# Econ - a Highly Testable Concept.

There are 2 concepts in Economics, that I find highly testable. 1. For a downward sloping Demand Curve, Price Elasticity of Demand is high at higher Prices and low at lower Prices. 2. This leads to Total Revenues increasing as Demand moves up the Demand Curve to a point where Price Elasticity is unitary. At this point Total Revenues are maximized. Then, as Demand moves further up from this point, Total Revenues start to decrease. Please go thru texts for these concepts and make sure you understand them. It is highly likely that you would see questions from these in both sessions.

Can you please explain one thing here: why is total revenues maximized at unitary elasticity? Assume price increase by 20% and quantity reduces accordingly 1. When elasticity is high Change in Revenue = 1.2x.7 = .84 2. When elasticity is unit Change in Revenue = 1.2x.8 = .96 3. When elasticity is low Change in Revenue = 1.2x.9 = 1.08-----> revenue is maximized here - not at unit elasticity???

Total Revenue is: Price x Quantity You have to take the effect of both, when calculating Total Revenues. At high elasticity, any change in Price, will affect bigger change in Quantity demanded. And at lower elasticity, any change in Price will not affect so much change in demanded Quantity. It is mathematically proven that their product (Price x Quantity) is maximized at unitary elasticity. I dont understand your example above. Take 3 specific elasticities (-0.5, -1, -2) and take a smaller %age change in Price. (20% change in Price is too big. With that change in Price, you would travel a long distance on your Demand Curve and thus change elasticities while moving along the curve). And then you should see desired results. Anyways, you dont have to prove this theory for the exam, you just need to understand it and retain it.

Hey, rus1bus, can you do this with macro economics?

Hey Spirit, that would be a pure speculation and probably your guess would be as good as mine, if not better. For this one, it had struck me the very first time I read it. That time I thought, if there could be any question framed on this reading (it was in the first reading, last LOS), this would stand a big chance. And it actually came true in Jun 09 exam. So, I wanted to share it with you all.

Very important concepts, indeed. Those 2 concepts can also be used to derive elasticity of demand: a) If there is a direct relationship between price and total revenue then the demand is inelastic, i.e. increase in price leads to an increase in total revenue b) If there is an inverse relationship between price and total revenue then the demand is elastic, i.e. increase in price leads to a decrease in total revenue Question: Mathematically, the derivation of elasticities mirrors that of a slope - but it seems this is not entirely true. Can someone please explain why this is so. Thanks.

Very true on on both your points, Sujan. Yours was a CFAI way to test this concept To answer your other question, Elasticity is not a Slope for 2 reasons: 1. Slope is change of amount in Y axis with change of amount in X axis. In case of elasticity, Quantity is on X axis and Price is on Y axis. And Elasticity is %change in Quantity / % change in Price. So, it is actually reverse of Slope definition. 2. Also, for Slope, it is delta change, which is (new amount - old amount). Whereas for Elasticity, it is %change, which is change/old value. So, Elasticity is not Slope, though it is confused with Slope quite often.

Thanks rus1bus. This is very interesting stuff. Agreed that #1 proves that elasticity is not a slope. Not important for the exam, but just out of curiosity - would like to get your views on #2. The %change is a similar methodology used in deriving the slope of a duration. I think the %change implies a first derivative of the xy function with respect to x. So, I am not entirely convinced that %change in values means that it is not a slope. The following is from Schweser on one of the definitions of duration: “…duration is the slope of the price-yield curve at the bond’s current YTM. Mathematically, the slope of the price-yield curve is the first derivative of the price-yield curve with respect to yield…” Source: Schweser, SS16, page 140 Many thanks for your help! Cheers

Wow Sujan, great thinking. If you have a curve, THEN slope of the curve at a given point is the derivative. But, if you have a linear line, then slope of that line is simply (Y2 - Y1) / (X2 - X1). (no need of derivative) And coming back to Elasticity, it is ((X2 - X1)/X1) / ((Y2 - Y1)/Y1) So, you see, there is difference in equations for Slope and Elasticity.

does this concept means that effect is opposite when deamnd moves down? if demand is elastic - 1% price cut - increases revenue as we move down if inealstic - revenue decreases at unit elasticity - no change this from eco curriculum book so the effect is opposite

hkalra32 - yes, the effect is opposite. I would slightly rephrase your sentence this way: 1% price cut ‘…increases revenue as we move down…’ to the point of unitary elasticity (the point of highest total revenue)- from this point the ‘…revenue decreases…’. rus1bus - good point, although demand curves, however, can be non-linear. For example, a demand curve for marginal revenue product tends to be convex. And I suppose this just proves that because we use the elasticity formula, ((X2 - X1)/X1) / ((Y2 - Y1)/Y1), to solve for elasticity even though the curve is convex, the end result is just the elasticity (and no where near a slope). Good stuff!