The aim of our paper is to determine the conditions under which firms tend to offer the best nutritional quality of food products, and the public regulation required to obtain this in a context where diet and nutritional status plays an important part in maintaining health and preventing disease, and with increasing pressure for public intervention on food quality in developed countries. To this end, we develop a duopoly model where products can be horizontally (variety) and vertically (quality) differentiated. We analyze the perfect Nash equilibriums in a two period competition game where in the first stage, the firms decide simultaneously on the variety and the quality of the product to be sold and in the second stage, firms set prices. The model firstly highlights that in the absence of the public intervention, the spontaneous choice of the firms will not lead to the desired level of nutritional quality. An imposition of a minimum quality threshold is also necessary. Secondly, without assistance from authorities, firm that engages in the “upmarket” may have some difficulties such as the loss of customers due to a high price associated with high quality, a loss of traditional taste (for example, products containing less sugar), or a high cost of innovation (to induce the loss of customers) which casts doubt on the wisdom of taking such an approach. To correct this, the subvention and tax policies are suggested.