Of albedo, emissivity and Calvo pricing

I’ve said before that the climate change discussion reminds me a lot of macroeconomics. This similarity has driven my skepticism that the science is locked. I know we don’t have macroeconomics figured out; it seems unlikely we have the climate figured out.

Here’s a great discussion on the sensitivity of temperature to changes in CO2. The earth is absorbing energy and its emitting energy. Where these balance determines the temperature. The earth doesn’t perfectly absorb all the energy it receives and similarly it doesn’t perfectly emit energy. The efficiency of absorption is called the albedo and the efficiency of emission is called emissivity. Of course, the efficiency of absorption and emission determines the equilibrium temperature. There’s lots of factors that determine efficiency, albedo and emissivity, but a simplifying assumption is to assume they’re both constant. This is something economists are used to… “assuming all else is equal, blah blah blah.”

Assuming albedo and emissivity are constant is an ok thing to do as long as we’re talking about small changes in the climate.

Where climatologists talk about the relationship between CO2 and temperature, macro economists like to talk about the relationship between inflation and the economy’s output. The relationship comes about because prices companies charge and the wages people earn don’t change very fast to economic conditions. All else equal (!), we’d expect workers to demand higher wages the moment inflation is higher and we’d expect firms to change their prices just as quickly. But this doesn’t happen. It takes a while for workers to renegotiate their wages and it takes a while for companies to change the price tags on their goods. We call this sticky prices.

One way to model sticky prices is by assuming only a fixed percentage of firms can update their prices at a time (pdf). A random number of firms is selected each quarter. For those lucky firms the Calvo Fairy taps the firm’s managers on their shoulders and they swing in to action changing prices. They set their prices to the best prices today (to maximize profit) and they know the fairy may not visit them next time (or the time after that or the time after that) so they make sure to set the price to give them the highest expected profit in the future. The rest of the firms have to live with whatever prices they set in the past.

That the number of firms that update their prices is a constant fraction is an ok assumption as long as we’re talking about small changes in the economy.

However, as you can imagine, if inflation is really high firms will have a bigger incentive to raise their prices and the assumption that only a fixed number of companies will update their prices becomes unrealistic. Similarly, constant albedo and emissivity become unrealistic assumptions when big changes happen to the climate.

BTW, here’s another great write-up on that site about the long term connection between CO2 and temperature.