This is a question we consider in 11th grade and in 12th grade and (very briefly) in Theory of Knowledge classes. But no conclusion is ever reached. Some argue that a certain level of inequality provides the rich with the assets (from savings) and incentives to invest and even become entrepreneurs. While other people contend that very low levels of income for the poor lead to lower consumption overall and, in particular, less spending on education and health, which harms productivity.
The IMF has done more research into the topic. After looking at the data from 77 countries over a period of 20 years, it concluded that the effect of income inequality on economic growth can be either positive or negative! However, more usefully, it suggests that when the Gini coefficient (for disposable income) exceeds about 0.27, the direction of the relationship changes. Increased inequality begins to hurt economic development.
Even when inequality is increasing, the research found two factors that can help development and growth. These were (i) enabling more households and businesses to use banking services for transfers and borrowing (perhaps through micro-credit schemes) and (ii) promoting participation of women in the labor force. However, they could also make things worse by encouraging poorer households to get into debt or generating an oversupply of labor.
This is evidently a question with no easy answers, but nonetheless a very important question for policy makers and economic advisers.
For more information and some unusual graphs, look at https://blogs.imf.org/2017/05/11/a-new-twist-in-the-link-between-inequality-and-economic-development/?utm_medium=email&utm_source=govdelivery