Question

Use a written essay format to answer the following questions

1. The Metropolitan Transit Authority (MTA) just measured the Price Elasticity of Demand (E_p) for its ridership, and observed the following absolute value:

E_p = 1.25

1. Given the E_p value, what action could the MTA take to create a predicted increase in total revenue? Why? Defend your answer.

          The MTA also did a study on Cross Price Elasticity (E_x) to determine the      sensitivity of MTA ridership to fees charged by Uber and Lyft. The study revealed this value:

                                      E_x = +2.78

2. Given the E_x value, should the MTA managers be concerned about its own ridership if Uber and Lyft both announce considerable fee decreases for their services? Why? Defend your answer.

Answer 1

Answer

The price elasticity of demand (E_P) for a good shows the responsiveness of the change in quantity(Q) demanded for the good for the change in its price(P). It is measured as the ratio of the percentage change in quantity demanded for a good and the percentage change in its price.

E_P = - (dQ / Q ) / ( dP / P ) ..... (1)

As the price of a good, and its quantity demanded are inversely related, so the coefficient of price elasticity of demand, E_P is negative(-).

The Metropolitan Transit Authority (MTA) observed the absolute value of price elasticity of demand for its ridership as, E_p = 1.25; i.e.if the price changes by 100%, then the demand for ridership changes by 125%. So the change in quantity demanded is more than the change in price.

a. Now, given the value of price elasticity, which is elastic, if MTA plans to increase the total revenue, it must decrease the price of ridership.

The total revenue or simply revenue(R) is the product of price and quantity.

i.e., R = P * Q.....(2)

Now, the quantity demanded of a good is the function of price.

So, Q = f(P)

We can now write equation (2) as,

R = P * f(P)

Now, differentiating the above equation with respect to price, we get,

dR / dP = f(P) * dP / dP + P * f^'(P)

Or, dR / dP = f(P) + P * f^'(P)

Now, as f(P) = Q, we can write the above equation as,

dR / dP = Q + P * f^'(P)

Now, multiplying and dividing the second part of the right hand side of the above equation, i.e., 'P * f^'(P)' by 'Q', we get,

dR / dP = Q + { P * f^'(P) * Q} / Q

Or, dR / dP = Q[1 +  {f^'(P) * (P /Q)}] ......(3)

Now, Q = f(P)

dQ / dP = f^'(P)

Now, putting dQ / dP in place of f^'(P) in equation (3), we get,

dR / dP = Q[1 + (dQ/dP) * (P / Q)]

From equation (1), we see that (dQ / Q ) / ( dP / P ) = - E_P

So, dR / dP = Q[1 + ( - E_P)]

Or, dR / dP = Q[1 - E_P]

Now, let us find what happens to the change in revenue for the change in price of a good(dR/dP), when the price elasticity of demand for a good is elastic, i.e.,value of the coefficient, E_P is greater than 1.

If E_P1 , then [1 - E_P] 0 , dR / dP 0

So revenue and price are inversely related. If price decreases, then revenue increases

When the price elasticity of demand is elastic, the percentage change in quantity demanded is more than the percentage change in price.So when the price decreases; the increase in quantity demanded surpasses the decrease in price.As a result the total revenue (P*Q) rises when price decreases.

So,given the E_p value, MTA should decrease the price of ridership to increase its total revenue.

__________________________________________________________________

b. Yes, given the E_x value, the MTA managers should be concerned about its own ridership if Uber and Lyft both announce considerable fee decreases for their services.

The Uber and Lyft are the substitutes of MTA in ridership ,and thus competitors.

The cross price elasticity of demand between two goods shows the responsiveness of the change in quantity demanded of a good for the change in the price of another good. In case of substitute goods, the cross price elasticity of demand is positive , because the demand for one good, and the price of another good are positively related. If the price of a good rises, then the demand for that good decreases, and thus demand for its substitute good increases, if its price remains unchanged.

We see that the cross price elasticity of demand(E_x) of MTA ridership is E_x = +2.78; i.e., percentage change in ridership demand of MTA is 2.78 times the percentage change of the ridership price of Uber and Lyft.

So, if Uber and Lyft both announce considerable fee decreases for their services, it will highly affect the demand for MTA services.The demand for MTA services will decrease by 2.78 times of the decrease of the services fee of Uber and Lyft.

So, the MTA managers should be concerned about it, and will think about its own service price.

_______________________________________________________________