The Interesting Economics Related to the Marginal Cost of Avoiding Heat Exposure

This has been a very hot summer.  For every person on the planet, what is her willingness to pay to avoid this hot summer?  So, on a day when it s 93 degrees on average — how much is Sally in Seattle willing to pay for this day to have been 78 degrees instead?

In a “make versus buy” economy, one can either pay God to not face the 93 degree day in Seattle or one can use a suite of adaptation strategies to cope with the high heat.  Basic economic logic teaches us that one’s willingness to pay to avoid the heat is bounded by what it would cost you to adapt to the heat.   This blog post focuses on the microeconomic determinants of adapting to the heat.

I will argue that at any point in time, this adaptation strategy set is almost infinite dimensional and that the dimensions of the adaptation strategy set grow over time so that it gets ever easier for us to adapt to the high heat.  This means that our willingness to pay to avoid facing the extreme heat actually declines over time because it is getting cheaper for us to adapt on our own to the heat.   In my 2021 Adapting to Climate Change book, I expand on this point that the Social Cost of Carbon can actually decline over time for many people as their adaptation choice set grows.

Let’s start with the marginal cost curve that is familiar to anyone who has taken Econ 101.

Case #1:   A firm produces pizza using a linear production function such that pizza=10*Labor and the price of Labor = 2 each.

Given the linear production function, the firm can always make one more pizza if it hires .1 workers. It costs $2 per worker so the marginal cost to the firm of producing an extra pizza =2*.1 = 20 cents and this is a constant function.

Case #2:   A firm produces pizza using a concave production function such that pizza=10*square root of Labor and the price of labor is .4 each.

In this case the amount of labor needed to make a pizza can be expressed as =  Pizza*Pizza/100  and the $ expenditure to purchase this labor equals Pizza*Pizza/25  .   This mechanical marginal cost function is convex.

Given this definition of marginal cost, now let’s turn to the marginal cost of avoiding heat.  Consider a person in Spain today confronted with high heat where she currently lives and works.  Here is her strategy set for adapting;

#1   Move to a cooler place (either outdoors or inside such as below ground).  Such migration can be permanent or temporary in an economy featuring cross-city transportation services and AirBNB short term housing.  

#2   seek out a shady place with a breeze 

#3  turn on air conditioning or go to a public place with air conditioning,   A theme in my 2010 Climatopolis book was that if an area is known to face rising summer heat then people will change their durables and their home and work place architecture to be better prepared for the heat. We are not passive victims!!

#4 wear lighter clothing

#5  use a damp towel

#6  drink water

#7  take a Siesta and stop working during the hottest hours

#8   Eat lightly

I will stop here but note the following.  Taking permutations of these various options yields an almost infinite dimensional adaptation choice set.  Modern climate economics assumes that this choice set is stationary. In truth, it expands on a daily basis as we make progress building higher quality durables such as housing and air conditioning units and as we retire older capital and install newer capital.  Modern economics is weak on capital updating problem.  John Rust wrote a famous bus engine replacement paper but climate economists haven’t incorporated this logic into the updating of the spatial capital stock.  My paper with Devin Bunten is one attempt to address this issue.

Once we acknowledge that we have an ever growing set of adaptation strategies that are becoming cheaper and cheaper to use then one becomes more optimistic about the ability of the rich and the poor to adapt to the new serious challenges we face.

One example of the rising permutations.  More and more educated people now have the opportunity to engage in Work from Home.  These individuals can now more easily take a Siesta on a hot day.  This is an example of the permutations of the strategy set listed above.  

My critique of modern climate economics is that so many researchers are content to estimate reduced form empirical regressions of the form;

Person i’s suffering on day j in location q =  constant +  b*Extreme heat on day j in location q +   U

and take “b” as a physics constant.   Assume that “suffering” is measured by lost income and that this can be measured by the statistician.  

“b” is an interesting reduced form parameter. It represents a slope that measures at a point in time how much suffering extreme heat has caused to the average person who lives at location q at day j.

My Point  is that “b” is determined by all of the factors I discussed above.   As society’s innovation and urban planning continues;  “b” converges to zero over time and this pace of “b” shrinking from a positive number towards zero over time is a measure of our adaptation progress.

I want to see more climate economists exploring the microeconomic determinants of when does “b” change over time and when does it remain constant.   Government policies that distort adaptation decisions such as subsidies will likely turn out to be a major determinant of slowing down adaptation.

As the marginal costs of climate adaptation decline, simple economics predicts that more individuals and firms will engage in adaptation (as they compare the benefits to the costs of adaptation) and as they engage in such self protection, the empirical reduced form researcher will estimate climate damage functions showing an ever declining amount of damage caused by climate change.

The Climate Change adaptation literature needs to take basic microeconomic logic about rational choice more seriously and then we will make more progress understanding the pace of adaptation and the frictions that slow down adaptation.