The Time Inconsistency of Dietary Policy

Thomas Wu


October 11th, 2012

How to apply RBA policy to your diet should you want to target a level of weight.

While dieting and health are issues that have long been dominated by nutritionists, physiotherapists and personal trainers, I thought it was high time that the field of economics took a crack at it.

Essentially, I believe that the logic behind a healthy lifestyle is not too dissimilar from that of the Reserve Bank’s monetary policy decision. While the RBA has to balance the levels of inflation and unemployment within an economy, the health-conscientious individual has to manage the amount of exercise and healthy eating that occurs in their lives.

Consider the following model:

Assume that fatness (F) is a function of laziness (L) and junk food (J) as represented by:

F(L,J) = L2 + J2

Thus, the healthy individual should try and minimize this ‘fatness function’ by decreasing laziness and junk foods:

 Additionally, we assume that laziness, which is characterized by a lack of exercise, is dependent on the guilt we feel in relation to our diet. The guiltier we are, the less lazy we will be. This guilt will be determined by the difference between the amount of junk food we plan to eat (E(J)) and the amount of junk food we actually eat (J).

L = 10 – (JE(J))

Where (JE(J)) is the guilt premium

We can now use this model to analyse the strengths and weaknesses of adopting a stringent diet.

Consider the case where we stick to a diet of absolutely zero junk food. Providing we follow the diet, our guilt premium will be equal to zero (J = E(J) = 0) , our laziness will be a constant (L = 10)  and our ‘fatness function’ will equate to (F = 100).

These values will persist so long as we follow our diet, and as each month goes by we can expect a consistent level of health.

However now consider the case where we do not follow a diet. Pretend you plan to eat no junk food this month (E(J) = 0) but in a moment of weakness you manage to consume a McDonald’s Family Dinner Box (J = 5). According to our laziness function, this overwhelming guilt compels you to go out and run a half marathon the next day in an attempt to burn off the fat (L = 5). Your ‘fatness’ for the month will now equate to F = 50.

Clearly, it’s working out great. You’ve had a ton of junk food but because you’ve exercised you’re actually healthier than if you were following a diet!

The problem is that due to adaptive expectations, in the next period you will allow yourself to eat more junk food because you are under the belief that you can still arrive at a healthy outcome. This can be represented by an increase in the planned amount of junk food (increase in E(J)). This lowers your guilt premium so in order to achieve the same level of exercise as before you will have to consume more junk food (increase in J).

This is a dangerous trap to fall into. Without the stringency of a ruthless diet, the expectations of junk food consumption will increase with every subsequent period, and you will have to consume more junk in order to maintain a constant level of exercise. With L staying constant and J increasing with every period, the ‘fatness function’ will approach infinity.

Clearly, how a policy works in practice (whether monetary or dietary) is dependent on not just current variables but also on future expectations. Following a strict and enforceable diet wherein future expectations remain unchanged is the healthiest option. While in the short term there may be more effective alternatives, it is one of those curious situations in economics where the best sustainable outcome may not in fact be optimal.

The views expressed within this article are those of the author and do not represent the views of the ESSA Committee or the Society's sponsors. Use of any content from this article should clearly attribute the work to the author and not to ESSA or its sponsors.

  • Monika

    If the most sustainable outcome is eventually to live the dream (ie to just…keep…eating…) then who is to say what is optimal. My happiness may be maximised as fatness function tends to infinity. Practically that is a lot of mi goreng and nachos.

    • Thomas Wu

      Indeed! My assumption was that most individuals would value health over deliciousness- admittedly this can go astray.
      However there could exist a convenient positive externality, as those that do decide to consume that much Mi Goreng would be providing a much needed boost to the retail sector!

  • Monika

    upon reflection though, this works even if deliciousness is taken into account – as in the real world fatness will not acheive infinity and intermittent crises events (ie health event) can reset the whole thing…as indeed they have in western economies in recent times considering inflation and unemployment.

    chickens come home to roost, and not just the deep fried kind.

    • Thomas Wu

      True. I would imagine that just as there are a few drastic remedies for hyperinflation, there surely would be analogous mechanisms in place to deal with excessive weight gain.

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