Piketty's Capital in the Twenty-First Century documents long-run trends in wealth and income distribution across several industrialised economies, some for as long as the last two centuries. He uses this data to show that the share of income accruing to wealth holders has increased in recent decades to levels last seen at the end of the nineteenth century (Piketty 2014). Observing that returns to wealth (designated r) have historically been at around 3 or 4 percent in recent decades, and at around 4 or 5 percent for much of the last two millennia (2014), he theorises that inequality between those with and those without income from wealth will increase as long as returns to wealth exceed economic growth (designated g). Summarising this finding, Piketty provides a formula for the conditions in which inequality will, in the absence of corrective measures, continue to increase: r>g. If this is correct then, in the presence of positive returns to wealth, the adoption of policies that either deliberately or incidentally reduce growth are predicted to increase inequality (Pressman and Scott 2017). 

Piketty has therefore provided a new perspective on longstanding debates about the economic forms that a future nongrowing economy may take, and has renewed debates surrounding possible policy proposals intended to prevent inexorably increasing inequality in a future postgrowth economy, including debt cancellations (Hudson and Goodhart 2018), a global tax on wealth (Piketty 2014), the elimination of returns to wealth altogether (Van Griethuysen 2012, Gerber and Gerber 2017), decreasing the savings rate of the wealthy and introducing stronger labour protections and more labour intensive industries (Jackson and Victor 2016), establishing a basic income (Daly 1972, Jackson 2018), setting up public employment programs such as a Job Guarantee (Lawn 2011, Pressman and Scott 2017), increasing worker ownership (Booth 1995, Pressman 2015, Pressman and Scott 2017, Milanovic 2016), and creating incentives for workers to increase their holdings of more diversified shareholding portfolios (Milanovic 2016). Though Jackson and Victor (2016, 2018) have modelled the parameters within which three such proposals might prevent increasing inequality as growth declines, they do not attempt to extend their logic from declining to negative growth scenarios, nor extend their reasoning to providing more general parameters within which such policies will be successful.

The purpose of this paper is to examine Piketty's arguments and those of his critics in order to assess the solutions that have been proposed to prevent rising inequality in economies with zero and negative growth. We briefly review Piketty's critics, building upon those critiques to propose a simple framework, based around the formula sr>g, for assessing four broad classes of strategy for addressing this problem: increase the rate of growth g; decrease the savings rate s; decrease the rate of returns to wealth r; and to reorganise the economy so that even if sr>gobtains, inequality does not increase. However, since negative growth means that total incomes decrease from one period to the next, if those with higher incomes even just maintain their incomes, then those with lower incomes must receive less, and so income inequality will increase. It is hard to escape the simple logic that growth is the sum of increases in total incomes, and that income inequality reduces only if the income of the poorest increases or the income of the richest declines.