Raymond B. answered • 12/05/19
Math, microeconomics or criminal justice
Price Elasticity of demand is the percentage change in quantity demanded divided by the corresponding percentage change in price. It's unit elastic if the elasticity = -1. It's inelastic if >-1. It's elastic if <-1. Answer to part a is inelastic, as -0.58 is >-1 I'm assuming you must have meant a negative sign in front of the 0.58. The usual demand curve always has quantity demanded go down as price increases. It's an inverse relation, indicated by the negative sign. It's a downward sloping demand curve, graphically with price on the vertical axis and quantity demanded on the horizontal axis.
IF the price increased 30%, that's the same as a 0.30 increase Divide the percent by 100. Given elasticity is -0.58
then % change in quantity demanded divided by +0.30 = -0.58 %Q=-0.58)(.3)=-0.174 or a 17.4% decrease in quantity demanded.
Or if you want to keep the percentage 30%, then %Q/30%=-0.58, so %Q=-0.58(30%)=-17.4%
-0.58 is slightly more than -1/2 so the percentage increase in quantity demanded is slightly greater than one half of 30%. Half would be 15%. 17.4% is slightly larger than 15%.
Always clearly distinguish between "demand" and "quantity demanded" Instructors will take points off for not making the distinction. "demand" is the entire demand curve. "quantity demanded" is a point on the demand curve, read off on the x-axis directly below the point on the curve.
Also there's two types of elasticity of demand. This problem was about price elasticity. There's also income elasticity of demand, which is %change in quantity demanded divided by %change in income. That's positive. as an increase in income means you can buy more. Price elasticity of demand is negative, as price increases lead to buying less. There's one minor exception, the 'Giffen good" usually illustrated by the demand for potatoes during Ireland's famine. But that rarely happens, where an increase in price could cause an increase in quantity demanded. It virtually never happens. If you really did mean 0.58 to be positive, in that sense, then you're dealing with a very rare "Giffen good," where an increase in price could cause an increase in quantity demanded. I doubt you meant that though. Apples don't fit the Irish situation of potatoes, even during a general famine, where buyers put more of their remaining money into a most basic necessity. Apples just aren't that much of a necessity to most anyone.
It's interesting that your question is listed as a "calculus" question. In the usual price elasticity of demand problems, it's just arithmetic or algebra. But it does bear a basic similarity to a calculus first derivative, where elasticity could change at every point on the demand curve. If you had the equation for the demand function, such as maybe Q(P)=k/P then as P increases, Q decreases. It's an inverse relation. Then take the derivative of the function to get Q' = (k/P)' = (kP-1)' = -k/P2 which is negative. That's the elasticity at a point, where the change in price and change in quantity approach zero. But your problem isn't about one point or point elasticity of demand.
