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Chapter 5


Rational Bankruptcy in the Regulated Utilities - 
A Real Problem, a Credible Threat or Cheap Talk

Stephen Regan

Cranfield School of Management 

Cranfield School of Management

Cranfield University 
England  MK 43 0AL

Telephone: +44(0)1234 754311

Fax:        +44(0)1234 752136

email:          s.regan@cranfield.ac.uk 



Rational Bankruptcy in the Regulated Utilities - 
A Real Problem, a Credible Threat or Cheap Talk



A model is presented which predicts that it is rational for a regulated firm to create a positive risk of bankruptcy  by excessively high levels of gearing, in order to extract a higher price (ie a price above Short run marginal social cost) than the official rules of the game allow. As such this is a model of capture with the (perhaps interesting) property that it is rational for the regulator to allow all three of these departures from the  welfare optimum. One of the main predictions of the model is that issuing debt will prevent the regulator from acting opportunistically by reducing prices during a regulatory period.   Equally, allowing the firm to issue debt, may be a commitment by the regulator not to reduce prices later.   The intuition is that the regulator trades-off static welfare for a dynamic gain of  increased investment, which is otherwise underincentivised, in a risky, price capped environment. There are empirical phenomena in both the UK and California which suggests that such a model is timely. The paper concludes with certain indications of explicit empirical work which could usefully test its validity before any policy implications may be drawn.




Introduction: The nature of regulation in Public Utilities

There are certain facts in regulatory environments which indicate that strategic gearing  is a feature of the game.   For instance, regulated firms are consistently amongst the most highly leveraged firms.1   Bradley, Jarrell and Kim (1984) survey 25 industries over 1962-1981 and find that regulated industries (such as telecomms, electricity, gas and airlines) are populated by very highly geared firms.   The question is whether these high levels of debt are a strategic attempt to extract higher prices from the regulator, or whether they emerge for some other reason, such as ineffective control over the board by investors.   This paper presents a model which argues that the former is a credible possibility.   However, there are important differences between the UK and US environments, due to the different historical paths the utilities have taken in these economies. 

For instance, Hyman Toole and Avelis (1987) find that the Regional Bell Holding Companies were highly geared in relation to comparative firms in a sample of 104 industries.   Specifically, they found that the average debt ratio of the Bell Holding Companies in 1986 was 40% although their beta was only .63.   In comparison, in 27 other industries with low risk (beta between 0.60 and 0.99) gearing  was just 28%.   However UK regulated utilities do not have the same stance - their privatizations in the early 1980s were accompanied by low levels of debt, and thus they were subject to speculative attack by the regulator as a US utility might not be, due to the effect of gearing acting as a 'regulatory shield' in the US.2, since the assumption is that the choice of capital structure is inherently a strategic commitment in a game of generalised signalling between the firm and the regulator. 

Moreover, the model developed here is inherently one in which the firm is a regulated monopoly and thus faces no threat of entry, whilst the facts are against us in using such a model in the UK where the regulatory framework in both electricity and gas is seeking to evolve a more competitive framework, where entry accommodation is a specific objective of regulation. This has been the history of telecoms regulation in the UK (and the US) and is increasingly so in gas and electricity in the UK. 

Such a parametisation obviously makes the model more complex, since there is a well known literature which looks at the role of capital structure as a form of strategic entry deterrence in oligopolistic but 'unregulated' markets.  The broad sweep of these oligopoly models of capital structure is to amplify the pressure to increase gearing, since they find that the threat of entry deterrence should induce higher levels of gearing as a form of strategic commitment. If  UK firms resist the strategic pressure to gear up, they may find that low gearing becomes an effective entry inducement in their industries, and also that it makes them more subject to regulatory risk. Both of these factors should increase the cost of capital and thus firms have to  balance  two effects of gearing: the cost of capital reducing effects of deterring entry and reducing regulatory opportunism, with the cost of capital increasing efects of higher financial risk.3 

Traditional theories of capital structure have focused on tax shields (Myers, 1984) and broadly defined agency theories (Harris and Raviv, 1991) as the main determinants.   These theories are important, but they are incomplete in that they do not consider the strategic role which capital structure may play - either in an unregulated competitive game or a regulated game as here.4 

In an early contribution to the second of these problems, Spiegel and Spulber (1994) use  a three stage game to model the regulatory context.   In the first stage, a firm chooses capital investment and its financial structure (debt and equity).   The capital market then values the debt and equity in the second stage, and the regulator sets the price at the third and final stage. 

This type of game can be thought of as a game theoretic version of the Averch Johnson effect.   However, in the AJ (Averch & Johnson 1962) effect, firms increase the rate base by over investing, and rates rise as a result. In this game, regulators get a chance to observe investments, and thus may be able to punish the AJ effect after it has occurred.   This possibility of regulatory opportunism may underincentivise investment (the reverse of the AJ effect). 

For this reason, regulators may allow gearing to rise, as a form of implicit commitment not to punish investment, and thus firms may be incentivised to both invest and issue debt for regulatory reasons.   It is still the case that firms may underinvest, since the commitment not to punish investment is a weak one.5 

Where gearing is used in this way, as a commitment, it only works if, in the equilibrium of the game there is a positive possibility of bankruptcy for the firm (which mitigates the AJ effect) and a regulatory price premium due to this.   Thus the costs of regulation can be calculated via the lost welfare, in the form of price above marginal cost, and thus reduced consumer surplus.


2 The model


The regulatory process in price caps and rate bases are similar to each other, and can both be captured by the following description of the sort of game we wish to use. 

2.1 The phenomenon we are modelling: the basic facts of regulation 

The regulated firm files a tariff (a price or set of prices or average price) with the regulator, and the regulators adjust this in line with their own views of what is necessary.   In the US the regulator is a public commission, and its deliberations are transparent.   In the UK the regulator is not a public "court", but a private office.   Nevertheless, when tariffs are adjusted, reasons are given.   The secrecy of the UK system and the inability to challenge the rate ex ante, is a possible weakness indicating a high level of regulatory opportunism compared to the US.   This may or may not increase 'strategic gearing' - one of the aims of this research is to find out if it does. 

In both rate regulation and price cap regulation (e.g. RPI-X) it is ultimately prices that are set by the regulator.   In both cases, the prices that the firm is allowed to set are such that the firms expected revenues equal its expected revenue requirement (ERR).   The latter includes a normal rate of profit, and this in turn depends on an estimate by the regulator of what is the risk adjusted cost of capital that is properly de to the investors in the industry.   This allowed rate of return (ARR) is computed as a percentage of the capital stock - the rate base.   Generally what is allowed in the rate base is closely regulated (to guard against the Averch Johnson effect) both qualitatively and quantitatively.   The return on this allowed rate base is generally a weighted average of the costs of debt and equity, where the weights are the proportions of debt and equity, usually measured at book value. 

The cost of debt is usually taken to be the average interest rate over the whole of the firm's debt.   However, the cost of equity is often more troublesome, especially given the need for an equity risk premium.   Generally this is calculated via the Capital Asset Pricing Model (CAPM) where 

      re = rf + b (rm - rf)

      re = the return on equity

      rf = the risk free rate of return

      rm = the rate of return to a fully diversified portfolio of market stocks

      b = the variability of the share vis a vis the market portfolio, and thus the non-

             diversifiable proportion of the business risk. 

There is an important circularity in evaluating the value of b in a regulated setting.   b determines the re the regulator will use, but also the regulator's likely actions will determine b.6   Thus regulatory activity is endogenous to the model, making us hypothesise that the outcomes of the interaction between the regulator, the firm and the investors are likely to be determined strategically.   Thus the regulator's choice of re will depend upon his assessment of how re will be responded to by the investors and the firm itself.   It is this sort of logic which is at the heart of the model.   Estimates of the cost of equity by investors, depend on their assessments of what the regulator will do in the future, and thus regulator assessments of what investors assess as the cost of equity are determined in part by their own likely actions.   Information asymmetries between regulators (who know quite well what they are likely to do) and investors (who know a great deal less well) are thus a potential source of regulatory failure analogous to market failure.   This indicates that regulation (when opportunistic) is net welfare reducing, and there is a great temptation by the regulator to try to signal a commitment to a future course of action.   One hypothesis, is that allowing changes in the level of gearing is a way of doing this.


2.2  Assumptions


(a) Structure 

The firm is a monopolist in its regulated industry. This assumption is important in that it defines quite sharply the phenomenon under investigation. Specifically the model is looking only at the use of gearing in  relation to the regulator, and thus the model rules out the possibility of entry deterrence in many regulated industries.    The firm produces a single product q with a single price p (ie the price is not a weighted tariff over a range of products, as may be found in many regulated utility industries).    

(b) Demand and Revenue 

The industry (and firm)  demand function is q = Q(p) which is twice differentiable, with Q(p) downward sloping ie Q (p) < 0.


Figure 1: The demand curve for a regulated utility




Where Qp(p) and Qpp(p) represent the first and second derivatives of this function, respectively, and where the strict negativity of the sign on each defines the strict concavity of the function concerned. 

(c) Costs 

The firm's cost function is C(q, z, k) where k is the firm's investment in physical capital, and z is an efficiency parameter representing cost-shifts, which are randomized. 

The firm's operating profits7 are defined as R(p, z, k) where 

      R (p, z, k) � pQ(p) - C(Q(p), z, k)  (1) 

There is a specialist finance literature on the efficient use of debt as a tax shield, much of which is now well known (see for instance Modigliani and Miller (1966) or Brealey and Myers (1991)). The focus of this model is on the use of gearing for regulatory purposes, and any specific treatment of tax would greatly complicate the model without making its results more applicable in the context considered, and for this reason tax effects are not explicitly modelled. Later refinements to the model may allow the treatment of any taxation effects specific to the utility sector (such as putative windfall taxes) but modelling these involves considerable loss of generality if the models are to be of any applied relevance.  

We assume that costs are well behaved, ie C(�) is twice differentiable in all its arguments (q, z, k).

In particular, marginal costs are positive cq > 0, and non decreasing Cqq � 0 where the subscripts denote the partial derivatives.8 

Investment k reduces both total and marginal costs, so Ck < 0 and Cqk <0.

Investment is not treated as a charge against revenues, and hence k has no cost increasing effect.   We also assume that the reduction in total costs is at a decreasing rate from investment, so Ckk > 0.    

(d) Risk 

z is an efficiency parameter, which is a random variable distributed over the unit interval with a probability density function of f(z) and a cumulative density function of F(z) as illustrated in Figure 1.


Figure 2: the Probability distribution of randomized states of nature, captured as an efficiency variable, z


As z increases, efficiency increases, and costs shift downwards.   Thus Cz < 0, Cqz < 0 (ie total and marginal costs fall as z increases). 

Thus, z can best be thought of as a variable which models states of nature.9   Thus when z = 0 we have the worst state of nature, when z = 1 the best. 

(e) Ownership and Agency 

Initially the firm is owned by a set of equity holders, and has no debt.   If the equity holders decide to finance the cost of any new planned investment in physical capital k, by external means, then they will issue a mix of debt and equity to acquire these funds. 

We define a as the amount of new equity as a fraction of the existing value of the firm (its equity).   D is the face value of any bonds which the firm issues.   Thus a = 0.2 implies the firm issues new shares which dilute the existing shareholdings by 20%.   If a<0 the firm is repurchasing shares - which it will do by using a positive amount of debt D. 

Given E is the market value of the new equity (the share price) and B the market value of the debt (the bond price), we define 

      k = E + B  (2) 

as the firm's investment constraint.

The firm can only pay for investment by issuing debt and equity, so k � E + B is an investment constraint, but the constraint binds strictly, since if k<E + B firms are able to attract external finance for no investment purpose.   The regulator is assumed not to allow this.   Thus we have k = E + B as a strict equality.   We allow the firm to choose k and also the mix of a and D provided E(a) and B(D) meet the above constraint. 

The implicit assumption is that the firm is able to issue debt for equity for as long as E+B = k, which means that  E=k-B, and thus whenever shares are purchased, which results in a negative E, then B>k must be the result. All this means is that the regulator allows the firm to alter its own capital structure directly, but constrains the total financing of the firm within an investment cap.


2.3 Modelling bankruptcy risks as a threat


For each debt obligation D, regulated price p and investment level k there is a critical value of the random variable z, ie: a value below which the regulated firm is unable to repay D, its debt.   We call this value z* 

      z* � min {z � 0:R(p, z, k) �D} (3) 

thus z* rises as the level of debt issued by the firm rises. Since z* is a critical value of a randomised variable, this means that the firm increases its risk of bankruptcy if it increases its level of debt. However , whilst D has this direct effect it also has certain indirect effects on the possibility of bankruptcy, since D may be used to increase k, which reduces costs and thus increases R, and D may also impact on prices by encouraging the regulator to include a risk premium in the regulated price. Thus the z distribution is the bankruptcy risk variable and this value is increasing in D, increasing or decreasing in k (since k affects both D and costs) and decreasing in p. 

Where z > z* (ie whenever the observed value of z is greater than the critical value) the firm remains solvent.   This is because R(p, z*, k) = D and with z > z*,  R(p, z, k) > D and thus (R - D) > 0 is the residual paid to new  (where a is greater than zero) and existing equity holders, according to their claims.   These new equity holders will price E (the market value of a) on the basis of calculations they make about R(p, z, k) - D.   They will be able to do this, because in this game they can observe k and D and a after the firm has made its decisions.   However the sequential element of the game  is incorporated in the fact that valuations of R(�) - D can only be made ex ante of the regulators price p*, and that choices of k, a and D by the firm have to be made before either of the other players has  to make their move. 

Thus, equity and debt are both valued on the basis of a jointly determined subgame perfect Nash Equilibrium in this three stage game.   The essential game theoretic characteristic of this model is that the firm, the financial markets, and the regulator all choose their strategies given the optimum strategies of the other players.10

z* is defined as the level of z (the state of nature) above which the firm is able to meet its debt obligations.   Where z < z* limited liability applies for the firm's owners, so when R(p, z, k) < D the firm is transferred to bondholders, who become the residual claimants and the value of E is zero.   Thus F(z*) represents the probability of insolvency, as indicated in Figure 4.2. 

Figure 3: The Critical Value of z = z* 

Figure 4: Increasing z* increases the risk of insolvency 

For instance, in the case above Figure 4.3, the probability of insolvency rises from F(z1)* to F(z2)* as a result of a rise in the critical value z* from z1* to z2*.   This in turn was caused by either a fall in p, a change (rise or fall) in k, or a rise in D.11 

2.3.1  Transactions Costs and Insolvency 

Additional complications arise as a result of the transaction costs of insolvency to the bondholders.   For instance, there are legal fees to be paid, and other transactions costs related to taking ownership of and managing the firm. 

These costs are modelled as a positive function of the shortfall of profits R from debt obligations, D.   Thus, 
H(D - R(p, z, k)) is the transaction cost of insolvency to the bondholders. For all 
D � R (p, z, k) then H = 0, ie for all z > z*, H(�) = 0. 

Bondholders are (like equity holders) protected by limited liability.   If H(�) is greater than the residual value of the business, then they will make a loss by taking over a claim to the residual assets, this occurs whenever 

      H(z) > R(p, z, k) (4) 

In effect bondholders limit their cost of bankruptcy to min {H(z), R(p, z, k)} so that when H(z) < R(p, z, k) and (H(z)> 0) then the firm is taken into administration by the bondholders ; ie: the banks which hold the bonds will appoint an official receiver, whose fees are an important element in H(.).   However, whenever the firm has revenues less than the costs of administration the firm is liquidated.   In effect the bondholders limit their liability by not taking over ownership of the business, but merely allow the business to fold.   The costs of liquidation are in this case exactly equal to the revenues left in the business and the bondholders receive a net payoff of zero. 

We call z** the critical value of z at which R(p, z, k) becomes lower than H(z) and the firm is liquidated12, with R(p, z, k)  not going to bondholders, but being used to defray the costs of liquidation.  Thus the bondholders use their limited liability not to incur the extra transaction costs of taking over control of the firm.  

Thus the ex ante expected value of insolvency costs to the bondholders are:

      T(p, D, k) =  (5)

where the first term on the right is the cost of liquidation, and the second term is the cost of restructuring. 

Note that the possibility of  D>R(p,z,k) is positive in D, negative in p, negative in z (which is stochastic) and ambiguous in k due to first and second order effects being in different directions.   Thus, k reduces costs, and thus increases R(.) but it also reduces p and this has a second order effect of reducing R. The impact of k thus depends on the relative weight of these first and second order effects, and is therefore ambiguous, 

The firm is thus incentivised to increase debt in order raise the risk of bankruptcy, which will extract from the regulator a higher regulated price p*.13


The firm's profit  function net of expected insolvency  costs ( returns due to the investors, both equity and debt)14 is the expected revenues of R(�) net of these expected costs T(�),

ie, P(p, D, k) �  (6)

These profits are the expected returns to both types of investors net of T(�) and they are divided between the two types of investors according to their respective claims.

Note that investment enters the profit function as a positive argument.   Thus the impact of investment (k) is to reduce costs (Ck < 0, Ckk � 0) and thus to increase profits.   The costs of investment are thus not treated as a charge on profits, since the model treats them as a sunk cost, whose value is realised in the revenue they create in the final round of the model, when all profits and costs are realised. If they were treated as a charge against revenues, then the Averch Johnson effect would incentivise firms to extract price increases merely by investing, even without a possibility of bankruptcy.   In effect this means that investment is treated as a sunk cost rather than as an operating expense.



3 Definition of Strategies and Equilibrium

.3.1 Strategies

The game takes place over three stages and is thus a dynamic  game. The model uses the solution concept of subgame perfection. Subgame perfect games are solved by the foldback or backwards induction method, and thus we define the strategies in the last  period of the game first, which is to say we describe the regulator's strategy in setting the price first and then the capital market (investor's) strategies in terms of valuing the debt and the equity. Then we describe the strategies of the regulated firm, which is the firm's optimisation problem, and which precedes  chronologically the other strategies.15 

In the third stage of the game the regulator maximises a welfare function of the form


where CS(p) = is consumer surplus, P is defined as in equation 4.5 above and b is a welfare weight which satisfies 0<b<1.  

The regulator maximises W subject to the constraint that k and D are determined by the firm and thus we have the regulated price as a function of k and D. The properties of the welfare function are determined by  the explicit functional form of W, thus

p*(k, D)  is the regulator's actual strategy choice. 

In the second stage of the game, investors in the firm's debt and equity choose their strategies in terms of pricing debt and equity in the stock and bond markets, that is the markets for equity and debt. The strategies are the choice of the optimal values of B=B*(k,a,D)  and of E=E*( k,a,D). We assume these assets are priced in competitive (efficient) markets and thus prices adjust to achieve the appropriate rate of return on the firm's debt and equity. 

This assumed rate of return is ex ante: it precedes the regulators price and the assumption of the model is that the markets will set their price in a manner consistent with the subgame perfect equilibrium of the game we are modelling. In other words the investors have to think ahead to the sort of prices the regulator will set before they will be able to set their values of B* and E* since p* enters as an argument in each of the functions determining these values. Similarly, the firm has to calculate both the investors' strategies and the regulator's strategies in order to maximise their objective (profit) function. This logic is the essential game theoretic element in the model: that decisions are taken which incorporate beliefs about the equilibrium strategies of the other players.  

The firm makes these choices in the first stage of the game by choosing its vector of strategies, namely investment, k, equity participation (new equity) a; and the face value of its bonds, D.   Thus, the firm's strategic choices are over its inputs, namely investment and financing. 

The firm's objective is to maximise the payoffs to its original investors (ie excluding a) via  


where V(.) is the value function for these payoffs. In the subgame perfect solution to this game the firm chooses k,a and D which are the best response to the strategies of the other players (which are themselves best responses to the firm's strategies). These other strategies are the valuation of the firm's debt and equity by the capital market and the regulator's price, p*. 

Thus the game can be summarised as follows


Table 1: 

Strategies {k*,a*, D*}   {E*(k,a,D), B*(k,a,D)}  {p*(k,D)}

Move order  I              II          III

Player   Firm           Markets                    Regulator 

Where the * variables are the solution values to the game, representing a  unique subgame perfect Nash equilibrium which solves this regulatory problem.   Having briefly outlined the structure of the game we now turn in more detail to a characterisation of the actual choices made by the agents, again in reverse order16.


3.2 Results: The Equilibrium Properties of the Game


3.2.1 The Regulator's Pricing Strategy


We aim to show how the regulator will take into account the firm's capital structure when setting the regulated price p* and, in particular, that higher levels of debt can be used to achieve higher regulated prices.   Effectively this is a problem in information economics, since we are assuming that the regulator is imperfectly informed about the risk of bankruptcy associated with a particular level of debt, and this is because there is asymmetry of information between the regulator and the regulated firm concerning the value of R(p,z,k) =pQ(p)-C(Q(p),z,k).   This asymmetry could be on the cost or the revenue side of the above function but in either case it is what allows the level of capture which is implicit in the model.   Alternatively the asymmetry could be due to the degree to which the regulator is either uncertain of, or certain of but values differently, the risk aversion between the firm and himself.   This work is most closely related to treatment by Baron and Myerson (1982) and Laffont and Tirole (1986) as well as Vickers and Yarrow (1988, Ch 4). 

We assume that the regulator sets a high value on keeping the firm solvent, so high that whatever the debt level, the regulator will set the price at such a level that the firm is able to cover its debt obligations.   Thus given the values of k and D which are observed by the regulator, p* is chosen to maximise W(p,k,D) subject to the constraint that  R(p,0,k) > H(D-R(p*,0,k)).   The implication is that the regulator will set price to prevent liquidation, but a positive risk of administrative receivership will be allowed at very high levels of debt, ie R(p,0,k) < D is entirely possible.   The regulator's problem is thus one of constrained optimisation . 

The regulator's objective is to maximise the following utilitarian welfare function with a social welfare weight, b


W(p,k,D)=CS(p)+b(p,k,D)      (9)

Where CS(p) = Q(p)dp and 0<b<1 

subject to the constraint


R(p,0,k) � H (D-R(p,0,k)) which is the non-liquidation constraint (NLC). 

Thus the regulator chooses p* to optimise the above function given the optimising behaviour of the other agents, and given that k* and D* are chosen by the firm in the first round of the game. 

The first order conditions for maximisation are 

Q (p*)  =  b?p(p*, k, D)  if R(p*, 0, k) > H(�)                                         (10a)

R(p*, 0, k) = H(D-R(p*, 0, k)) otherwise     (10b) 

To interpret these conditions note that the regulator's objective function is

W(p, k, D)  = S (p, k) - bT(p, k, D)      (11) 

Where S(p,k) represents the sum of consumer surplus CS(p) and producer surplus (Economic Rent, R) which is the ex ante weighted R(�). 

Thus, S (p, k)  = CS(p) + bR(p, z, k) dF(z)    (12) 

Giving us 

W(p, k, D)  =  CS(p) + bR(p, z, k) dF(z) - bT(p, k, D)   (13) 

And thus when the NLC is non binding then the first order conditions for p* are 

Sp(p*, k)  =  bTp (p*, k, D)       (14) 

In other words the regulator sets the price to equate the weighted marginal welfare gain (Sp) in terms of producer and consumer surplus to the weighted marginal welfare costs of bankruptcy, bTp.17

Otherwise, the regulator sets the regulated price at the lowest one which will ensure the firm is not liquidated (10a).   The fact that 10a solution equates the expected weighted costs of  bankruptcy, with the expected weighted welfare effect of a price, means that the regulated firm may force the regulator to set prices above marginal costs, ie p*>c.   Thus p*>c is the lower bound on the regulator's price.   The implications of the above equilibrium can be stated in the following propositions.


Proposition 1


The optimal regulated price p* always exceeds expected marginal cost, and at the optimal regulated price, if D>0, F(z*)>0 

In other words, a regulated firm issues debt to earn supernormal profits (p*>c), but the probability of bankruptcy is positive, ie: the regulator does not fully protect the regulated firm, due to the impact of S(p, k) and especially CS(p). 

If the no liquidation constraint is non-binding (ie if R(p, 0, k) > H(D - R(p, 0, k)) so there is no z at which the firm will become insolvent, then the regulator has freedom to set prices, and will set prices which are increasing in the value of b (the welfare weight on profits), thus


Proposition 2


If R(p, 0, k) > H(D - R(p, 0, k))

then    > 0

otherwise   = 0

In other words, the NLC has to strictly bind for the welfare weight to have a net positive impact on price.   We have to deal with the effect of debt on the regulated price at different levels of debt, ie, when issuing the debt would reduce the cost of capital18.   For instance, for UK regulated firms, immediately post-privatization, we would expect that < 0, as debt has a strong second order effect on the cost of capital, which outweighs the first order effect on prices in this model.

This implies


Figure 7






Thus we have the possibility that p* is not monotonic in D, since Debt has an ambiguous impact on the regulated price, dependent on the existing level of Debt.

The ability to raise price due to the effect of leads to proposition 3.


Proposition 3


The  regulated price is less than the unregulated monopoly price, but the Lerner index is positive in equilibrium. 

Thus, the optimal regulated price satisfies 

0<   <  - 


Figure 8




p* lies between pm and Cq





Marginal Cost

Average Revenue


  Marginal Revenue


for all k and D 

Thus we have a Lerner index which is positive (since p*>c) but less than the unregulated monopoly price of     19 

3.2.2 The Capital Market's 'Strategy' 

The capital market clears in Stage II of the game - after the firm has chosen its investment and capital structure.   The market values adjust to give the firm's investors an expected rate of return of l+ i applied to their investments (debt and equity), where i is the market determined cost of capital. 

In equilibrium the investors perfectly anticipate the regulator's optimal pricing strategy, they use it to calculate the revenues it generates, and thus price the firm's securities correctly. 

The firm's equity is thus fixed at 

      E* = E*(k, ?, D) =    (16) 

The RHS of the above expression represents the discounted value (at the relevant rate) of the net revenues of the business in all states where the firm remains solvent. 

Bonds are priced similarly:

B* = B*(k, ?, D) =     (17) 

The first term on the RHS of this expression is the discounted value  of states of nature where bondholders are paid in full.   The last two terms represent the expected value of states of nature when the firm goes bankrupt and the bondholders get the residual claims, net of bankruptcy costs (T). 

In this model, the level of ? has no impact on the price of bonds directly, and thus we are not modelling a standard WACC motivated capital structure where the firm issues debt to achieve an optimum level of gearing via reductions in the costs of capital.   The above capital market equilibrium suggest propositions 4 and 5.


Proposition 4


The effect of k (investment) on the market values of equity (E*) and debt (B*) is ambiguous.20 

Investment reduces costs, and thus has a positive effect on E and B (Direct Effect).

But investment also impacts on the regulated price, and may raise or lower the price set by the regulator (Indirect Effect). 

There is thus a 'minority' case possibility that investment could reduce the value of debt in the market and of equity in the market.


Proposition 5


The Effect of Debt on the Market Values of Equity and Debt is ambiguous. 

The direct effect is due to the increase in the face value of the bonds, and this is positive, given the first term in the above. 

The indirect effect is the impact of debt on the regulated price - when constraint holds.   The indirect effect is always positive: issuing more debt raises the face value of the debt (in the aggregate). 

Thus the net effect of debt is ambiguous, since the direct effect is ambiguous, and the indirect effect generally positive.


3.2.3 The Regulated Firm's Strategy


The firm's equilibrium strategy correctly anticipates the response of the capital market and the regulator - which means that the firm's responses are the best responses to the regulators and the capital market's best responses. 

This means the firm will maximise profits subject to E*, B* and p* and subject to the constraint k = E* + B*. 

This is a requirement that the equilibrium strategy of the firm must also satisfy the equilibrium conditions of the capital market. 

If we add these two equilibria as conditions together, plus the firm's budget constraint k = E + B. 

So, in equilibrium

k* = E* + B*

     +         (18) 

to rearrange for ?*(k,D), we can use (l+i)k= ?E* + B* thus ?E* =(l + i) k - B*

so ?*(k,D) =  

Thus we have


which is the optimum level of new equity the firm issues in equilibrium.




Baron DP (1989):"Design of Regulatory Mechanisms and Institutions" in R Schmalensee and RD Willig (eds) Handbook of Industrial Organisation Amsterdam: North Holland 

Bradley M, Jarrell G A and Kim E H (1984): On the Existence of Optimal Capital Structure Theory and Evidence, Journal of Finance, vol 39(1984)( 857-878 

Brander J A and Lewis T R, (1988): Oligopoly and Financial Structure: the Limited Liability Effect, American Economic Review, vol 776, 956-970 

Brealey R and Myers S (1991): Principles of Corporate Finance, 4/e McGraw Hill, New York, (Chapter 18) 

Harris M and Raviv A (1991): The Theory of Capital Structure, Journal of Finance, vol 46 pp297-355 

Hyman L, Toole, C and Avelis R M (1987): The New Telecommunication Industry: Evolution and Organization, Arlington VA: Public Utilities Reports, lnc 

Miller M H and Modigliani F (1960): Some Estimates of the Cost of Capital in the Electric Utility Industry 1954-1957, American Economic Review 56: 333-391 

Myers (1984): The Capital Structure Puzzle, Journal of Finance, vol 39, 575-592 

Spiegel Y and Spulber D (1994): The Capital Structure of Regulated Firms, Rand Journal of Economics, 25(3) 424-40 

Vickers J, and Yarrow G (1988): 'Privatization: An Economic Analysis', MIT Press, Cambridge, Mass


1 There is a case in the US, where privately financed monopolies have a much longer tradition, and have thus had the time to evolve their 'equilibrium' financial structure.

2 Note the OFFER (1998) and OFWAT interim rate reviews which were used to tighten price caps after firm behaviour (and profits) have been revealed.

3 The aim is to study the evolution of gearing in the UK regional electricity industry as a case study in order to detect the strength or otherwise of these forces.

4 Note:  Brander and Lewis (1986, 1988) on the use of debt as a commitment device in an oligopoly setting.

5 Regulators find it difficult to establish binding, credible commitment not to bow to political pressure to lower rates expost.

6 Stock markets are forward looking.

7 Operating  profits are equivalent to profits before interest and tax( PBIT).  So Interest and dividends are not included: these come later.

8 In general we will use F� and F�� to represent the first and second derivatives of single valued functions, and use Fx,, and Fxx, Fxy to denote the appropriate first and second partials of multi valued functions.

9 Things such as input costs, network breakdowns, the weather.   All important in utility industries.

10 Subgame perfection rules out strategies such as where a player in round 3 (the regulator) pre commits to actions in round 3 which if carried out, could cause the other players in rounds 1 and 2 to alter their strategies..   However, in the subgame beginning at round 3, these are not his best response if they do not in fact alter their strategies in rounds 1 and 2.   The essence of subgame perfection is thus that each player's strategies have to be credible in each subgame - any threat which is not subgame perfect is referred to as cheaptalk, and will be ruled out of the set of solutions to the game where subgame perfection is involved as the solution concept.   The key paper is Selten (1978).

11 Thus we have the strategic (ie game theoretic) use of k and D, by the firm, in order to tighten the insolvency constraint on the regulator, and reduce the regulator's chance of dropping prices.

12 ie, when the bondholders use limited liability and simply liquidate the business without taking ownership.

13 The * superscript refers to the realised (equilibrium) value of the relevant variable, such as p*, a*.

14 Both old and new, equity and bondholders.

15 The logic here is that all players are able to calculate each others strategies (the ability to do this depends on an assumption known as common knowledge rationality or strategic rationality).   Thus they all choose their strategies at the same time, but move at different times.

16 Note also that the regulated price p*(k,D) gives the implied rate of return


which equates the regulatory problem in either a price cap or a rate of return regime.

17 Reassuringly intuitive.

18 Note that if we turn b into a random variable ,  this will allow us to model regulatory uncertainty.

19 Note that ?(p*)  =  - pQ(p)/Q(p)

= - p (dQ/dp)/Q

= = elasticity of demand, absolute value

20 See Section 6.1 about the empirical content of the thesis to address this ambiguity.

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