In this paper we develop a monetary economy model where dollarisation emerges endogenously as an optimal decision of individuals and firms in an environment where the exchange rate is uncertain and individuals are heterogenous in their asset holdings and in their consumption baskets. We show that in this environment income distribution plays a key role in explaining the pattern of price dollarisation and its links with asset dollarisation. The model shows that for economies with relatively high income inequality, price dollarisation is not important at the aggregate level, even when asset dollarisation is high. In this case, only luxury goods, those associated to the consumption basket of high-income customers, are endogenously priced in foreign currency, whilst necessity goods, those associated to the consumption basket of low-income customers, are priced in domestic currency. This result may explain why in countries with remarkably high levels of asset dollarisation, countries like Argentina, Bolivia and Peru, the levels of transaction and price dollarisation are relatively low. We also show that asset dollarisation causes price dollarisation and that the relationship depends on income distribution.