Age structure and capital dilution effects in neo-classical growth models

Economists often over estimate capital dilution effects when applying neoclassical growth models which use age structured population and depreciation of capital stock. This occurs because capital stock is improperly characterized. A standard model which assumes a constant depreciation of capital intimates that a population growth rate equal to a negative constant savings ratio is preferable to any higher growth rate. Growth rates which are lower than a negative constant savings ratio suggest an ever growing capital/labor ratio and an ever growing standard of living, even if people do not save. This is suggested because the natural reduction of the capital stock through depreciation is slower than the population decrease which is simply unrealistic. This model overlooks the fact that low or negative growth rates result in an ageing of the capital stock, and this ageing subsequently results in an increase of the overall rate of capital depreciation. In that overly simplistic model, depreciation was assumed independent of the age of the captial stock. Incorporating depreciation as a variable into a model allows a more symmetric treatment of capital. Using models with heterogenous capital, this article explores what occurs when more than 1 kind of capital good is involved in production and when these various captial goods have different lengths of life. Applying economic models, it also examines what occurs when the length of life of capital may vary. These variations correct the negative impact that population growth can have on per capital production and consumption.