Price-cap Regulation of Congested Airports

Price-cap Regulation of Congested Airports Hangjun (Gavin) Yang, Anming Zhang Sauder School of Business, UBC

January 2011

Yang & Zhang (UBC)

Price-cap Regulation of Congested Airports

January 2011

1 / 33

Introduction

Starting with the privatization of airports in the UK in late 1980s, more and more airports became privatized or partially privatized all over the world. As the ownership of airports changes from public to private, the objective will likely become profit maximization instead of welfare maximization. Price regulations may thus be called upon so as to contain potential market power of an airport, which is a “local monopoly” candidate.

Yang & Zhang (UBC)


January 2011

2 / 33

Price Regulation

The exact form of price regulation appears to vary both across countries and over time. A number of countries have adopted cost-based regulation. Price-cap regulation has been popular in countries such as the UK, Denmark, and Australia. While German airports have traditionally been regulated by cost-based regulation, price-cap regulation has been in place since 2000 for Hamburg airport and a few other airports (Mueller et al., 2010).

Yang & Zhang (UBC)


January 2011

3 / 33

Price-cap Regulation

There are mainly two versions of price-cap regulation: the single-till approach and the dual-till approach. Under single-till, operating revenues from all airport activities, including both aeronautical operation and commercial operation, are considered in determining the price-cap on airport charges. Aeronautical operation refers to aviation activities associated with runways, aircraft parking and terminals Commercial operation includes terminal concessions (duty-free shops, restaurants, etc.), car rental and car parking.

By contrast, under dual-till, the airport charges are determined based only on aeronautical activities.

Yang & Zhang (UBC)


January 2011

4 / 33

Single-till Vs. Dual-till Price-cap Regulation

Czerny (2006) shows that single-till price-cap regulation dominates the dual-till approach at non-congested airports with respect to welfare maximization. A major critique of the single-till approach is that the airport charges are set too low at congested airports. It is generally believed that dual-till price-cap regulation is more desirable at congested airports. No rigorous theoretical work has compared the single-till approach with the dual-till approach at congested airports.

Yang & Zhang (UBC)


January 2011

5 / 33

Research Objectives

Compare single-till with dual-till price-cap regulation at congested airports. Identify situations when single-till regulation performs better and when dual-till regulation performs better in terms of overall social welfare.

Yang & Zhang (UBC)


January 2011

6 / 33

Model A single airport with n competing airlines Let ρi be the passengers’ perceived full price of airline i; and let qi be airline i’s output (number of passengers), i = 1, · · · , n. Assume linear demands and horizontally differentiated outputs X ρi = a − bqi − qj . j6=i

Following the airport pricing literature, assume each flight has an equal number (denoted by S) of passengers ˜ and Q be the total numbers of flights and passengers of all Let Q airlines. Then ˜ = Q/S. Q

Yang & Zhang (UBC)


January 2011

7 / 33

Model Full price ρi is the sum of ticket price and congestion cost: ˜ K ), ρi = pi + αD(Q, where α is the passengers’ value of time, D is congestion delay time ˜ and airport’s (runway) capacity K . which depends on Q Assume linear delay function (De Borger and Van Dender, 2006; Basso and Zhang, 2007) ˜ K) = θ D(Q,

˜ Q Q =θ , K KS

where θ is a positive parameter. We assume airport capacity K is exogenously given. Without loss of generality, we normalize KS = 1. Yang & Zhang (UBC)


January 2011

8 / 33

Treatment of Concession Demand Our treatment of concession demand is different from Oum, Zhang and Zhang (2004), and Zhang and Zhang (2010) They assume the price of concession good is exogenously given and the concession demand is taken simply as a fixed proportion of aeronautical demand. We assume passengers’ valuation for the concession good has positive support in the interval [0, u]. Let G and g be the distribution functions of passengers’ valuation, with a non-decreasing failure rate, g (x) ¯ ¯ (x) is non-decreasing in x, where G (x) = 1 − G (x). G Many common distribution functions satisfy this property, e.g. uniform, exponential, truncated Normal, etc. Yang & Zhang (UBC)


January 2011

9 / 33

Interaction Between Aeronautical and Concession Demand

Our modeling of interaction between aeronautical and concession demand is related to but different from Czerny (2006). Czerny assumes consumers make decisions simultaneously on buying flights and commercial services at the airport. Consumers will buy a flight as long as the joint surplus from consuming flight and commercial services is positive

It is perhaps more reasonable to assume consumers make these two decisions sequentially (Currier, 2008) Consumers first decide whether to fly. When they are at the airport, they decide whether to consume commercial services. Concession demand depends on both the concession price and the number of passengers, which in turn depends on the ticket price.

Yang & Zhang (UBC)


January 2011

10 / 33

A Three-stage Game

We consider a three-stage game. In stage 1, regulator chooses the price-cap on airport charge In stage 2, airport decides airport charge pa and concession price pc per passenger. In stage 3, each airline chooses its output qi to maximize its own profit.

Yang & Zhang (UBC)


January 2011

11 / 33

Stage 3 In stage 3, airline i’s profit is ˜ K )]qi , πi = [pi − c − pa − βD(Q, where c is airlines’ unit operating cost, and β denotes their value of time. Imposing symmetry, we obtain qi∗ =

a − c − pa . (n + 1)(α + β)θ + 2b + n − 1

Note that (α + β)θ is the total (adjusted) value of time taking both passengers and airlines as a whole. For simplicity, we denote it by v .

Yang & Zhang (UBC)


January 2011

12 / 33

Airport Profit, Consumer Surplus, and Social Welfare The airport’s profit is ¯ (pc ) − F , Π = (pa − ca )Q ∗ + (pc − cc )Q ∗ G where ca is airport’s unit operating cost, cc is the unit cost of the concession good, F is airport’s fixed cost. Consumer surplus is CS = U(q1∗ , · · · , qn∗ ) −

n X

ρ∗i qi∗ +

Z

SW = Π +

n X

¯ (x)dx. Q ∗G

pc

i=1

Social welfare is

u

πi + CS.

i=1

Yang & Zhang (UBC)


January 2011

13 / 33

Welfare-maximizing Airport Proposition 1 For a public welfare-maximizing airport, the optimal concession price is pcw = cc , and the optimal aeronautical charge is (a − c − ca )[(n − 1)v − b] − I (cc )[(n + 1)v + 2b + n − 1] , 2nv + b + n − 1 Ru ¯ (x)dx is the per-passenger consumer surplus from where I (cc ) = cc G concession consumption. paw = ca +

Alternatively, we may write paw as 1 1 w pa = ca − I (cc ) + 1 − vQ w − bQ w . n n

Yang & Zhang (UBC)


January 2011

14 / 33

Profit-maximizing Airport Proposition 2 For a private profit-maximizing airport, there exists a unique optimal concession price pcπ > cc , which is determined by ¯ (pcπ ) − g (pcπ )(pcπ − cc ) = 0. G The (privately) optimal aeronautical charge is paπ = ca + [a − c − ca − H(pcπ )]/2, ¯ (pcπ )(pcπ − cc ) is the per-passenger airport profit from where H(pcπ ) = G concession operations. Alternatively, we may write paπ as 1 2b − 1 π π π pa = ca − H(pc ) + 1 + vQ + 1 + Qπ. n n Yang & Zhang (UBC)


January 2011

15 / 33

Efficient Airport Charge We show that for any given airport charge pa , a profit maximizing airport will always set concession price at pcπ . Thereafter, the concession price is fixed at pcπ unless otherwise specified. Given pc = pcπ , the aeronautical charge that a welfare-maximizing regulator will choose is determined by max

SW

s.t.

pc = pcπ .

pa

We shall refer to the solution as the “efficient” aeronautical charge. We can show that the efficient aeronautical charge pae is increasing and concave in the value of time. Yang & Zhang (UBC)


January 2011

16 / 33

Regulation Benchmark

A privatized airport needs to be financially self-sufficient. A natural benchmark is that the regulator maximizes social welfare by setting the airport charge, subject to the airport’s cost recovery constraint: max

SW

s.t.

Π≥0

pa

pc = pcπ .

Yang & Zhang (UBC)


January 2011

17 / 33

Single-till Price-cap Regulation Under price-cap regulation, the optimization problem faced by a profit-maximizing airport is max Π pa ,pc

s.t.

pa ≤ p¯a ,

where p¯a is the price-cap being chosen by the regulator. Single-till price-cap p¯a = pas is the smallest root of Π(pa , pcπ ) = 0. The price-cap constraint will be binding, i.e. under single-till, the profit-maximizing airport will choose pas as the airport charge. Single-till price-cap is increasing but is convex in the value of time.

Yang & Zhang (UBC)


January 2011

18 / 33

Dual-till Price-cap Regulation Dual-till price-cap p¯a = pad is the smallest root of Πa (pa ) = (pa − ca )Q ∗ − λF = 0, where λ is the fraction of airport’s fixed cost attributed to aeronautical operations (Czerny, 2006). Dual-till price-cap is increasing and convex in the value of time. The dual-till price-cap constraint is not necessarily binding. Let paD be the airport charge chosen by the profit-maximizing airport under dual-till price-cap regulation. Then we must have paD = min{pad , paπ }.

Yang & Zhang (UBC)


January 2011

19 / 33

Airport Charge

Proposition 3 (a) The efficient airport charge, pae , is increasing and concave in the value of time v . (b) The airport charge under single-till price-cap regulation, pas , is increasing and convex in v . (c) The airport charge under dual-till price-cap regulation, paD , is increasing and convex in v when v < v0 , and remains constant at paπ when v ≥ v0 . (d) The airport charge under single-till price-cap regulation is less than that under dual-till price-cap regulation, i.e. pas ≤ paD .

Yang & Zhang (UBC)


January 2011

20 / 33

Single-till Vs. Dual-till There are three scenarios. Scenario 1: The efficient airport charge curve is always below the airport charge curve under single-till regulation. To guarantee the model to be meaningful, we must have v < v¯

D a

p

pas e a

p

v0 is the critical point pae < pas < paD SW is concave in pa Single-till dominates dual-till

ca Yang & Zhang (UBC)

v0 Price-cap Regulation of Congested Airports

January 2011

21 / 33

Single-till Vs. Dual-till Scenario 2: The efficient airport charge curve intersects with the aeronautical charge curves under both single-till and dual-till.

paD pas pae

ca

Yang & Zhang (UBC)

v0


v v

January 2011

22 / 33

Scenario 2 Case 1 Let v1 and v2 be the zeros of Π(pae (v ), pcπ ) = 0 When v < v1 or v > v2 , Π(pae (v ), pcπ ) < 0, i.e. with the efficient airport charge and its concession profit, the airport is not able to cover the fixed airport cost. pae < pas < paD ⇒ Single-till dominates dual-till

paD pas pae


v1

v0 v2 v


v January 2011

23 / 33

Scenario 2 Case 2 Let v3 and v4 be the zeros of Πa (pae (v )) = 0 When v3 ≤ v ≤ v4 , Πa (pae (v )) ≥ 0, i.e. with the efficient airport charge only, the airport covers the airport cost associated with aeronautical services. pas ≤ paD ≤ pae ⇒ Dual-till dominates single-till

paD pas pae


v1

v3

v4

v0 v2 v


v January 2011

24 / 33

Scenario 2 Case 3 What if v1 ≤ v < v3 or v4 < v ≤ v2 ? SW is a quadratic and concave function of pa pas ≤ pae ≤ paD ⇒ we only need to compare pae − pas and paD − pae

paD pas pae

ca

v1 v3

Yang & Zhang (UBC)

v4

v0 v2 v v


January 2011

25 / 33

Scenario 2 Case 3 What if v1 ≤ v < v3 or v4 < v ≤ v2 ? SW is a quadratic and concave function of pa pas ≤ pae ≤ paD ⇒ we only need to compare pae − pas and paD − pae pae − pas = paD − pae ⇒ pae = (pas + paD )/2 ⇒ v = v5 , v6

paD

pas + paD 2 pas e a

p

ca

v1v5 v3

Yang & Zhang (UBC)

v4

Single-till is better when v1 ≤ v ≤ v5 , or v6 ≤ v ≤ v2 Dual-till is better when v5 < v < v3 , or v4 < v < v6

v6 v0 v2 v v


January 2011

26 / 33

Scenario 2 Summary

∆SW = SW (pas , pcπ ) − SW (paD , pcπ ) ∆SW > 0 ⇒ single-till is better, ∆SW < 0 ⇒ dual-till is better DSW

0

v1

v5

v3

v4

v6

v2 v v

Single-till dominates dual-till when the value of time is sufficiently small (v < v5 ) or sufficiently large (v > v6 ) Dual-till performs better when the value of time is intermediate (v5 < v < v6 )

Yang & Zhang (UBC)


January 2011

27 / 33

Intuition of Scenario 2 When the value of time is sufficiently small, the airport will be congested. However, both passengers and airlines do not care about congestion delays. They behave as if there were no airport congestion. So, airport congestion is not a problem. This result is consistent with Czerny (2006): Single-till is better at non-congested airports. When the value of time is sufficiently large, the number of passengers will be very small, and so the level of congestion and hence absolute delays will be, in equilibrium, very low. However, the low equilibrium quantities are due to the fact that passengers and airlines are very sensitive to congestion delays. In this sense, airport congestion is a major problem. When the value of time is intermediate, airport congestion exists and matters to passengers and airlines as they do care congestion delays. Dual-till is better when the value of time is intermediate Yang & Zhang (UBC)


January 2011

28 / 33

Single-till Vs. Dual-till Scenario 3: The efficient airport charge curve intersects with the airport charge curve under single-till price-cap regulation, but it is always below that under dual-till price-cap regulation.

pas + paD 2

paD

pas pae


v1 v5

v6

v0 v2


v v January 2011

29 / 33

Single-till Vs. Dual-till Summary Proposition 4 From the perspective of welfare maximization, (a) If the airport is not able to cover the fixed airport cost with the efficient airport charge and its concession profit, i.e. Π(pae (v ), pcπ ) < 0, then single-till dominates. (b) If with only the efficient airport charge the airport covers the airport cost associated with aeronautical services, i.e. Πa (pae (v )) > 0, then dual-till performs better. (c) Otherwise, the comparison depends on whether or not the efficient airport charge is greater than the average of the airport charges under the single-till and dual-till regulation, i.e. pae > (pas + paD )/2. If the answer is yes, then dual-till dominates. Otherwise, single-till is better.

Yang & Zhang (UBC)


January 2011

30 / 33

Conclusions

We show that when airport congestion is not a major problem, single-till price-cap regulation dominates dual-till price-cap regulation with respect to overall social welfare. Furthermore, we identify situations where dual-till regulation performs better than single-till regulation when there is significant airport congestion. For instance, when the airport can cover the airport costs associated with aeronautical services simply through an efficient charge, then dual-till regulation yields higher welfare.

Yang & Zhang (UBC)


January 2011

31 / 33

Future Research

It would be interesting to see whether the results are robust in a more general setting. We have assumed that the airport capacity is fixed. Incorporating airport capacity as a decision variable is an important direction for future research.

Yang & Zhang (UBC)


January 2011

32 / 33

Thank you. Questions & Comments?

Yang & Zhang (UBC)


January 2011

33 / 33