Investment rules and time invariance under population growth

We propose an adaptation of Hartwick’s investment rule to models with population growth and show that following is equivalent a time-invariant real per capita net national product. In the so-called DHSS model capital accumulation resource depletion proposed equates capital, dilution effect growth, value resource, gross effect. investigate why this asymmetry arises by analyzing general multiple goods, in which we obtain formulation where gains play role if positive. Since accrue only but not get apparent model. both as corollary keeping investments equal zero leads constant consumption constant.