The idea that aggregate income equals aggregate expenditure emerges from a simple model of the economy in which all the money that is earned by people is then spent on stuff that was made by people. In this case the “leading foot” is aggregate income and the “trailing foot” is aggregate expenditure. There is an equation in economics textbooks that states:Īggregate expenditure = aggregate income *

The answer is that many economists have made the same mistake as our proverbial bad mathematician. Hopefully you can see that this statement is wrong, and if taken too seriously could erroneously lead people to believe that “slopes are impossible” and that therefore “the earth is flat”! So what has this all got to do with economics?

YL = YT (warning, this equation is wrong) If both the gradients and the step sizes are small, a poorly trained mathematician may sloppily pronounce that: If we now consider smaller and smaller step sizes, in the limit as W approaches zero, YL becomes closer and closer to being equal to YT. The difference in height will clearly depend on the width of the step and the gradient (G) of the slope. Let us label the exact height (Y) of each foot as YL and YT (L stands for “leading” T stands for “trailing”). Now imagine a man traversing this curve from left to right in small steps of width W.

Prove that the earth is flat