It's also worth studying the generational aspects of poverty. What makes some poor people stay poor while others are able, despite similar family and societal circumstances, to rise from poverty into productivity and prosperity. What is which drives some people to escape poverty while others tend to wallow in it--with a large group which may do neither. Poverty is not inherent; it's something one can change, given the right elements. What are those elements and how can we create the opportunity to improve for anyone in the straits of poverty. These things are worth studying.
In many countries, the division between the "haves" and the "have nots" has become great, with the poor in increasingly larger numbers. In the United States, for instance, with the "Great Recession" as it is now coming to be called, sociologists and politicains alike are watching an ever-increasing growth in the lower socio-economic class.
With the latest statistics revealing that 53% of the residents of the United States pay taxes while 47% do not, the economic future of this country is precarious, indeed, as it is difficult--to say the least--for nearly one-half of a population to support the other half. As exemplification of this point, you may wish to do some research on the state of California and examine the effects that the increase of population of the impoverished has made upon this state.
To me, poverty would be of interest to sociologists for two reasons.
First, I would think that they would be interested in knowing (or trying to learn) how society and its institutions help cause some people to be poor and others to be rich. Since sociology looks at the ways in which society affects various groups of people, sociologists should be interested in this question.
Second, I would think that sociologists would be interested in the impact that poor people have on society. Poor people could be seen as a distinct sociological group and sociologists would want to know how their presence affects society. For example, does a society with more poor people automatically have more crime?
So, sociologists would be interested in poverty because it is both a phenomenon that is affected by the institutions of a society and one that affects the society as a whole.
Sociologists study various aspects of the society. This includes the economic conditions prevailing in a society. This way society is interested in the nature and extent of poverty as well as riches in a society. In addition to this purely academic interest in poverty, academic also study poverty to understand the characteristics of the society which tend to increase or decrease the levels of poverty in the society. Such an understanding enables governments, and other public spirited organizations and individuals to make efforts to create social conditions that will reduce poverty and inequality in the society.