Question
Use the following hypothetical demand schedule for movies.
QuantityDD Price Elasticity
100 $5
80 $10
60 $15
40 $20
20 $25
10 $30
1a. Determine the price elasticity of demand at eachquantity demanded using the formula: Percentage change in quantitydemanded = (Q2 -Q1)/Q1 divided by percentage change in price =(P2-P1)/P1
b. Redo the exercise 1a using the pricechange of $10 rather than $5.
c. Plot the price elasticity data given inthe demand schedule. Indicate the price elasticity value at eachquantity demanded. Explain why the elasticity value gets smaller asyou move down the demand curve.
Explanation / Answer
Hmh, this question lays out what it wants you to dostep-by-step. I'll give you an example to help you getstarted. . From the wording of part (b), I infer that in part (a) theywanted you to compare each price to the point $5 moreexpensive. So the elasticity at (100,5) should be calculatedby comparison to (80,10). (In part b, you'll compare to(60,15), since that's the point $10 more expensive than in parta. Make sure to eyeball your table and see what sort ofdifference the bigger steps makes.) . Plug into the formula: elasticity = [(100-80)/100] / [(5-10)/5] . . I've noticed that two things tend to trip students up at thispoint. First, you have to be careful to enter the numbers inthe same order for both quantities andprices. If you subtract 100-80 for quantities, you haveto subtract 5-10 for prices. Hint: the priceelasticity of demand should always turn out to be negative. . Second, many students get sort of freaked out by all thesestacked fractions. Just take them in small steps. Dothe numerator first, and then do the denominator, and then put themtogether. . Numerator: (100-80)/100 = 20/100 = 0.2 Denominator: (5-10)/5 = -5/5 = -1 Numerator/Denominator = 0.2/(-1) = -0.2 . . So your first elasticity in part a is -0.2. . OK, part c is written very confusingly. If you havetime, you might ask your teacher to clarify just what they want youto plot there. (Your teacher will probably be more receptiveto clarifying questions if you show that you've actually done somework already.) My best guess is that they want you to make agraph with the quantity on the X-axis and the elasticity on theY-axis. . . As for why the elasticity value gets smaller as you move downthe demand curve.... Notice that elasticities are all aboutproportional changes. We're comparing the percentage changein Q to the percentage change in P. Notice that when Q is bigand P is low, a small change in both of them will be a smallpercentage change in Q and a big percentage change in P. Canyou finish the logic on your own?