Understanding the High Cost of Military Drone Use Using a Rebound Effect Model

The Economist Magazine’s March 13th 2021 issue has a great story about drone use and drone expenditure.

The piece starts by talking about Tom Cruise in the movie “Top Gun” and says that manned airplanes are expensive.  One justification for substituting such flights and instead using drones is to save costs.

Per hour of flying drones are cheaper than manned aircrafts (even if Tom Cruise isn’t the pilot!),   But, the Rebound Effect lurks

 Since Drones are cheaper per hour of flying, the Military chooses to fly more hours.  The military’s Demand curve slopes down and apparently is price sensitive.  So, the total expenditure on flights has increased as drones have replaced Tom Cruise!

This is the Rebound Effect in action.   When I teach environmental economics, I give the following example from my $2 textbook,  

Suppose that Matt always drives 10,000 miles.  If he owns a car that achieves 10 MPG, then he consumes 1,000 gallons of gas. If he owns a car that achieves 100 MPG, then consumes 100 gallons of gas.  In this case, there is no rebound effect. Now suppose that Matt’s demand for driving (measured in miles) can be expressed as:

Miles Driven = 20000 – 20000*Price per Mile of driving

 If Matt owns a vehicle that achieves 20 MPG, then this vehicle consumes .05 gallons per mile.  If the price of gasoline is $2 per gallon, then Matt’s price per mile when he owns a 20 MPG vehicle is 2 * .05 = 10 cents per mile = .1 dollars. Now, plug this into the demand curve.  Matt will drive his 20 MPG vehicle = 20,000 – 20,000 * .1 = 18,000 miles, and he will consume 18,000 / 20 = 900 gallons.  Now, suppose Matt is handed a vehicle that achieves 40 MPG.  Assuming the price of gasoline remains at $2 per gallon, then his new price per mile is 2 * (1 / 40) = 5 cents per mile = .05 dollars.  Plug this price into the demand curve to obtain Miles = 20,000 – 20,000 * .05 = 19,000 miles.  So, Matt drives more miles now, but his gasoline consumption now equals (19,000 / 40 = 475)