Guest post by Anshuman Kamila.
Economists have a knack for modelling everything. Keeping up with the tradition, I would like to put forth a simple model, in context of a recent, heavily publicized, and somewhat popular government policy.
Apart from the fanciful and more involved facets of the ‘Swachchh Bharat Abhiyan’ (or the ‘Clean India Mission’; roughly translated), the most fundamental objective of this cleanliness mission is to motivate a civic sense in our masses to reduce littering in public. Most of us who see litter around dismiss the thought of giving it its due place in the garbage bin, thinking what difference would our ‘tiny’ act make. Those of us (and I hope this category is in a minority compared to the former) who close our eye to our own ‘minute’ act of spreading waste around, rationalize it by saying we’re just adding a speck of sand on a beach. Consequently, those with a better civic sense also often don’t bother cleaning up a dirty place while people with a subdued sense of public hygiene litter unabashedly. The driving force behind either act is the negligible nature of our act or the insignificant magnitude of our contribution, as perceived by us.
The model I develop here persuasively rectifies this problematic perception. The model attempts to give us reason to think ‘big’ about our capability of cleaning our surroundings.
The assumptions of the model are as follows:
- Litter is despicable.
Keeping in tune with a basic human affinity for aesthetically pleasant surroundings (and the need for a hygienic environment), this assumption is not too demanding. We all agree that waste strewn around creates a site which we all want to wish away.
- The incentive to clean garbage lying around and/or the impulse to add to the litter depends on the density of litter already present in our surroundings.
It’s quite plain and simple – we don’t want to single-handedly clean an area overflowing with litter or don’t mind emptying our own dustbins in it because we see our act doesn’t alter the situation already prevalent. On the other hand, we’d think umpteen numbers of times before throwing garbage in a well-kept-and-swept environment because our littering would create a stark difference.
Neither of these two assumptions is too restrictive, and they also do not signal a significant departure from the reality of rational preferences and behaviour.
Giving mathematical insight to the second assumption, we find that the rate of change of density of garbage strewn, dy/dt, in our surroundings depends on the already existing density of garbage strewn, i.e.
And so, if we are to solve this simple differential equation, we get
Where Y represents the boundary condition, i.e. y = Y = eC at t = 0
So the behaviour of garbage strewn varies in accordance with Figure 1 (graph of a normal exponential function):
We derive the following lessons from the above model:
- By cleaning up some strewn garbage (adding to strewn garbage), we move left (right) on the graph [our actions change y, not t]. Consequently, we not only lower (increase) the density of the garbage strewn, but additionally slow down (accelerate) the pace of increase of density of strewn garbage. So, our actions are not all that minute – neither in cleaning garbage nor in increasing it!
By suitably choosing the value of Y, we can have an equilibrium at y = 0 for all t. That is, if all of us understand the implication of the model above, remain committed to assumption 1 and begin with a neighbourhood free from strewn garbage, we’ll never have to cover our nostrils with a handkerchief! (Since y = 0 to begin with, = 0 and hence garbage density stays at the best level of 0. One might object to this assertion saying that y = 0 is not the socially optimal level of garbage density – but let’s recall that any non-zero ‘socially optimal’ level is arrived at by accounting for costs of a desirable commodity, which in the instant model is zero. So in Figure 2 below, it is depicted that the graph for garbage density is discontinuous at t = 0.)
A quick implication of the model may be that it inspires us to contemplate the long term ramification of a ‘small’ public vice which we so often trivialize. We are a mature nation; we of course do not need a dedicated multi-million-mission (completely funded now, by a cess) to impress upon us the need for cleanliness. If each one of us takes up the mantle of disseminating the import of this model, we’d leave no garbage unattended for our celebrities to cash in on. It’d seem then, as though garbage were swept away each day by an invisible hand!
(Anshuman Kamila is an ex student of Delhi School of Economics.)