Question

2. Using the demand function, Qd = -4P +200, determine elasticity when price falls from $25 and $20 using both the midpoint (arc elasticity) formula and point to point formula. For extra practice repeat the above for a price decrease from $10 to $8.

Answer 1

When p = 25, Q = -4*25+200 = 100

When p = 20. Q = -4*20+200 = 120

Arc elasticity when P falls from 25 to 20

E = [Q2-Q1/(Q2+Q1/2)]/[P2-P1/(P2+P1/2)]

= [120-100/(120+100/2)]/[20-25/(20+25/2)]

= [20/110]/[5/22.5]

= 0.1818/0.2222

= 0.82

Arc elasticity when P falls from 10 to 8

When P=10, Q = -4*10+200 = 160

When P=8, Q = -4*8+200 = 168

E = [168-160/(168+160/2)]/[8-10/(8+10/2)]

=[8/164]/[2/9]

= 0.04878/0.2222

= 0.22

Point elasticity:

When P falls from 25 to 20

% change in demand = 120-100/100*100 = 20%

% change in price = 20-25/20*100 = 25%

E = 20/25 = 0.8

When P falls from 10 to 8

% change in demand = 168-160/160*100 = 5%

% change in price = 8-10/10*100 = 20%

E = 5/20 = 0.25