Decarbonisation of the electricity sector has led to the adoption and deployment of a large number of consumer-sited flexible assets. Simultaneously, consumers are becoming increasingly aware of their consumption patterns and are eager to reduce their energy expenses making demand response a significant source of flexibility in energy markets. In this paper, we discuss the policy measures that influence a consumer's ability to respond to price signals and offer flexibility in the day-ahead market. We propose two methods to quantitatively analyse these policy instruments through their inclusion in market clearing models for the Dutch day-ahead power market. A single-level optimisation model with social welfare maximisation objective can be used to perform a simplified assessment of changes in demand bids due to policy-based financial influences. This model is suitable for studying simple policies such as time-independent taxes but unsuitable for complex policies such as network tariffs and subsidies. A bi-level optimisation model with consumer surplus maximisation on the upper level and social welfare maximisation on the lower level allows more sophisticated modelling of policies but is limited by its scalability and computational complexity. The two methods can be compared on the basis of their ability to incorporate different policy instruments and market design choices, model consumer bidding behaviour, their computational complexity and challenges to implementation.