Healthy nutrition promotions and regulations have long been regarded as a
tool for increasing social welfare. One of the avenues taken in the past decade
is sugar consumption regulation by introducing a sugar tax. Such a tax
increases the price of extensive sugar containment in products such as soft
drinks. In this article we consider a typical problem of optimal regulatory
policy design, where the task is to determine the sugar tax rate maximizing the
social welfare. We model the problem as a sequential game represented by the
three-level mathematical program. On the upper level, the government decides
upon the tax rate. On the middle level, producers decide on the product
pricing. On the lower level, consumers decide upon their preferences towards
the products. While the general problem is computationally intractable, the
problem with a few product types is polynomially solvable, even for an
arbitrary number of heterogeneous consumers. This paper presents a simple,
intuitive and easily implementable framework for computing optimal sugar tax in
a market with a few products. This resembles the reality as the soft drinks,
for instance, are typically categorized in either regular or no-sugar drinks,
e.g. Coca-Cola and Coca-Cola Zero. We illustrate the algorithm using an example
based on the real data and draw conclusions for a specific local market
