used in economics to measure the contribution of different factors to economic growth and to indirectly compute the rate of technological progress, measured as a residual, in an economy. [1] Growth accounting decomposes the growth rate of an economy's total output into that which is due to ...
The Harrod–Domar model makes the following a priori assumptions: 1: Output is a function of capital stock only (labor is irrelevant). 2: The marginal product of capital is constant; the production function exhibits constant returns to scale. This implies capital's marginal and average products are equal. 3: Capital is necessary for output.
A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert Malthus, who wrote An Essay on the Principle of Population (1798), one of the earliest and most ...