Question

• Price of tickets increased from $200 to $250.The demand equation Qd=2000-5p is the representative for train tickets between point A and Point B.

a)Calculate the old price quantity demanded level.

b)calculate new price quantity demanded level.

c)work out the price elasticity of demand for tickets from point A to point B between $200 and $250.

d)briefly discuss the price elasticity of demand for tickets from point A to point B between $200 and $250 and clarify how train fleets revenues are expected to respond to the price increase.

e) what would be the price elasticity of demand for tickets from point a to point b if the price rises again $250 to $300?

f)explain why the answer in part d)and e) are different

Answer 1

a)

Given

Old price 200

$We=2000-5p$

Then

$Q=2000-5(200)\\=2000-1000\\=1000$

b)

Given

new price 250

$Qs=2000-5p$

Then

$Q=2000-5(250)\\=2000-1250\\=750$

c)

price elasticity of demand$=\frac{\frac{Q_2-Q_1}{\frac{Q_2+Q_1}{2}}}{\frac{P_2-P_1}{\frac{P_2+P_1}{2}}}$

e_(p)=price elasticity

Q₁=old quantity demanded

Q₂=new quantity demanded

P₁=old price

P₂=new price

$=\frac{\frac{750-1000}{\frac{750+1000}{2}}}{\frac{250-200}{\frac{250+200}{2}}}$

$=\frac{\frac{250}{875}}{\frac{50}{225}}$

$=\frac{-0.286}{0.222}\\=-1.288$

d)

The price elasticity of demand is less than 1, meaning the demand is inelastic.Demand decrease with increase in price.

e)

Given

new price 300

$Qs=2000-5p$

Then

$Q=2000-5(300)\\=2000-1500\\=500$

price elasticity of demand$=\frac{\frac{Q_2-Q_1}{\frac{Q_2+Q_1}{2}}}{\frac{P_2-P_1}{\frac{P_2+P_1}{2}}}$

e_(p)=price elasticity

Q₁=old quantity demanded

Q₂=new quantity demanded

P₁=old price

P₂=new price

$=\frac{\frac{500-750}{\frac{500+750}{2}}}{\frac{300-250}{\frac{300+25}{2}}}$

$=\frac{\frac{250}{625}}{\frac{50}{275}}$

$=\frac{-0.4}{0.182}\\=-0.22$

f)

The answer in part d)and e) are different because as the price keeps on increasing , the quantity demanded decreases with a high margin.