Tax evasion and deductible expenses

Public finance is strongly affected by tax evasion, which implies that public sector resources are very limited. Most of the analysis on how to fight tax evasion focused on the ways to deter evasion through incentives to people not to evade. This model has a different approach: instead of directly rewarding/punishing agents, it gives incentives to an agent to ensure that some other agents are obliged to declare their revenue. In particular, the idea is to give incentives to consumers (through itemised deductions) to declare their expenditure. This forces sellers to declare their earnings or, at least, it makes it more costly for them to convince buyers to buy on the black market. I show that under few conditions, for a given level of taxation, it is optimal to allow for partial itemised deductions.