How does predistribution affect redistribution?

This paper presents an analysis of the consequences for optimal redistribution policies of achieving a more equal predistribution, that is, a more equal distribution of the predetermined productivities that individuals bring to the market. We make two principal contributions. First, we show that the narrative in the literature that a more equal predistribution allows less progressive optimal income taxation, ie less redistribution, is robust to a five significant variations and generalizations: (i) more general individual preferences, (ii) alternative functional form for the distribution of productivities, (iii) focusing on mean preserving spreads of productivities to isolate the pure inequality effect, (iv) assessing both structural and effective progressivity, and (v) considering Utilitarian, Prioritarian and Rawlsian social welfare functions. Second, we develop a money metric measure of the social value of predistribution to set against its cost. We show that a more equal predistribution increases this measure for Utilitarian, Prioritarian, and Maximin Social Welfare Functions.