One-sided sustainability tests with amenities, and changes in technology, trade and population

If an economy with multiple consumption goods (including environmental amenities) uniquely maximises present value with constant discounting, it is unsustainable at some time if either of two measures—augmented net investment, or the change in augmented green net national product—are zero or negative then. “Augmented” denotes that time is treated as a productive stock, which includes in each measure the value of future, exogenous changes in technology or terms of trade. Adjustments are found to make each measure a test for individual sustainability when population grows exogenously. The practical and philosophical rationale for testing sustainability in a present-value-maximising, and therefore fully prescribed, development path is discussed.