Public private partnership with government included demand risk a case study from viet nam

Being part of the city’s ongoing ring road project, the Phu My Bridge provides a quick way to move from East to West of the city, and in the near future the bridge would link up two majo

Public-Private Partnerships with induced demand risk: A case study from

Keywords: Vietnam, Phu My Bridge, Public-private partnerships, Demand risk

1 INTRODUCTION

Over the last decade, infrastructure has gathered renewed interest, especially from institutional investors given its particular characteristics as an investment (Sawant 2010) However, roads, bridges or aqueducts have been around for millennia, constructed by

1 Université Paris-Dauphine

Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16

civilizations both ancient and modern to drive trade, integration and progress Once being the responsibility of the governing body, with time the private sector is increasingly called upon as well

On the other hand, as the ongoing AIIB (Asian Infrastructure Investment Bank) initiative is any indication, emerging markets and particularly Asia is where a significant portion of infrastructure demand will be This demand is estimated at USD 800 billion per year from

2010 to 2020 (Bhattacharyay 2010) Asian countries such as Vietnam are also massively turning towards the private sector to finance their infrastructure

In this paper, the author has chosen to explore this link between infrastructure and emerging markets by providing a case study of the Phu My Bridge in Vietnam Located in Ho Chi Minh City whom it connects two key districts, the bridge had been one of the largest in Vietnam at the time of its construction However, it is in financial distress for reasons detailed later in this paper Understanding these reasons will therefore provide valuable lessons for Vietnam in enlisting the private sector in infrastructure development, and this is the first reason that motivates this paper

From an academic standpoint, the Phu My Bridge is also worth considering The paper will argue that the public sector’s behavior may be interpreted as opportunistic and this has contributed to the bridge’s financial difficulty For this, the paper will develop a theoretical model and show even with simplifying assumptions we can come upon a number of results worth interpreting

The remainder of this paper is organized as follows Section 2 provides a background to this research Section 3 develops a theoretical model to analyze the behavior of the government in this project Section 4 points out the limitations of the model compared to real life and what

we may learn from them The final section concludes

2 BACKGROUND TO THE STUDY

2.1 Background on Vietnam

2.1.1 Economic context

Since the country’s opening up during the late 80s, Vietnam has made some great strides on creating a market economy Real GDP growth averaged 6.9% from 1990 to 2013, according to the World Bank’s data In parallel, vast institutional changes were introduced to attract foreign investments, resulting in Vietnam becoming one of the top destinations for foreign direct investments (FDI) in the region FDI commitments amounted to USD 22.4 billion in

2013 (Báo Đầu Tư 2014)

The private sector in Vietnam was also a big beneficiary of the sweeping reforms The number of State-Owned Enterprises (SOEs) declined from 6545 in 1992 to about 3000 in

2010 and they only account for about 10% of the country’s employment (Le Hoang Cuong, Helen and Ruhul 2014) The private sector’s contribution to the national economy, on the other hand, rose to between 57% and 67% of the GDP (ADB 2005)

2.1.2 Private participation in infrastructure development

When the reforms began in Vietnam, the country’s infrastructure was in shambles due to lack of investment However, over the next two decades the country has ramped up its infrastructure spending, which now represents a significant percentage of GDP According to Vietnam’s General Statistics Office (GSO), the country spent on average 10.6% of its GDP on infrastructure from 2009 to 2011 This estimate is on the higher end of the regional range, as

a research report showed none of Vietnam’s emerging neighbors in the ASEAN2 spent more than 10% of GDP (Goldman Sachs 2013)

Faced with this intensifying need in infrastructure spending, Vietnam’s government budget

is currently under increasing scrutiny from the public and capital markets, and the budget deficit was estimated at 5.5% in 2013 (ADB 2014) Domestic bank financing have become

2 ASEAN: Association of Southeast Asian Nations

more difficult since 2008 with rates sometimes as high as 20% Foreign bank financing is also challenging due to more stringent international banking regulations The Bank for

International Settlement itself admitted emerging countries were “particularly concerned”

about Basel III’s impact on the availability of funds (Bank for International Settlements 2014)

Consequently, Vietnam is relying more and more on the private sector to keep up with infrastructure demand, something recognized very early by the government The first amendment of the country’s Law on Investment in 1992 introduced the first legal framework for BOT (Build-Operate-Transfer) contracts Subsequent Decisions issued by the government detailed other frameworks such as BT (Build-Transfer), BOO (Build-Own-Operate) or BTO (Build-Transfer-Own) Since then, 82 projects with private participation reached financial close in Vietnam until 2013, with a total cost of USD 11.6 billion (World Bank 2014)

2.2 The Phu My Bridge

2.2.1 The context

The Phu My Bridge connects Districts 2 and 7 of Ho Chi Minh City, Vietnam’s economic powerhouse with 9% of the national population and 20% of the national GDP in 2012 At the time of its construction, the bridge had been one of the largest infrastructure projects ever undertaken in the city After completion, it would create a profound impact both for the city and for Vietnam as a whole Being part of the city’s ongoing ring road project, the Phu My Bridge provides a quick way to move from East to West of the city, and in the near future the bridge would link up two major sections of Vietnam’s 1800-km under-construction national expressway (VnExpress 2014)

A map of the Phu My Bridge’s location is provided below:

Figure 1: Location of the Phu My bridge and the ring road project – (Tang Quoc Cuong 2010, 139)

in what would traditionally be a public sector project” (World Bank 2014) For the Phu My

Bridge, the developer is Phu My Bridge Corporation (PMC), an entity backed by a number of investors

The main EPC (Engineering, Procurement & Construction) contract was awarded to BBBH consortium, which consisted of Germany’s Bilfinger Bergerm and Australia’s Balderstone Hornibrook The main debt financing package was co-syndicated by two French banks Société Générale and Crédit Agricole CIB It consisted of a USD 60 million buyer credit and another untied USD 34 million loan The buyer credit is insured by Germany’s Euler Hermes

and reinsured by France’s Coface and Australia’s EFIC3, and the entire debt facility is lent to

Ho Chi Minh City Finance & Investment Company (HFIC), a public entity established by the

city’s government HFIC then lent the proceeds to PMC, thus allowing the latter to benefit de facto from the guarantee of the City’s government (this technique is known as on-lending)

Loan repayments from HFIC are in turn guaranteed by Vietnam’s Ministry of Finance (MoF) The lending contract was signed in 2005 and entered into force in 2007 However, a number of domestic banks such as BIDV and Sacombank also provided financing to PMC Below is a summary of the key parties:

Figure 2: Summary of the main parties involved

End-users Main contractors Bilfinger Bergerm,

Baulderstone Hornibrook

Sub-contractors

Freyssinet, CC620

Export finance guarantors

Coface, Euler Hermes, EFIC

People’s Committee of

HCMC

Ticket price regulator &

BOT contract signatory

Construction started in 2005, was delayed by two years due to in land acquisition issues but wrapped up successfully in 2009 PMC began to collect tolls starting from April 2010, after the ticket price was approved by the City’s government

Second, fee revenue has been largely underneath what was needed to repay loans and recoup the initial investment Ho Chi Minh City-based economist Nguyen Xuan Thanh investigated real traffic going through the bridge and found out that in terms of Passenger Car Units (PCU), real traffic only represented 53.7% of traffic assumptions made in the initial financial plan (Nguyen Xuan Thanh 2013) In a letter addressed to the city government in 2011, PMC put the blame on the city for low traffic demand According to the company, the ring road projects of Ho Chi Minh City were incomplete and the city government had not prohibited heavy vehicles from going through the city center (VnEconomy 2011)

From an economic standpoint, these claims are not without merit The rationale behind the project was to capture traffic from the South and West of the City to the North (see Figure 12 below) As the Eastern ring road project (managed by the city’s government) is not yet completed (dotted line on Figure 12), vehicles would choose to follow the old National Road

1A (red line) or going through the busy city center instead of the Phu My Bridge (VnExpress 2014) As of February 2015, there were still at least one bridge to be constructed to close the ring road completely, and construction would only begin in the future (Official Journal of Ho Chi Minh City 2015)

Figure 3: Uncompleted sections of the ring road project (VnExpress 2014)

Initially, the government had agreed in the initial contract to have the Eastern ring road

ready three years after the bridge’s completion at the latest (Nguyen Xuan Thanh 2013) If this is not the case, the government would receive back the project and reimburse PMC for the investment outlay plus interest This outcome, however, would have to be pronounced by a

court Although PMC seems to have an advantage in this situation, there are actually reasons to believe the company had allegedly committed violations of the initial contract itself by overleveraging the project, all of which will be the topic of a later section of the paper At present, therefore, two parties are pursuing negotiation to resolve the issue

2.3 Theoretical background and contribution

Public-private partnerships (PPPs) have long been a focus of research both in academia and

in international organizations, but there is no clear-cut definition of a PPP both in academic research (De Clerck, Demeulemeester and Herroelen 2012) and in publications by

Phu My Bridge

international organizations (World Bank PPP IRC 2015), (OECD 2008) There seems to be agreement, however, on the necessity to analyze PPPs as mechanisms of risk allocation by which each risk is borne by the party better positioned to do so

PPPs are themselves contract, and they been the subject of a particular strand of contract theory literature One of the earliest references on the subject was done by Jean Tirole and Jean-Jacques Laffont, who provided a game-theoretic analysis of regulation and procurement contracts (Laffont and Tirole 1993) One of the concepts proposed by Laffont and Tirole to

analyze the public sector’s decision-making process is called shadow cost of public funds,

which will be used again later on in this paper This provided the groundwork necessary for subsequent authors’ research In a 2005 paper, the economists Dewatripoint and Legros showed if it was too costly to avoid cost overruns then letting cost overruns happen would be

a better solution overall PPPs are therefore not a silver bullet to cure the ills of infrastructure projects The role of institutions is crucial in opening up public projects for competition and ensuring the latter is respected by all stakeholders (Dewatripont and Legros 2005) In another study, it is shown that PPP might be less efficient than other financing modes due to transaction costs that may be incurred by choosing the PPP model These transaction costs come from three sources: (1) principal-principal problems, (2) renegotiation and hold-up problems, and (3) soft budget constraints (Ho and Tsui 2009)

Renegotiation was the particular focus in an earlier paper by Ping Ho (S P Ho 2006), which used a game structure First, the project encounters an unfavorable event such that the developer can either request a public subsidy or let it go bankrupt The government may choose to negotiate to lower the subsidy or reject the request altogether If the project goes bankrupt, the government has a negative payoff reflecting political costs of restructuring the project If the subsidy request is accepted, then the government suffers from another type of political costs due to budget spending to rescue a private sector company These specifications reflect shadow cost of public funds, a concept used later in this paper’s model

The recent PPP market in Vietnam has not so far captured interest from researchers, with the exception being a short case study by economist Nguyen Xuan Thanh specifically about the Phu My Bridge itself (Nguyen Xuan Thanh 2013) Therefore this paper, by focusing on the Phu My Bridge, is making a contribution as it is among the firsts to study PPPs in Vietnam and the first to do so with a formalized analysis of a particular project Secondly, while some papers may focus on the moral hazard of the private-sector party who is supposedly better informed, this paper studies a possible moral hazard of the public sector concerning their ability to deliver and realize its prior commitment As the paper would try

to demonstrate, such decision to deliver (or not) may be interpreted as an equilibrium decision

In short, the paper’s approach is pragmatic: it starts from a real project, presents a simple theoretical model and uses the model to analyze one key aspect of the project which is the possible opportunistic behavior of the public sector In doing so, it voluntarily departs from

other issues The paper asks the following questions: What is the motivation of the government in the Phu My Bridge? Why would the government be induced to not give an effort

in constructing the ring roads? And finally, what lessons can Vietnam learn from the project?

By searching for answers to these questions, the paper tries to contribute to both the existing literature and Vietnam’s still nascent PPP market

3 THE MATHEMATICAL MODEL

3.1 Preliminary assumptions

We consider two parties, the government of Ho Chi Minh City (public sector) and Phu My

Corporation (private sector) The government wants to have a bridge constructed across the Saigon River, and at the same time it also has to invest in the City’s ring road project Each party has no information on the real intents of the other party and do not make assumptions regarding the behavior of their co-signatory

Construction cost of the Phu My Bridge project is assumed to be fixed, known perfectly

in advance by all and consists only in the initial investment outlay 𝐾:

𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 = 𝐾 There is no variable cost, and marginal cost (𝜕𝑇𝐶𝜕𝑄) is zero To simplify further, we normalize 𝐾

at 1, therefore 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 = 𝐾 = 1 This feature is a departure from real life, where the project cost was not certain and subject to dispute

We also make other simplifying assumptions regarding operations:

 Under public management, the city allows free access to the bridge for everyone;

 The bridge has unlimited capacity;

 The government only allows toll pricing at average cost so that PMC can break even4

We consider traffic demand to be completely inelastic with regards to toll price (this is

also a simplification) However, we suppose the traffic level on the Phu My Bridge will depend on the government’s investment on the city’s ring road project:

𝑄 = 𝛼𝐼 Where:

 𝑄 is actual traffic demand

 𝐼 is the investment made by the city’s government in the ring road projects Traffic demand is an increasing function of this investment

 𝛼 is a parameter and measures the sensitivity of demand on 𝐼, i.e 𝛼 =𝑑𝑄𝑑𝐼 The higher

𝛼 is, the higher the impact of each unit invested in the ring road on the Phu My Bridge’s traffic demand We suppose 𝛼 > 1

4 The government cannot make Phu My Corporation provide free access by sacrificing the project’s financial viability, but at the same time we assume the government does not want to leave out rent to PMC either

There is a timeline but no discounting and other time-related matters The timeline of the

project depends on whether it is under public or BOT management and is visualized below:

Timeline (A): Public management

Construction

 The public manager begins construction

of the Phu My bridge and the ring road

 At 𝑡 = 0, the parties sign the contract

 Each party proceeds to invest/construct

accordingly without observation of and

from the other party

Concession period (BOT)

 At 𝑡 = 1 , information about effective

demand arrives

 Demand during the concession period is

𝑄 1 =𝑄2=𝛼𝐼2 (half of total demand)

2 (the other half of total demand)

Figure 4: Timelines used in the model

These two timelines were inspired by a paper about BOT concessions by two French economists (Auriol and Picard 2013), where the authors used a continuous-time framework with separate intervals that represent the concession period the post-transfer period

3.2 Baseline model (0): Public management

In this first model denoted with the subscript 0, we assume complete public-sector financing and management Timeline (A) above is therefore the relevant one

Being responsible for financing two projects at once (Phu My bridge plus the ring road), the government’s expenditure consists in two components:

 Investment in the Phu My Bridge project, normalized at 1

 Investment in the ring road, denoted 𝐼

From 𝑡 = 1 (when construction is over) to 𝑡 → ∞, the public manager will make the bridge available free of charge for all (𝑃0= 0 where the subscript 0 denotes model 0) As such, the bridge produces no revenue for the city’s government at all levels of traffic (and we suppose that no tax is being raised to directly finance the project) The P&L of the government is:

Π0𝐺 = 𝑃0𝑄 − 𝐾 = 𝑄 × 0 − 1 = −1

The government makes a loss equal to the initial investment outlay This loss, or in other words the investment outlay itself, has to be drawn from the government’s budget However,

in so doing the government subjects itself to “shadow cost of public funds”, which is now

developed in more details

This notion was used in a theoretical paper (Auriol and Picard 2013) to model the total cost

of public fund and this approach is also similar to (S P Ho 2006) The authors gave the notion’s origin to Laffont and Tirole’s book (Laffont and Tirole 1993) In this paper, we consider a slightly modified specification for shadow cost of public funds

Definition of shadow cost of public funds: Let 𝑥 be the amount the government spends to

develop infrastructure The real cost of this spending from the government’s perspective, denoted 𝐿(𝑥), will be:

The government’s welfare takes the following form:

𝑊0𝐺 = 𝑄 ⏟

=𝛼𝐼

− 𝐿(𝐾) − 𝐿(𝐼)

In other words, the government would be “happier” if more people use the bridge, but it has

to balance this with the cost to invest in two infrastructure projects at once The control variable for the government is 𝐼, the amount invested in the ring road project However, in contrary to certain models of benevolent governments such as (Auriol and Picard 2013), the government in our model does not take into account consumer surplus since the demand

function is absolutely inelastic Absolute price inelasticity (zero elasticity) means consumers

would not modify their demand no matter the price, and therefore there is no consumer

Verification of the second-order condition: 𝜕2𝑊0𝐺

𝜕𝐼 2 = −2𝛽 < 0 Therefore 𝐼0∗ maximizes the government’s welfare

Having the investment amount at equilibrium, we can compute the other variables Traffic demand resulting from the investment is:

𝑄0∗= 𝛼𝐼0∗=𝛼(𝛼 − 1)

2𝛽The maximum welfare amount of the city government is:

𝑊0𝐺∗ =𝛼(𝛼 − 1)

2𝛽 − 𝛽 − 1 −

𝛼 − 12𝛽 − 𝛽 ×

We suppose that when the city’s government and Phu My Corporation sit together, they

agree to maximize their collective welfare (recall that there is no consumer surplus) The

general expression of collective welfare (public and private) is defined as the following:

𝑊1 = Government′s welfare + Profit of PMC = 𝑊1𝐺+ Π𝑃𝑀𝐶Two comments/assumptions are made to simplify the expression of 𝑊:

 The government’s welfare takes the same form as in model 0 and they still have no revenue from both projects since there is no toll under public management;

 Section 3.1 (Preliminary assumptions) supposes the BOT regulatory framework allows PMC to price toll at a level which allows them to recoup the initial investment

of 𝐾 = 1, but not more Therefore Π𝑝𝑟𝑖𝑣𝑎𝑡𝑒 = 0 in the expression above In other words, there is no profit maximization for Phu My Corporation

These simplifications gives the following form for 𝑊1:

𝑊1= 𝛼𝐼1− (𝐼1+ 𝛽𝐼12) The term −(1 + 𝛽) is no longer present in 𝑊1, as the government no longer has to spend its budget to construct the Phu My bridge At the signing of the contract between the government and PMC, the parties agree to maximize this expression:

𝐌𝐚𝐱

𝐼1 𝑊1 = 𝛼𝐼1− (𝐼1+ 𝛽𝐼1) First-order condition is the same as in model (0):

𝜕𝑊1

𝜕𝐼 = 𝛼 − 1 − 2𝛽𝐼 = 0 ⟹ 𝑰̅ =𝟏 𝜶 − 𝟏

𝟐𝜷The overhead bar ( ̅ ) notation designates a feature written in the contract between the two parties In this section, we suppose the government honors this commitment to make an investment equal to 𝐼̅ for the ring road project By using the superscript ∗ to designate an 1actual quantity, we can write 𝑰̅ = 𝑰𝟏 𝟏∗

The traffic amount resulting from an investment of 𝐼1∗ is:

𝑄1∗=𝛼(𝛼 − 1)

2𝛽Notice that 𝑄1∗= 𝑄0∗ and 𝐼1∗= 𝐼0∗, therefore so far nothing has changed compared to model (0) The government invests the same amount into the ring road Other results have changed, however, as detailed below

First, toll price during the concession period has changed The traffic demand

addressed to PMC between 𝑡 = 1 and 𝑡 = 2 is:

𝑄1𝟏∗=𝑄1

∗

2 =

𝛼(𝛼 − 1)4𝛽The superscript 1 indicates this is the demand during the concession period

Since the company prices the toll to break even, the implied toll price is:

Π1 = 0 ⟹ 𝑃1∗𝑄11∗= 𝐾 ⟹ 𝑷𝟏∗ = 𝑲

𝑸𝟏𝟏∗= 𝟒𝜷𝜶(𝜶 − 𝟏)

In the previous section, under public management the Phu My Bridge could be used free of charge, in other words 𝑃0∗= 0 < 𝑃1∗ Introducing a private sector company increases the price charged to consumers

After 𝑡 = 2, the project is given back to Ho Chi Minh City’s government who again collects no toll

Second, collective welfare has also changed, since the government no longer has to

spend its own money on the Phu My Bridge, while the private project developer is able to charge a breakeven price The new welfare level is calculated as:

𝑊1∗= 𝑄1∗− (𝐼1∗+ 𝛽𝐼1∗2) =𝛼(𝛼 − 1)

2𝛽 − [

𝛼 − 12𝛽 + 𝛽

(𝛼 − 1)2

4𝛽2 ]

=𝛼 − 12𝛽 (𝛼 − 1 −

𝛼 − 1

2 ) =

(𝛼 − 1)2

4𝛽

Note that 𝑊0∗=(𝛼−1)2

4𝛽 − 𝛽 − 1, hence 𝑊1∗> 𝑊0∗ The two changes explained above can be interpreted as follows:

 This simple model shows it is possible to attain the same level of infrastructure investment (Bridge plus ring road: 𝐼0∗+ 𝐾 = 𝐼1∗+ 𝐾) by delegating financing and construction to the private sector This interpretation is consistent with the growing trend of private participation in infrastructure projects in Vietnam and elsewhere

 By inviting PMC to participate in the project, collective welfare is higher by an amount of (𝛽 + 1) Therefore from a welfare point of view, private participation in infrastructure is desirable

 However, this increase in welfare has been made in detriment of consumers who

“suffer” from a price hike (𝑃0∗< 𝑃1∗) Again, the impact of this price increase is not considered in our model since consumers have zero price elasticity, but this point is worth mentioning

 In our model, toll price regulation (Π𝑝𝑟𝑖𝑣𝑎𝑡𝑒 = 0) is there to “protect” consumers from price increase In reality, price regulations are commonly seen in infrastructure projects In the case of the Phu My Bridge, if PMC wants to increase toll price or start collecting toll on motorcycles, they have to secure the city government’s approval

estimate 𝛽 What is more, Vietnam’s institution quality and transparency has much to improve, which exacerbates the problem

We make two additional assumptions regarding 𝛽:

 The government does not reveal its true sensitivity 𝛽 to PMC Instead, before signing the contract the company believes the sensitivity of the government to shadow cost of public funds is another value, 𝛽̅ This inaccurate value of 𝛽̅ is used in the contract and forms the basis of the city government’s obligations

 Furthermore, we suppose Phu My Corporation is unsuspecting of this behavior This

is a simplifying assumption, but it supports the paper’s perspective which is to focus

on the public sector’s opportunism

Let us look at the model as two key phases: signing of the contract and life of the contract

3.4.1 Signing of the contract

The collective welfare’s expression is similar to model (1), with the only difference being the sensitivity parameter used At this stage (signing), the relevant sensitivity is the one revealed by the city government, which is 𝛽̅ and not 𝛽 The parties maximize the expression:

𝐌𝐚𝐱

𝐼2 𝑊2= 𝛼𝐼2− (𝐼2+𝜷̅𝐼22) Which yields the following results:

𝐼̅ =2 𝛼 − 12𝛽̅ ⟹ 𝑊̅̅̅̅ =2 (𝛼 − 1)2

4𝛽̅

Recall that the overhead bar ( ̅ ) designates a contracted feature, which may or may not be honored

In private, the government decides using 𝜷 as the relevant parameter It maximizes its

own welfare (collective welfare and the government’s welfare have the same expression given our assumptions):

𝐼 𝑊2𝐺= 𝛼𝐼2−𝜷𝐼22

And therefore:

𝐼2∗=𝛼 − 12𝛽 ⟹ 𝑊2𝐺∗ =

(𝛼 − 1)2

4𝛽The superscript * indicates actual results (not contractual results) By investing 𝐼2∗ and not 𝐼̅, 2the government has deviated in private

Why would the government choose to deviate? To answer this question, we can

compare the welfare corresponding to each option If the government sticks to its word, then its welfare is 𝑊̅̅̅̅̅ =2𝐺 (𝛼−1) 2

4𝛽̅ , whereas deviating would give a welfare of 𝑊2𝐺∗ =(𝛼−1)4𝛽 2 A quick comparison between the two expressions allow us to conclude that:

Deviation ⟺ 𝛽̅ is revealed but 𝛽 is used ⟺ 𝑊2𝐺∗> 𝑊̅̅̅̅̅ ⟺ 𝜷̅ < 𝜷 2𝐺

In other words, the government voluntarily understates its sensitivity to shadow cost of public funds In doing so, they overstate their ability to bear political costs that stem from public expenditure The government has the incentive to misrepresent 𝛽 because this would improve their welfare

For the remainder of the paper, we assume 𝛽̅ < 𝛽

What are the consequences of this misrepresentation? First, we calculate every

quantity implied by the contract between the government and PMC

First, since 𝛽̅ < 𝛽 we can conclude that 𝐼2∗< 𝐼̅ , or in other words the city government under-2invests compared to the contract

Implied traffic demand is:

𝑄2

̅̅̅̅ =𝛼(𝛼 − 1)

2𝛽̅

This demand is split evenly between the concession period and the public management period:

Investment made by the city government in the

ring road project 𝐼 ̅ =2 𝛼 − 1

Profit of Phu My Corporation Π̅𝑃𝑀𝐶 = 0 Toll price during concession period 𝑃 ̅̅̅ = 2 4𝛽̅

𝛼(𝛼 − 1) Collective welfare 𝑊 ̅̅̅̅ =2 𝛼(𝛼 − 1)

4𝛽̅

Table 1: Model (2) - Features implied by the contract between the city government and Phu My

Corporation

These contracted quantities are not realized during the life of the contract

3.4.2 Life of the contract

Between the signature at 𝑡 = 0 and 𝑡 = 1 when construction is complete, each party deploys its resources to construct their respective projects The actual commitment of the government is not verified by PMC, and the government puts in an insufficient investment

At 𝒕 = 𝟏, construction of both projects is finished and traffic demands across the bridge

becomes known Since the government invested 𝐼2∗=𝛼−1

2𝛽 instead of 𝐼̅ =2 𝛼−1

2𝛽̅ and 𝐼2∗< 𝐼̅, traffic 2demand is lower than expected: