Question

7. In a study of the New York Transit Authority, Steven discovers that subway ridership elasticity with respect to subway fares is 0.15 while the cross elasticity of demand for subways with respect to bus fares is 0.6.

A. On basis of the information given above, would a reduction in fares increase or decrease the Transit Authority’s revenues?

B. Are buses and subways substitutes or complements in New York? Briefly explain.

C. If subway fares are expected to rise by one-third, how will bus fares have to change so as to offset the effects of this increase in subway fares on subway rides demanded?

Answer 1

A)

A reduction in fares would DECREASE the Transit Authority's Revenue.

Price Elasticity of subway ridership is 0.15 . As price Elasticity is less than 1, it implies that demand for subway ridership is INELASTIC. As such, a given percentage reduction in the price of subway fares would increase the quantity demanded of subway ridership by a smaller percentage and hence TOTAL REVENUE WILL DECREASE.

Cross Elasticity of demand for subways with respect to bus fares is 0.6. A positive cross Elasticity of demand indicates that a reduction in the price of bus fares would reduce the demand for subways and hence total revenue will DECREASE.

As such, a reduction in the fares would DECREASE the Transit Authority's Revenue.

B)

Buses and subways are SUBSTITUTES in New York.

Cross Elasticity of demand for subways with respect to bus fares is 0.6 . A positive cross Elasticity of demand of 0.6 indicates that there is a direct relationship between the price of bus fares and demand for subways. As such, an increase in the price of bus fares would increase demand for subways and a decrease in the price of bus fares would decrease demand for subways . As such, buses and subways are Substitutes. SUBSTITUTES have a positive cross Elasticity of demand.

C)

First we shall calculate effect of increase in subway fares on subway rides demanded.

Given price Elasticity of demand for subways= 0.15,

Increase in subway fares= 1/3= 33% .

By how much the quantity demanded of subways will decrease as a result of increase in subway fares by one - third ( 33%)-

Price Elasticity of demand= % change in quantity demanded / % change in price

Substituting the given values-

0.15= % change in quantity demanded / 33%

Cross multiplying -

% change in quantity demanded= 0.15 x 33%

% change in quantity demanded of subways= 4.95%

Hence, as a result of increase in subway fares by one-third (33%), the quantity demanded of subways will DECREASE by 4.95% .

Bus and subways are Substitutes. To offset the decrease in quantity demanded of subways by 4.95% , the bus fares should change in such a way so as to increase the quantity demanded of subways by 4.95% . As bus and subways are Substitutes, bus fares should increase so as to increase the demand for subways.

Given cross Elasticity of demand for subways with respect to bus fares is 0.6 ; percentage increase in demand for subways= 4.95% ( increase because to offset the decrease in demand for subways caused by an increase in fare of subways)

Cross Elasticity of demand= % change in quantity demanded of subways / % change in bus fares

Substituting the given values-

0.6= 4.95% / % change in bus fares

Cross multiplying-

% change in bus fares= 4.95%/0.6

% change in bus fares= 8.25 %

Hence, the bus fares should INCREASE by 8.25% so as to offset the decrease in quantity demanded of subways due to change in subway fares by one-third. ( Answer).