Yang Gailan, 28, of Agushan village, Gansu Province, axed her son and three daughters, aged between three and six, to death before drinking pesticides and killing herself on August 26.
Her husband Li drank poison and killed himself eight days later.
The murders exposed grave problems in the work of local officials, the Kangle county government said in a statement.
Chen Guangjian, deputy township head, and two village level officials Li Jinjun and Wei Gonghui, were suggested to be removed from office.
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Ma Yongzhong, vice head of the Kangle county, was given a warning by the Party, with two township officials, Bai Zhongming and Lyu Qiang, given a more severe warning, state- run Xinhua news agency reported.
Inequality in China has long been a concern.
The Gini coefficient, a widely used measurement of inequality, stood at 0.469 in 2014.
The World Bank considers a coefficient above 0.40 to represent a severe wealth gap.
The incident was widely reported in the international media, bringing bad publicity for China.
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