jmherbenerIn actual history, these three factors (population growth, technological improvement, and capital accumulation) have been intertwined in rising standards of living. Before standards of living began to rise around 1200 A.D. in western Europe, population rose very slowly, technology progressed very little, and capital per head did not accumulate significantly. Presumably, more people were added to the existing trade nexus, but that didn’t seem to raise standards of living appreciably.
Theoretically, the difficulty in answering your question comes from the contingent conditions involved in holding technology and capital accumulation constant while increasing population. For example, what complementary capital goods will the rising population work with if there is no capital accumulation? Presumably, the productive activity of the additional population would be placed on less productive land since the most productive land sites are already in use. So unless there was some reason to think that the larger populations enhanced the comparative advantage of different people in different places as they, too, came into trading relationships, then it seems unlikely that merely having more people to trade with would raise everyone’s productivity and therefore standards of living.