Final answer:
The housing shortage in NYC is likely due to high demand for housing and rent control policies, not low population density or overproduction of housing.
Step-by-step explanation:
The most likely cause of the housing emergency in New York City, where apartments are hard to find and the vacancy rate has been below 5 percent since World War II, is a combination of factors. Particularly, a) High demand for housing driven by the attraction of urban centers for both economic opportunity and lifestyle, and b) Rent control policies which can disincentivize the creation of new rental properties or the rental of available units due to caps on rent increases, hindering market responsiveness. Low population density and overproduction of housing are not likely causes, given the context of the question which highlights a scarcity in housing availability.