1 Consider congestion tolls in the context of airport traffi

1. Consider congestion tolls in the context of airport traffic. We will repeat some math presented in class (and available on the class website) to further focus attention to some analysis and insights. Suppose that an airport is congested, so that an airline\'s cost per flight, denoted by C, is higher as more flights are scheduled to take off (or land). Letting f denote the total number of scheduled flights at the airport, C(f)>0 holds. Now, suppose that two airlines operate at the airport, with the airlines denoted by A and U, respectively. Let fA denote the number of flights operated by A and fu denote the number of flights operated by U. The total number of flights at the airport is then f = fit ft. The total cost for airline A is f,C(f) and that for airline U is fpC(f). The aggregate cost of the two airlines, denoted by K, is where f - fA +fu has been substituted To find the optimal toll schedule, the airport manager derives the social cost of adding an extra flight by airline A, .e., the change in K from an increase in fA. So, K was differentiated with respect to fa to give: OK . = C(fAHO + f.CU1 + fo) + ftC(A+ fe). of (a) From the differential above, what is the term representing the external congestion cost imposed on airline A itself? And what is the external congestion cost imposed on the other airline (U)? Explain

Solution

1.a) The total number of flights f is denoted as f(A)+f(U) where A and U are the two airlines operating in the airport.The total cost of operating airlines A flight is given as f(A)C(A) and the totak cost of operating the airlines U flight is f(U)C(U).

The total cost of the two airlines is expressed as:-

K=f(A)C(f)+f(U)C(f)

K=f(A)C(f(A)+f(U))+f(U)C(f(A)+f(U))

K=f(A)Cf(A)+f(A)Cf(U)+f(U)Cf(A)+f(U)Cf(U)

K=f(A)^2C+2Cf(A)f(U)+f(U)^2C

Now,taking the partial of K with respect to f(A) we get:-

dK/df(A)=2f(A)C+2Cf(U)+f(U)^2C

In the above equation 2f(A)C+2Cf(U) represents the external congestion cost imposed on airlines A as notice that with an additional flight f(A) launched by airlines A the overall cost of two airlines increases by 2f(A)C+2Cf(U).It implies that the share of the cost increase that can be attributed to new flight launched by airlines A is represented by that particular term.

Additionally,the rest of the term in the above equaltion or f(U)^2C denotes the external congestion cost of airlines U which is the cost contribution of airlines U in the toal cost of two airlines.

b) We already derived dK/df(A) as:-

dK/df(A)=2f(A)C+2Cf(U)+f(U)^2C

As stated in part a) the above equation denotes the addtional airlines cost incurred by the airport due to the launch of another flight by airlines A.Hence,to compensate the additional increase in K the airport would want to impose an equivalent toll schedule identical to the additional cost increase due to additional flight launch by airlines A.Now,in this particular instance we consider that this additional increase in cost also includes the pollution cost of additional flight,noise pollution,runway damage cost due to increase in number of flights and other additional maintenance expenses.Hence,to ensure a socially optimum toll schedule the airport authorities have to account for these costs when determining the toll schedule as some of these costs can be considered as externality costs that are negatively affecting other airport users or the neighborhoods located close to the airport due to increased airport traffic.

c) We already calculated:K=f(A)^2C+2Cf(A)f(U)+f(U)^2C

dK/df(U)=f(A)^2C+2Cf(A)+2f(U)C

The above equation represents the incremental increase in K or the total cost of airlines to the airport due to the launch of an additional flight by airlines U.

d) The part of the above equation that represents the external congestion cost imposed on airlines U is 2Cf(A)+2f(U)C which denotes the share of airlines U for the additional launch of flight that can be attributed to the increase in the overall cost of airlines.On the other hand,f(A)^2C denotes the external congestion cost of airlines A based on the same line of argument.

Again,the toll schedule for airlines U should be theoretically identical to f(A)^2C+2Cf(A)+2f(U)C which is the additional cost incurred by the airport due to the launch of additional flight by airlines U.Similar to part b),the toll schedule for airlines U has to include the additional negative externality costs due to business operation to achieve the social optimum.Hence,we consider that the above equation already accounts for these negative externalities due to the launch of another flight by airlines U.

e) Part-i)

In the previous scenario we basically considered a duopoly model of airlines where only two airlines operate.Now,an absolute monopoly implies the lack of any competitive market structure thereby providing absolute market power to the monopoly airlines.In this case,the monopoly airlines can charge flight fares driven by marginal profit per commuter indicating flight fare per customer higher than the marginal revenue earned per commuter.Hence,the flight fare will be higher in the case of monopoly compared to a duopoly model without collusion.The profit level of the monopoly airlines will also be higher than the individual airlines under duopoly model.The monopoly will also expand business operation or flight launch based on their profit maximizing principle taking advantage of lack of any competition.However,due to only one airlines operating at the airport the traffic level in the airport will be lower and the total airlines cost of th airport will also be reduced as the monopoly will take advantage of the higher flight fare with less number of flights to save operational costs and maximize profit. Under such circumstances,the airport can impose a lower socially optimum toll schedule for the monopoly airlines relative to the previous scenario due to lower traffic/congestion level and less number of flights operating at the airport thereby having less airlines cost and externality costs as well (here we are not considering the social welfare impact that the monopoly airlines might have at least theoretically).

Part-ii)

The competitive level in airport indicates increase in the number of airlines operating in the airport.This possibly alludes to more airport traffic,higher congestion level and operational and maintenance cost of airlines.Additionally,higher congestion and number of flights also indicate the higher externality cost.Hence,socially optimum toll schedule will possibly be higher than the previous case of duopoly model.