# On the design of an optimal non-linear tax/pension system with habit formation

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## Abstract

We study the optimal tax/pension design in a two-period model where individuals differ in both productivity and discount rates or projection bias and where their utility of the retirement period consumption is not independent of the earlier standard of living. We consider both welfarist and paternalistic social objectives. The paternalistic government attempts to correct the projection bias by using a higher discount factor. We derive general mathematical expressions that characterize optimal tax/pension design (marginal tax/subsidy rates). They suggest that the pattern of marginal labor income taxes depends on habit formation. Negative marginal labor income tax rates are possible. To gain a better understanding, we examine numerically the properties of an optimal lifetime redistribution policy with habit formation. We find support for non-linear tax/pension program in which some types of individuals are taxed while some are subsidized. The effect of changes in the degree of habit formation is explored in the numerical simulations as well as the implications of different degrees of correlation between skill and projection bias.

## Keywords

Optimal taxation Habit formation## JEL Classification

H21 H55## References

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