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Prices, non-homotheticities, and optimal taxation: the amplification channel of redistribution

What is this research about and why did you do it?

Over the past twenty years, heterogeneous inflation rates across products consumed by low- and high-income households are key to understanding purchasing power inequality in the US. It is therefore important to analyse how the redistributive effects of prices affect the optimal design of tax policies. Empirical studies show that product markets with larger demand tend to have higher productivity and lower prices (as higher demand leads to more competition, lower mark-ups, and more innovation). By changing the size of product markets, redistribution policies affect these outcomes, and as a result, prices. We characterize optimal redistribution policies considering both price and market size effects.  

 

How did you answer this question?

We use a Mirrlees framework for income tax design in which (i) preferences for consumption goods vary with household income and (ii) product prices decrease as demand for them expands. Our main finding is that the optimal tax system amplifies the redistributive effects of prices rather than offsetting them, and that this amplification is stronger when we consider the endogenous response of markets. Falling necessity prices increase the social value of redistribution towards low-income groups. With higher redistribution, demand for necessities increases, which leads to more innovation, reducing the costs of necessities, hence lower prices, further redistribution toward low-income groups, and so on.

What did you find?

To evaluate the effects of prices, preferences and market size on redistribution we compare an economy where households have homothetic preferences for goods (so price changes have no redistributive effects) with an economy where we match observed non-homotheticities in the US data.  First, the optimal tax system is significantly more progressive in the economy with non-homothetic preferences: tax rates increase by 12 percentage points at the bottom of the income distribution and the real incomes of poorer households increase by 35%. Second, in response to our finding that inflation was lower in product categories with higher income elasticities, it is optimal to lower redistribution and set lower marginal tax rates.

This figure shows the optimal income tax rates in an economy with homothetic preferences (dotted line) and non-homothetic preferences set to match spending patterns in the United States (solid line).

What implications does this have for the research on wealth concentration or economic inequality?

Our work highlights the quantitatively large impact of price changes on optimal taxes. This matters to understand how redistribution policies should respond to growing income and wealth inequality. Shifts in the income or wealth distribution affect the relative size of markets for luxury and necessity products and, therefore, affect redistribution policies through prices. At fixed prices, a more unequal distribution of income requires a more progressive income tax. Price effects amplify the progressivity of the income tax schedule if growing income inequality leads to an increase in the relative price of luxuries (or mute its progressivity if the relative price of necessities increases).

What are the next steps in your agenda?

In future work, we would like to analyse the joint design of redistribution policies and both  innovation policies (e.g. R&D tax credits) and trade policies. Indeed, changes in domestic demand can be even more important in an open economy than in a closed economy because they have an impact on the equilibrium patterns of specialization, which in turn affect the direction of productivity growth through market size effects.

 

Citation

Jaravel, X. and Olivi, A. (2022) 'Prices, Non-homotheticities, and Optimal Taxation'. An earlier version of this paper is available from the SSRN website.

About the authors

Xavier Jaravel
Alan Olivi

Assistant Professor of Economics, UCL.

Alan Olivi
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