Question

Example: If 50,000-200D, then D-(50,000-p)/200 · p i) Calculate E for p from 45,000 to 35,000 45,000 35,000 2 40,000, 50,000-45,000 200 50,000- 35,000 200 25+75 25, D = 75 and D 50 2 &D40,000 75-25 40,00050 50-1 So, E=- 4 - 50 35,00045,000 10,000 ii) iii) Calculate E for p from 30,000 to 20,000 Calculate E for p from 15,000 to 5,000 따 E = 1 → E = 0.25 To calculate E at any point on a line segment we can use the equation length of segment below the point length of segment above the point EXTRA CREDIT: Prove this

Answer 1

Solution:

p = 50000 - 200D so, D = (50000 - p)/200

i) E = 4 (as shown in the example). In similar way, we can calculate the elasticity, E for the remaining 2 parts.

ii) Change in p from 30,000 to 20,000

Average price, p(bar) = (pA + pB)/2

p(bar) = (30000+20000)/2 = $25,000

Change in p = pB - pA = 20000 - 30000 = -$10000

DA = (50000 - 30000)/200 = 100, DB = (50000 - 20000)/200 = 150

D(bar) = (DA + DB)/2 = (100 + 150)/2 = 125

Change in D = DB - DA = 150 - 100 = 50

E = -[p(bar)*Change in D]/[D(bar)*Change in p]

E = -[25000*(50)]/[125*(-10000)] =

E = [(-1250000)/(-1250000)] = 1

iii) Change in p from 15000 (say pA) to 5000 (say pB)

Then average price, p(bar) = (15000 + 5000)/2 = 10000

Change in p = 5000 - 15000 = -$10000

DA = (50000 - 15000)/200 = 175

DB = (50000 - 5000)/200 = 225

So, D(bar) = (175 + 225)/2 = 200

Change in D = 225 - 175 = 50

So, E = -[Change in D*p(bar)]/[Change in p*D(bar)]

E = -[50*10000]/[(-10000)*200] = 1/4 = 0.25