A note on sugar taxes and changes in total calorie consumption

ABSTRACT

This paper demonstrates the potential importance, when considering total calorie intake, of allowing for the substitution effects of imposing a selective tax on a commodity having a high sugar content, when non-taxed commodities exist and also have relatively high calorie content. A framework is presented which allows the elasticity of calorie consumption with respect to a price change to be derived. This brings out the role of relative budget shares, relative calorie content of goods and relative prices to be clearly seen, along with own- and cross-price elasticities. Their absolute values for each commodity group are not required. It is demonstrated that the focus of attention needs to be much wider than a simple concentration on the own-price elasticity of demand for the commodity group for which a sumptuary tax is envisaged.

KEYWORDS:

• Sugar-sweetened beverage
• calorie intake
• demand elasticity

Acknowledgements

I am grateful to Sarah Hogan, Matt Cowan and two referees for their constructive comments on an earlier version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. On the various arguments, see for example, Freebairn (2010), whose framework is used by Pincus (2018) to examine a particular sugar tax proposal. The present paper is concerned with the narrower technical question of estimating consumers' responses to higher prices.

2. For an early review, see, for example, Cutler, Glaeser, and Shapiro (2003). An extensive review of literature relating to the wide range of causes of obesity and the many possible policy interventions is given by Mozaffarian et al. (2012).

3. However, it is sometimes suggested that even if the direct demand reduction is small, the consequent revenue can effectively be used to finance other policies, such as education or extra resources for health care professionals, which may in turn affect the relevant demand schedules and their elasticity properties.

4. The way in which anticipated ‘direct’ demand reductions resulting from an SSB tax are calculated may also lead to an overstatement. Typically an elasticity is used to obtain the proportional change in demand, $\dot{q}$, following a proportional change in price of $\dot{p}$, using a ‘point’ elasticity, η, combined with an (implicit) linearisation of the demand function, such that $\dot{q}=\dot{p}\eta$. However, suppose the elasticity (rather than the slope) is thought to be constant, so that the demand curve is log-linear. In this case the appropriate formula is $\dot{q}=(1+\dot{p}{)}^{\eta }-1$. The difference is likely to be negligible for very small price changes, but proponents of an SSB tax usually argue for at least a 20 per cent ad valorem rate. For example, with $\dot{p}=0.2$, an elasticity of $\eta =-1.1$ gives $\dot{p}\eta =-0.22$ and $\dot{q}=(1+\dot{p}{)}^{\eta }-1=-0.1817$. If initial demand is 2 million units, the former overstates the demand reduction by 76,555 units. A ‘higher’ elasticity of $-1.2$ produces percentage reductions in demand of 24 and 19.65 for the two approaches, with the linearisation approximation overstating the reduction in demand by almost 87,000 units.

5. In a wide-ranging review of food taxes, Jeram (2016, p. 28–30) stressed problems arising from quality change within the taxed group and substitution towards other (untaxed) high calorie goods.

6. Colchero et al. (2015) also found full or over-shifting of the SSB tax for Mexico. Over-shifting is not uncommon for excise taxes, including alcohol and tobacco; see, for example, Kenkel (2005), Hanson and Sullivan (2009) and Dutkowsky and Sullivan (2017).

7. Aguilar et al. (2016) were concerned (like the present study) with aggregate calorie consumption. However, following their meta-analysis, Alexander et al. (2016) suggest that their composition can be significant in affecting health outcomes.

8. Ni Murchu et al. (2013) found cross elasticities were mixed for New Zealand, with some groups being complements, but they used very broad categories. Nghiem, Wilson, and Blakely (2011) examine demand elasticities for foods in Australia and New Zealand but the categories used are not helpful in the context of SSBs.

9. A general framework was also presented by Schroeter, Lusk, and Tyner (2008), who examined a food demand model involving maximisation of a utility function. The ‘arguments’ of the function include different food types (differing by calorie content) along with body weight. The latter is affected by exercise as well as total calorie intake. Utility is maximised subject to the budget constraint, involving food costs along with the cost of exercise (though a time constraint was not included). However, their focus was actually on the relationship between body weight, W, exercise and food consumption, which was used to provide an elasticity decomposition of weight change with respect to the price of the high-calorie food. Writing the general function, $W=W(x_1,x_2,\dots )$, straightforward total differentiation of W gives $dW/d{p}_1=\sum _i\left(\mathrm{\partial }W/\mathrm{\partial }{x}_i\right)\left(\mathrm{\partial }{x}_i/\mathrm{\partial }{p}_1\right)$. In general, let ${\eta }_{a,b}$ denote the elasticity of a with respect to a change in b. Then it is easily seen that: ${\eta }_{W,p_1}=\left(p_1/W\right)\left(dW/d{p}_1\right)=\sum _i\left(\right(x_i/W\left)\right(\mathrm{\partial }W/\mathrm{\partial }{x}_i\left)\right)\left(\right(p_1/x_i\left)\right(\mathrm{\partial }{x}_i/\mathrm{\partial }{p}_1\left)\right)=\sum _i{\eta }_{W,x_i}{\eta }_{x_i,p_1}$. Here ${\eta }_{W,p_1}$ is a total elasticity, while all others are partials (although Schroeter et al. use partial derivatives throughout). The authors examined evidence relating to the various elasticities.