Delta Fares

I missed a set of notes, could use some economics help. Price Elasticity of Demand.?

Any help is greatly appreciated. Once I figure out how to do a couple, I should be able to do the rest. This is exactly what the sheet asks. "A demand curve is given by the equation: P=25-0.25Qd Calculate the Ed when P= $10" And if you'd really like to help... "Instead of relying on a full-coach, round trip unrestricted fare of about $2000 between OKC and LA, Delta Airlines since June has offered a $716 unrestricted fare in that market. Through October, the test resulted in about the same revenue that Delta thinks it would have collected with its fare. What is the price elasticity of deman on this airline route? Any help is really really appreciated. Thanks.

Public Comments

1. GIVEN: P = 25 -0.25Qd P = $10 REQUIRED: Ed SOLUTION: (simple algebra) substitute the value of P in equation P = 25 -0.25Qd therefore, 10 = 25 - 0.25Qd then manipulate the equation, 0.25Qd = 25 - 10 Qd = 15 / .25 Qd = 60 (elastic) I answered this based on your assumed designates.
2. Don't pay any attention to George's answer above. This is one of the reasons he lost so many of Britain's colonies. He has calculated the quantity demanded under the given price. This is NOT the price elasticity of demand. To calculate the price elasticity of demand, Ed, you have to understand what price elasticity of demand is. A simple definition is "how much does the quantity demanded change, given a change in price." Mathematically, this is expressed as: Ed = (Change in Quantity Demanded)/(Change in Price) In the first sample problem, P = 25 - 0.25*Qd Rearranging this gives: Qd = 4*(25-P) Now, say we start at P1 and move to P2: Qd1 = 4*(25-P1) and Qd2 = 4*(25-P2) Taking the difference between these gives us: Qd2-Qd1 = 4*(25-P2) - 4*(25-P1) = -4*(P2-P1) Notice this means that if we move from a lower price to a higher price (P2 > P1), then the change in quantity is NEGATIVE. This is consistent with a downward sloping demand curve. Finally, we can just plug in some numbers to give us the answer. To do this, we have to assume a change in P. In this case it doesn't matter because the demand schedule is linear but in general this may not be the case. Anyway, we'll choose the change to be 1 here so, in other words, the price will move from $10 (as stated in the problem) to $11. (Qd2-Qd1) = -4*(P2-P1) = -4*(11-10) = -4*1 = -4 So, we now know that if the price goes from $10 to $11, the quantity demanded will go down by 4. Plugging this into the mathematical expression for Ed, we get: Ed = (Qd2 - Qd1)/(P2-P1) = (-4)/(11-10) = -4. So the price elasticity of demand at P = $10 is -4. I went through all the steps so you can see it all but there's actually an easy way to get it IF the demand is linear (like above). The way to do this is think about the the following mathematical expressions instead: Suppose P = a - b*Q. Now, consider the expression: (Change in Price)/(Change in Quantity Demanded). You should notice two things. First, the first expression is a linear qequation with a slope of "-b" and second, the second expression is the reciprocal of Ed (the price elasticity of demand). If you work it out, you will find that if the demand curve is linear then the following is true: (Change in Price)/(Change in Quantity Demanded) = -b ! Now, notice that this is the reciprocal of Ed and you can get Ed with tremendous ease: Ed = -1/b Let's check this for our sample problem. The original expression is: P = 25 - 0.25*Q Here, a = 25 and b = 0.25. Now, let's check: Is Ed = -1/b = -1/0.25 = -4. It is. So it works. You can work out algebraically why this is the case in detail but simply put, the arguments above work. Apply a similar reasoning to the second question and add to it the realization that revenue is equal to price times quantity and that the revenues are the same in both cases and you should be able to solve for Ed in this case.