Investment in better healthcare results in lower mortality rates (especially child mortality rates) and larger populations. If more people have to live from an equal amount of resources, every individual has less resources. Hence there will be more poverty.
This reasoning is typical of Malthusians and others who fret about overpopulation. They forget, however, that high mortality rates and inefficient insufficient healthcare lead to high fertility rates because people decide to have many children in order to offset the risk of mortality. Better healthcare brings down fertility rates because it reduces this risk, but also because it leads to less poverty and hence eliminates another reason to have a lot of children: extra labor force.
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