# Price elasticity of demand

The demand schedule for the GameToy portable game machine is a straight-line demand curve with the following specific points along that curve: Price__________ Quantity demanded per week \$80_____________________80 \$110____________________60 \$140____________________40 \$170____________________20 At which price is demand for MP3 players inelastic? (a) \$80 (b) \$110 © \$140 (d) \$170

B (-20/70) / (30/95) = -.9 |e|<1 --> inelastic

Now, how would you calculate the price elasticity of demand for a price of \$80?

you can’t in this situation because you lack the price and quantity change info

Well, to my very surprise, the Academic support responded, quote: For answer a: % change in Q = (60-80)/((60+80)/2) = -2/7 % change in P = (110-80)/((80+110)/2) = 6/19 elasticity = -0.37 (my note: this in fact is 0.9048, just as you calculated above) For answer b: % change in Q = (40-60)/((40+60)/2) = -2/5 % change in P = (140-110)/((140+110)/2) = 6/25 elasticity = 1.67 Answer a is inelastic; answer b is elastic. End quote. The solution provided in the PassMaster (question is L1-03907 for those using Stalla) is: Choice “a” is correct. Using the total revenue test, demand is inelastic when total revenue increases in response to a price increase. At a price of \$80, quantity demanded is 80 MP3 players and total revenue is \$6,400. If prices increased to \$95, quantity demanded would decrease to 70 MP3 players and total revenue would increase to \$6,650. Choice “b” is incorrect. At this price, demand is elastic. Solving for price elasticity of demand, at the price of \$110, price elasticity is 1.2 suggesting that greater levels of total revenue would be achieved at lower prices. Now, all being said, if you consider the sequence of numbers inversely, as if you would have a price decrease, than a price decrease from 140 to 110, and quantity increase from 40 to 60, has the elasticity as above calculated, greater than 1, according to the Total Revenue Test: price cut + price elasticity of demand greater than 1 + increase in producer’s revenue–> demand elastic. Further, for a price cut from 110 to 80 and quantity increase from 60 to 80, than price cut + price elasticity of demand lower than 1+ decrease in revenues–> inelastic demand.

you do raise a good point here. a question like this is likely to throw people off on the exam (it threw me off at least). often in a qbank question, all you will have to do is calc the elasticity. choosing the price here is tricky. good post map1

I am not 100% sure if this is the correct way to look at elasticity at any given point, but here is what I think. You can write P = mQ+C, now => dP = mdQ or (dP/p)*p = m*(dQ/q)*q (just a re-arrange) => (dQ/q)/(dP/p)=(1/m)*(p/q) or elasticity (p,q) = (1/slope)*(p/q) now using this equation at any the given point on the straight line elasticity (absolute value) can be calculated as, (slope of the straight line is -1.5). a. 0.67 b. 1.22 c.2.34 d.5.67 so answer is a.

I think here Price is X, and Quantity is Y, a change in price determines a change in quantity demanded.

I throw me off too, this is why I asked Stalla’s Academic support:) And even so, I am not completely sure of the answer, since going down with a price increase scenario, you end up with a total revenue increase, a less than 1 elasticity (0.9) therefore an inelastic demand:) vbcfa Wrote: ------------------------------------------------------- > you do raise a good point here. a question like > this is likely to throw people off on the exam (it > threw me off at least). often in a qbank > question, all you will have to do is calc the > elasticity. choosing the price here is tricky. > good post map1

And it doesn’t matter if you calculate it as a price increase from 80 to 110 or a price decrease from 110 to 80, elasticity is going to be the same, because it is an absolute value. vbcfa Wrote: ------------------------------------------------------- > you can’t in this situation because you lack the > price and quantity change info

thunderanalyst’s math is correct. If you don’t want to use derivatives, the easiest way to re-write the table as: p q 50 100 65 90 80 80 95 70 110 60 125 50 Since you are using the average of interval, you want to make sure that the price you are evaluating is the average of the upper and lower bounds. For 80: ((90-70)/(80)) / ((65-95)/(80)) 0.25 / -.375 = -.667 For 110: ((70-50)/(60)) / ((95-125)/(110)) 0.3333 / -.2727 = -1.222 As you keep increasing the price, the PED will go up in the absolute value.

I know thunderanalyst is correct, I realised it afterwards (and I felt really STUPID too). Thanks for the input, now is more clear. srosen Wrote: ------------------------------------------------------- > thunderanalyst’s math is correct. > > If you don’t want to use derivatives, the easiest > way to re-write the table as: > > p q > 50 100 > 65 90 > 80 80 > 95 70 > 110 60 > 125 50 > > Since you are using the average of interval, you > want to make sure that the price you are > evaluating is the average of the upper and lower > bounds. > > For 80: ((90-70)/(80)) / ((65-95)/(80)) > 0.25 / -.375 = -.667 > For 110: ((70-50)/(60)) / ((95-125)/(110)) > 0.3333 / -.2727 = -1.222 > As you keep increasing the price, the PED will go > up in the absolute value.