The aim of this paper is to examine the effects of nutritional policies on the behavior of firms, particularly in terms of food quality and prices, and to assess the potential impacts of such policies from a public health point of view. We determine how new products that are nutritionally improved can emerge in a market where incumbent firms offer competing unhealthy products. We also highlight a non-intentional effect of such policies: if consumer heterogeneity is high, then an information policy may simultaneously provide health benefits to the population as a whole but worsen the health of consumers that are less aware of nutritional effects. For a given level of nutritional tax, we determine the optimal threshold that firms must meet to avoid taxation. It appears that this threshold must not be too high if the goal of nutritional policies is to increase total health benefits without increasing health disparities between consumers. An increase in the tax level has two opposing effects. On one hand, it improves health benefits for consumers that are less aware of nutrition issues. On the other hand, because it leads to an increase in prices as a result of a reduction in the competition intensity, it decreases the cost-effectiveness of the policy.