The New York Times reported that subway use declined after a fair increase?

Question

: There were nearly four million fewer riders in December 1995, the first- full month after the price of a token increased 25 cents to $1.50, than in the previous December, a 4.3% decline’.

a) Use these data to estimate, the price elasticity of demand for subway rides.

b) According to your estimate, what happens to the revenue when the fair rises?

c) Why might your estimate of the elasticity be unreliable?

Answer 1

a)

Middle-point method should be used here instead of straight approach.

Initial price = 1.50 - 0.25 = 1.25

Final price = 1.50

Middle point for price: (1.5+1.25)/2 = 1.375

Change in price % = 0.25/1.375 = +18%

Initial quantity = 4'000'000 / 4.3% = 4'000'000 / 0.043 = 93'023'255.81 = 93M

Final quantity = 93'023'255.81 - 4'000'000 = 89'023'255.81 = 89M

Middle point for quantity = 89M + 4M/2 = 91M

Change in quantity = -4M / 91M = -4.4%

E=ΔQ% / ΔP% = -4.4% / +18% = -0.24

b)

Since |E| <1 or |-0.24| <1 thus revenue will increase

c)

Because this elasticity calculation method is only approximization and actually is reliable only on small ranges, (it's better to have full demand formula to derive elasticity). If we will increase price then at the beginning total revenue may increase over some range, then remain unchanged (for very short range) and after that total revenue will start to fall.

Answer 2

a. The price increased 20%, with a 4.3% decrease in demand. = .215

b. revenue therefore increased

c. other factors may have had an effect on the demand change