Does societal income inequality harm individuals' quality of life, their subjective well-being? No. In developing nations inequality increases well-being by 8 points out of 100. In advanced nations it has no effect.

- Kelley, J. & Evans, M. (2017). Societal inequality and individual subjective well-being: Results from 68 societies and over 200,000 individuals, 1981-2008.

When inequality loses its association with hope and instead becomes interpreted as a signal of a rigged society, higher inequality relates to lower well-being.

- Buttrick, N. R., S. J. Heintzelman, et al. (2017). Inequality and well-being.

...greater inequality was associated with higher life satisfaction in rural China but not significantly associated with life satisfaction in urban China. The positive inequality–happiness link in rural areas was mediated by hope.

- Cheung, F. (2015). "Can Income Inequality be Associated With Positive Outcomes? Hope Mediates the Positive Inequality–Happiness Link in Rural China.

...support for systemic transformations is determined more by the hope of improving material living conditions than by the perceptions of present actual conditions.

- Zagórski, K. (1994). "Hope factor, inequality, and legitimacy of systemic transformations: The case of Poland."

This is all food for thought. A few thoughts of my own:

Inequality has no direct relationship with happiness.  Inequality without hope is the problem.

What creates hope? The sense that there is something I can do to improve my situation. 

References:

Buttrick, N. R., S. J. Heintzelman, et al. (2017). "Inequality and well-being." Current Opinion in Psychology 18: 15-20.  https://doi.org/10.1016/j.copsyc.2017.07.016

Cheung, F. (2015). "Can Income Inequality be Associated With Positive Outcomes? Hope Mediates the Positive Inequality–Happiness Link in Rural China." Social Psychological and Personality Science 7(4): 320-330. http://journals.sagepub.com/doi/abs/10.1177/1948550615619762

Kelley, J. & Evans, M. (2017). Societal inequality and individual subjective well-being: Results from 68 societies and over 200,000 individuals, 1981-2008. Social Science Research, 62, 1-23. https://doi.org/10.1016/j.ssresearch.2016.04.020

Zagórski, K. (1994). "Hope factor, inequality, and legitimacy of systemic transformations: The case of Poland." Communist and Post-Communist Studies 27(4): 357-376.