Question

DD: p=1600-0.04Q^2

a) calculate the arc elasticity of demand between Q=50 and 60

b) calculate the point elasticity of demand at Q=55

c) are the two estimates same? Very close? Why or why not?

d) if price rises by 3%, calculate the corresponding percentage change in quantity demanded

Answer 1

At (Q = 50):

P = 1600 – 0.04 × 50^2 = 1600 – 100 = 1500

At (Q = 60):

P = 1600 – 0.04 × 60^2 = 1600 – 144 = 1456

At (Q = 55):

P = 1600 – 0.04 × 55^2 = 1600 – 121 = 1479

a.

Arc elasticity = PercentageChange in QD / PercentageChange in P

Percentage Change in QD = {(60 – 50) / 50} × 100 = (10/50) × 100 = 20%

Percentage Change in P = {(1456 – 1500) / 1500} × 100 = - (44/1500) × 100 = - 2.93%

Arc elasticity = PercentageChange in QD / PercentageChange in P

                        = 20% / - 2.93%

                        = - 6.83 (Answer)

b.

Point elasticity = [(Q2 – Q1) / Average QD] / [(P2 – P1) / {(P1 + P2) / 2}]

                        = [(60 – 50) / 55] / [(1456 – 1500) / {(1500 + 1456) / 2}]

                        = (10/55) / (- 44/1478)

                        = - 0.1818 / 0.0297

                        = - 6.12 (Answer)

c.

They are not same but very close.

It happens because formulas are different – Arc is based on percentage but point is based on average.

d.

Arc elasticity formula should be used here.

Arc elasticity = PercentageChange in QD / PercentageChange in P

-6.83 = Percentage Change in QD / 3%

-6.83 × 3 = Percentage Change in QD

Percentage Change in QD = - 20.49 % (Answer)

QD would decrease by 20.49%.