142 THE CHANGING WEALTH OF NATIONS
Total Wealth Total wealth can be calculated as ∞
Wt ∫C(s) e r(s t)ds t
where Wt is the total value of wealth, or capital, in year t ; C(s) is consumption in year s; and r is the social rate of return to investment.1 The social rate of return to investment is expressed as C r __ C where is the pure rate of time preference and is the elasticity of utility with respect to consumption. Under the assumption that 1 and that consumption grows at a constant rate, the total wealth can be expressed as ∞
Wt ∫C(t) e (s t)ds.
(A.1)
t
The current value of total wealth at time t is a function of the consumption at time t and the pure rate of time preference. Expression (A.1) implicitly assumes that consumption is on a sustainable path, that is, the level of saving is enough to offset the depletion of natural resources. The calculation of total wealth requires that two issues be considered in computing the initial level of consumption: ■ The volatility of consumption. To solve this problem we used the five-year centered average of consumption for each one of the three years: 1995, 2000, and 2005. ■ Negative rates of saving adjusted for depletion of produced and natural capital. When depletion-adjusted saving is negative, countries are consuming natural resources, jeopardizing the prospects for future consumption. A measure of sustainable consumption needs to be derived in this instance. Hence, the following adjustments were made: ● Wealth calculation for 2005, for example, considered consumption series for 2003–07. ● For the years in which saving adjusted for depletion of produced and natural capital was negative, this measure of depletion-adjusted saving was subtracted from consumption to obtain sustainable consumption, that is, the consumption level that would have left the capital stock intact. ● The corrected consumption series were then expressed in constant 2005 U.S. dollars. Deflators are country-specific: they are obtained by dividing gross domestic product (GDP) in current dollars by GDP in constant dollars. This rule was also applied to natural capital and net foreign assets. ● The average of constant-dollars consumption between 2003 and 2007, for example, was used as the initial level of consumption for wealth calculation of 2005.