# Fuzzy Profit Shifting: A Model for Optimal Tax-induced Transfer Pricing with Fuzzy Arm's Length Parameter

## TL;DR

This paper develops a fuzzy model for optimal transfer pricing under tax considerations, revealing how ambiguity in arm's length parameters affects firms' pricing strategies and tax compliance.

## Contribution

It introduces a fuzzy number approach to model arm's length parameters, providing new insights into optimal transfer pricing and anti-shifting mechanisms under uncertainty.

## Key findings

- Optimal transfer price is an alpha-cut of the fuzzy arm's length parameter.
- Low audit probability incentivizes firms to choose non-arm's length prices.
- Conditions are derived to prevent extreme profit shifting strategies.

## Abstract

This paper proposes a model of optimal tax-induced transfer pricing with a fuzzy arm's length parameter. Fuzzy numbers provide a suitable structure for modelling the ambiguity that is intrinsic to the arm's length parameter. For the usual conditions regarding the anti-shifting mechanisms, the optimal transfer price becomes a maximising $\alpha$-cut of the fuzzy arm's length parameter. Nonetheless, we show that it is profitable for firms to choose any maximising transfer price if the probability of tax audit is sufficiently low, even if the chosen price is considered a completely non-arm's length price by tax authorities. In this case, we derive the necessary and sufficient conditions to prevent this extreme shifting strategy