## _wp07192

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---

### I. Introduction — motivation and core questions
- Composition of sovereign debt and its effect on debt restructuring negotiations is central; renewed focus driven by:
  - IMF policy orientation toward “private sector involvement” (Rey Report, G-10, 1996) and how easily private debt-holders can be induced to agree to restructurings.
  - Recent restructuring episodes (defaults and private litigation) raising concerns that uncoordinated, dispersed creditors cause delays and inefficiencies.
- Conceptual emphasis:
  - Sovereign’s willingness-to-pay problem can make it ex-ante efficient to issue debt that is hard to renegotiate.
  - Paper extends prior work by highlighting lender incentives to protect against selective defaults on subsets of sovereign debt, not just generalized default.

### III. Mechanisms producing excessive “hard-to-restructure” debt
- Individual lender strategies that de facto create seniority or make debts hard to restructure:
  - lifting sovereign immunity,
  - widely dispersing debt and insisting on unanimity for restructuring,
  - lowering maturity,
  - denominating debt in dollars,
  - inserting acceleration clauses.
- Coordination externality: debt instruments that are hard to restructure can crowd out renegotiation-friendly debt (a Gresham-law–type effect), producing equilibria with excessively hard-to-restructure debt relative to ex-ante welfare.
- Burglary-alarm analogy: individually optimal protections can be collectively inefficient.

### Evidence on selective defaults (stylized facts)
- Sovereigns treat different classes of debt differently in defaults, creating implicit seniority.
- Examples over 25 years: Brady plan, Russia, Ukraine, Pakistan, Ecuador, Uruguay.
- Shift from syndicated bank loans toward bond finance in the 1990s; market perception that syndicated bank loans were easier to restructure.
- Empirical fact preserved from source: 93 sovereigns defaulted on syndicated bank loans since 1975; 20 had bonds outstanding while bank loans were in default, but only 9 of these 20 also defaulted on bonds (Standard and Poor’s, 2003).

### Model setup and assumptions
- Two-period small open economy; representative resident utility U = U(g) + V(c).
- Public expenditure g financed entirely by borrowing in period 1; assume 0 < g < E[y].
- Period-2 endowment y stochastic with pdf f(.) over support [0, ȳ], ȳ < ∞.
- Continuum of atomistic lenders, each can lend g; sovereign borrows from subset of mass 1 (total mass 1 + φ with 0 < φ small).
- Lenders choose debt type: renegotiable r or non-renegotiable n, and requested period-2 repayment d_i.
- Default cost modeled as proportional output loss γ y with γ = 1 (creditors can destroy all resources of a defaulting sovereign).
- Renegotiable debt can be renegotiated at no cost; non-renegotiable debt cannot be renegotiated.

### Repayment game and selective default conditions
- Notation: rD and nD denote total repayments to r-creditors and n-creditors respectively (rN and nN are masses with symmetric bids d_r and d_n).
- Sovereign fully defaults only if nD > y.
- In selective default, r-creditors receive fraction ω ∈ [0,1] of net surplus from renegotiation (nD − y) net after repayment of n-creditors.
- Sovereign chooses selective default over full repayment if rD + ω < y + nD (algebraic inequality preserved).
- Proposition 1 (ex post repayment strategy):
  - (i) if rD ≥ nD + y ω, sovereign fully repays both debt types;
  - (ii) if nD < rD < nD + y ω, sovereign repays n-creditors and renegotiates r-creditors down to nD − y ω;
  - (iii) if nD < y, sovereign defaults on both types of debt.

### Social planner benchmark (optimal debt structure)
- Lenders’ participation constraint: V_rn(d_r, d_n) ≥ g, where V is lenders’ total expected payoff (functional form preserved as in source).
- Sovereign (planner) welfare: U = E[y] − V_rn(d_r, d_n) − L_n(D_n), with L_n expected deadweight loss from full default.
- Deadweight loss can be reduced to zero only if D_n = 0 (no non-renegotiable debt), given output realizations can be arbitrarily small.
- Define ω* ≡ g/E[y]. If ω ≥ ω*, sovereign can finance g entirely with renegotiable debt (D_n = 0).
- Optimal D_n decreases with ω; limit case ω = 0 → sovereign must finance g entirely with non-renegotiable debt.
- Proposition 2:
  - Existence of threshold ω* = g/E[y] such that:
    - if ω < ω*, fraction of debt is non-renegotiable, decreasing in ω;
    - if ω ≥ ω*, debt is entirely renegotiable.

### Laissez-faire lending game — equilibrium characterization
- Market prices per dollar of promised repayment: P_r and P_n (equations (4) and (5) in source).
- Non-renegotiable debt is worth more on the dollar than renegotiable debt.
- In any Nash equilibrium lenders break even: V_r N_r = V_n N_n = g.
- Lemma 1: interior equilibria with both debt types (D_r > 0 and D_n > 0) cannot exist; only corner equilibria possible (all r-debt or all n-debt).
- Lemma 2 (existence conditions for corner equilibria):
  - Corner equilibrium with non-renegotiable debt exists only if ω ≥ 1/2.
  - Corner equilibrium with renegotiable debt exists only if ω ∈ [ω*, Ω] for some Ω with ω* < Ω < 1.
- Intuition: lenders may deviate from r to n if the positive private benefit from making their claim harder to restructure outweighs the negative externality they impose on r-debt prices; this trade-off depends on ω.
- Proposition 3 (Nash equilibrium characterization):
  - Corner equilibrium with n-debt iff ω ∈ [1/2, 1].
  - Corner equilibrium with r-debt iff ω ∈ [ω*, Ω].
  - If Ω > 1/2 and ω ∈ [max(1/2, ω*), Ω], two Pareto-ranked corner equilibria exist: inefficient n-debt equilibrium and efficient r-debt equilibrium.
- Proposition 4 (Gresham law for sovereign debt): socially optimal amount of n-debt ≤ amount of n-debt issued in Nash equilibrium for all ω (i.e., n-debt tends to be excessive).

### Calibration and numerical example from text
- Model specification used in figure: y ~ Uniform[0,2] and g = 0.4.
- For this specification: ω* = 0.4 and Ω = 0.625 (values preserved).
- Market-failure and multiplicity regions illustrated: "pure n-debt" and "pure r-debt" regimes plotted against ω.

### Additional technical results (threshold and monotonicity)
- There exists a threshold ω* ∈ [,1] (notation preserved) such that h(ω) is negative iff ω ≤ ω*.
- The equilibrium level of rD is implicitly defined by lenders' budget constraint (equation (11) in source).
- Differentiation steps in source show m(ω) decreasing in ω and imply the threshold properties used to establish existence of corner equilibria.
- Corner equilibrium with n-debt requires 1/2 < ω (derivation preserved).

### Public policy implications and recommendations (Section VI)
- No universal welfare-improving policy; effects depend critically on lenders’ bargaining power ω.
- Collective action clauses (CACs) interpreted as a move toward r-debt:
  - Voluntary CAC adoption may be welfare-improving when multiple equilibria exist (mild public pressure can shift selection from the n-debt corner to the r-debt corner).
  - Purely voluntary CAC adoption unlikely to work in other parameter regions.
- Sovereign bankruptcy regime:
  - May be necessary to facilitate renegotiations when voluntary contractual approaches fail.
  - Costs depend on ω:
    - If a regime makes all debt renegotiable and ω ∈ [1/2, ω*], sovereign may be credit-rationed (unable to issue n-debt and unable to borrow), reproducing Dooley (2000) and Shleifer (2003) concerns.
    - The regime is strictly beneficial only under conditions relating ω and ω* (text preserves conditional inequalities).
- Two policy reconciliations to ensure welfare improvement:
  - Ensure lenders have sufficient bargaining power within bankruptcy regime (guarantee ω ≥ ω*).
  - Allow issuers to opt out ex-ante from the bankruptcy procedure (sovereigns can choose whether to allow n-debt); this ex-ante opt-out ensures intervention is welfare-improving.
- Proposition 5 (optimal policy): A bankruptcy regime that makes sovereign debt renegotiable is optimal iff either:
  1) The regime guarantees lenders bargaining power such that ω ≥ ω*, or
  2) The regime allows the sovereign to opt out ex ante.
- Caution: model assumes g fixed and known; relaxing this introduces dilution risk that can make early lenders prefer n-debt. An efficient bankruptcy regime must address seniority/absolute-priority when borrowing amount is not fixed.

### Conclusion and extensions (Section VII)
- Endogeneity of debt structure matters: ex ante incentives can lead to excessive non-renegotiable debt even when orderly ex post workouts are socially desirable.
- Laissez-faire can produce excessive difficulty of restructuring; public intervention may be warranted but must be conditional on lenders’ bargaining power and institutional design.
- Noted extensions:
  - Debt maturity matters: short-term debt may deflect selective defaults but increases rollover crisis risk (Jeanne, 2004; Bolton and Jeanne (2005)).
  - Political agency problems could reverse welfare implications; under domestic policymaker self-interest, rationing may improve domestic welfare.

*Source: _wp07192 (extracted content).*

### References..............................................................................................................

### I.   INTRODUCTION

### Motivation and central questions
- The composition of sovereign debt and how it affects debt restructuring negotiations in the event of financial distress has become a central policy issue in recent years.
- Two major reasons for renewed focus:
  - The change in the IMF's policy orientation towards sovereign debt crises, with a proposed greater weight on “private sector involvement” (Rey Report, G-10, 1996), raising the question of how easy it is to get private debt-holders to agree to a debt restructuring.
  - Recent debt restructuring episodes—including defaults and private litigation—have raised concerns that uncoordinated efforts of dispersed debt-holders to renegotiate sovereign obligations lead to substantial delays and inefficiencies.

### Key conceptual points on debt structure and incentives
- Prior literature (Dooley, 2000; Shleifer, 2003) argues that because of the sovereign’s incentive to repudiate its debts (the willingness-to-pay problem), it may be ex-ante efficient to structure sovereign debt to make it difficult to renegotiate ex-post.
- Debt that is harder to restructure can serve as commitment device reducing repudiation risk, but policies that reduce restructuring costs could undermine ex-ante efficiency by raising sovereigns’ borrowing costs and reducing lending to emerging markets.
- The paper extends this view by emphasizing not only protection against generalized default but also lenders’ desire to protect themselves against selective defaults on subsets of sovereign debts.

### Mechanisms producing excessive “hard-to-restructure” debt
- Individual lenders can create de facto seniority for their claims by making debts more difficult to restructure, for example by:
  - lifting sovereign immunity,
  - widely dispersing the debt and insisting on unanimity for restructuring,
  - lowering maturity,
  - denominating debt in dollars,
  - inserting acceleration clauses.
- A coordination externality—analogous to a Gresham law—may occur: debt structures that are hard to restructure crowd out more renegotiation-friendly debt, producing an equilibrium with excessively hard-to-restructure debt even from an ex-ante welfare perspective.
- The burglary-alarm analogy: individually optimal protections (making debts hard to restructure) can be collectively inefficient.

### Policy implications and role for intervention
- There is a potential role for policy intervention to improve both ex-ante and ex-post efficiency by facilitating restructuring of hard debt.
- A bankruptcy regime for sovereigns could mitigate inefficiencies arising from competition between lenders to deflect selective default.
- However, interventions (e.g., mandating or subsidizing collective action clauses, or a bankruptcy regime) may be welfare-reducing if they give lenders too little bargaining power in renegotiations; careful design is required.

### Assessment of contractual approaches and CACs
- The contractual approach endorsed by the G-10—moral suasion to encourage majority-rule clauses for bond restructuring (collective action clauses, CACs)—is shown not to work in the authors’ model.
- Leaving sovereigns free to choose whether to include renegotiation-friendly clauses leads to inefficiently low adoption in equilibrium.
- Policies encouraging adoption of such clauses via taxes, subsidies, arm-twisting, or mandatory rules could achieve effects similar to a sovereign bankruptcy regime.

### Contributions to literature and paper structure
- The paper contributes to literature on sovereign debt default and restructuring by systematically exploring implications of selective default on sovereign debt structure—an issue noted but not previously explored systematically.
- Related works cited include Dooley (2000), Kenen (2001), Tirole (2002, chapter 4), and corporate finance literature on hard-to-renegotiate debt (Hart and Moore, 1995; Dewatripont and Maskin, 1995; Bolton and Scharfstein, 1996; Diamond and Rajan, 2001; Diamond, 2004).
- Organization: Section II reviews stylized facts on sovereign debt motivating the theoretical analysis; Section III lays out the model and assumptions; Section IV characterizes the socially efficient debt structure.

*Source: _wp07192 - References..............................................................................................................*

### Section V analyzes equilibrium debt structures. Section VI discusses public policy

### _wp07192 - Section V analyzes equilibrium debt structures. Section VI discusses public policy

### Evidence on selective defaults
- Sovereigns treat different classes of debt differently in defaults, generating an implicit seniority between debt classes.
- Differential treatment observed in restructurings over the last 25 years (Brady plan, Russia, Ukraine, Pakistan, Ecuador, Uruguay).
- Shift over two decades from syndicated bank loans toward bond finance; one reason: perception that syndicated bank loans were easier to restructure.
- Market observations: bonds regarded as harder to restructure because they typically involve many more investors and may be in bearer form.
- Empirical fact: 93 sovereigns defaulted on syndicated bank loans since 1975; 20 had bonds outstanding while bank loans were in default, but only 9 of these 20 also defaulted on bonds (Standard and Poor’s, 2003).
- Stylized facts to capture in theory:
  - Sovereigns do not default in the same way on different debt instruments; selectivity creates implicit seniority.
  - Seniority relates to structural features that affect ease of renegotiation.
  - International investors are aware and monitor determinants of implicit seniority.
  - Composition of international sovereign debt shifted toward instruments perceived as senior during the 1990s.

### Model: assumptions and setup
- Two-period small open economy; representative resident with utility U = U(g) + V(c) (notation preserved from source).
- Public expenditure g financed entirely by borrowing in period 1; assume 0 < g < E[y] where E[y] denotes expected endowment in period 2.
- Endowment y in period 2 is stochastic with pdf f(.) over support [0, ȳ], ȳ < ∞.
- Continuum of atomistic lenders; each can lend g; sovereign borrows from subset of mass 1 (total mass 1 + φ with 0 < φ small).
- Lenders bid in a common-agency bidding game; lenders choose type of debt (renegotiable r or non-renegotiable n) and requested period-2 repayment d_i.
- At end of bidding, sovereign faces r-creditors (renegotiable) and n-creditors (non-renegotiable).
- Default cost modeled as proportional output loss γ y; set γ = 1 for simplicity (creditors can destroy all resources of a defaulting sovereign).
- Assumption: renegotiable debt can be renegotiated at no cost; non-renegotiable debt impossible to renegotiate (e.g., bonds widely dispersed requiring unanimity).

### Repayment game and selective default conditions
- Notation: rN and nN are masses of r-creditors and n-creditors; symmetric bids d_r and d_n; total repayments D = d_r N_r + d_n N_n.
- Sovereign fully defaults only if nD > y (cannot repay n-creditors).
- In selective default, r-creditors receive fraction ω ∈ [0,1] of net surplus from renegotiation (nD − y) net after repayment of n-creditors.
- Sovereign chooses selective default over full repayment if rD + ω < y + nD (preserved algebraic inequality ordering as in source).
- Payoff summary (as in source table): outcomes and payoffs for Full Default, Selective Default, Full Repayment (notation preserved).
- Proposition 1 (ex post repayment strategy):
  - (i) if rD ≥ nD + y ω, sovereign fully repays both debt types;
  - (ii) if nD < rD < nD + y ω, sovereign repays n-creditors and renegotiates r-creditors down to nD − y ω;
  - (iii) if nD < y, sovereign defaults on both types of debt.

### Optimal debt structure (social planner benchmark)
- Lenders’ participation constraint: V_rn(d_r, d_n) ≥ g, where V is lenders’ total expected payoff defined by equation (2) (preserve functional form).
- Sovereign (planner) welfare: U = E[y] − V_rn(d_r, d_n) − L_n(D_n), where L_n is expected deadweight loss from full default (equation (3)).
- Objective: minimize expected deadweight loss subject to lenders’ participation constraint.
- Deadweight loss reduced to zero iff D_n = 0 (no non-renegotiable debt), given assumption that output realizations can be arbitrarily small.
- For given D_n, maximal pledgeable output when D_n + ω D_r = ȳ? (preserved relation: nD + ω rD = y) and maximum pledgeable output given by integral expression in source.
- Define ω* ≡ g/E[y]. If ω ≥ ω*, sovereign can finance g entirely with renegotiable debt (D_n = 0).
- Optimal D_n decreases with ω; in limit ω = 0 sovereign must finance g entirely with non-renegotiable debt.
- Proposition 2:
  - Existence of threshold ω* = g/E[y] such that:
    - if ω < ω*, fraction of debt is non-renegotiable, decreasing in ω;
    - if ω ≥ ω*, debt is entirely renegotiable.

### Equilibrium debt structure (laissez-faire lending game)
- Market prices: P_r and P_n are market prices (dollar values) per dollar of promised repayment for r-debt and n-debt (equations (4) and (5) preserved).
- Non-renegotiable debt is worth more on the dollar than renegotiable debt (inequality preserved in text).
- In any Nash equilibrium lenders break even: V_r N_r = V_n N_n = g (market clearing with excess supply of lenders).
- Characterization of equilibria:
  - Interior equilibria with both types of debt (D_r > 0 and D_n > 0) cannot exist (Lemma 1).
  - Only corner equilibria possible: either all renegotiable (D_n = 0) or all non-renegotiable (D_r = 0).
- Lemma 2 (existence conditions for corner equilibria):
  - Corner equilibrium with non-renegotiable debt exists only if ω ≥ 1/2.
  - Corner equilibrium with renegotiable debt exists only if ω ∈ [ω*, Ω] for some Ω with ω* < Ω < 1.
- Intuition: Individual lenders may profitably deviate from r to n when the negative externality on r-debt price (via higher selective-default risk) dominates the positive externality from reducing outstanding r-D; this depends on ω.
- Proposition 3 (Nash equilibrium characterization):
  - Corner equilibrium with n-debt iff ω ∈ [1/2, 1].
  - Corner equilibrium with r-debt iff ω ∈ [ω*, Ω].
  - If Ω > 1/2 and ω ∈ [max(1/2, ω*), Ω], two Pareto-ranked corner equilibria exist: inefficient n-debt equilibrium and efficient r-debt equilibrium.
- Calibration example in text: with y ~ Uniform[0,2] and g = 0.4 implies ω* = 0.4 and Ω = 0.625 (values preserved).
- Market failure possibilities:
  - If ω outside [Ω, ω*] laissez-faire equilibrium can be inefficient.
  - Market breakdown if 1/2 min(ω*, 1/2) condition violated: when 1/2 min{,}ω ω* < (text phrasing preserved), sovereign cannot raise financing g in laissez-faire.
- Proposition 4 (Gresham law for sovereign debt): socially optimal amount of n-debt ≤ amount of n-debt issued in Nash equilibrium for all ω (i.e., n-debt tends to be excessive).

### Public policy implications (Section VI)
- No simple universal welfare-improving policy due to complex effects of lenders’ bargaining power ω.
- Collective action clauses (CACs) interpreted as shift toward r-debt; voluntary adoption may be welfare-improving only when multiple equilibria exist (mild public pressure can facilitate equilibrium selection from n-debt corner to r-debt corner).
- Purely voluntary CAC adoption unlikely to work in other situations; a bankruptcy regime for sovereigns may be necessary to facilitate renegotiations.
- Costs of making all debt renegotiable (bankruptcy regime) depend on ω:
  - If the regime makes all debt renegotiable and ω ∈ [1/2, ω*], sovereign may be credit rationed (unable to issue n-debt and unable to borrow), reproducing concerns of Dooley (2000) and Shleifer (2003).
  - Bankruptcy regime is strictly beneficial only if ω > 1/2 max(ω*, 1/2)? (preserve textual condition as in source): regime benefits when 1/2 max( , ) ω ω* > (text condition preserved as in source).
- Two policy reconciliations suggested:
  - Ensure lenders have sufficient bargaining power within a bankruptcy regime.
  - Allow issuers to opt out ex-ante from the bankruptcy procedure (i.e., sovereigns can choose whether to allow n-debt), which guarantees policy intervention is welfare-improving.
- Proposition 5 (optimal policy): A bankruptcy regime that makes sovereign debt renegotiable is optimal iff either:
  1) The regime guarantees lenders bargaining power such that ω ≥ ω*, or
  2) The regime allows the sovereign to opt out ex ante.
- Cautionary note: model assumes g fixed and known; removing commitment on g introduces dilution risk that can make early lenders prefer n-debt; an efficient bankruptcy regime must establish seniority or absolute priority rule when borrowing amount is not fixed (Bolton and Jeanne (2005) referenced).

### Conclusion (Section VII)
- Endogeneity of debt structure matters; ex ante incentives can lead to debt structures with excessive non-renegotiable debt even though ex post coordination and orderly workouts are desirable.
- Laissez-faire can produce excessive difficulty of restructuring; public intervention can be warranted but is conditional on lenders’ bargaining power and institutional design.
- Extensions noted:
  - Debt maturity matters: short-term debt can deflect selective defaults but increases rollover crisis risk (Jeanne, 2004; Bolton and Jeanne (2005) examined).
  - Political agency problems (domestic policymakers not benevolent) could reverse welfare implications; rationing may improve domestic welfare under self-interested policymakers.

*Source: _wp07192 - Section V analyzes equilibrium debt structures. Section VI discusses public policy (extracted content).*

### 6. We show that there

### _wp07192 - 6. We show that there

### Threshold existence and monotonicity of h(·)
- There exists a threshold  [,1]ωω ∗ ∈ such that    (   )hω is negative if and only i  ωω≤.
- To establish that a threshold  [,1]ωω ∗ ∈ exists we must show first that    ( )h⋅ is an increasing function in ω.
- The equilibrium level of rD is a function of ω implicitly defined by the lenders' budget constraint:
  - 0
    ()() .
    r
    r
    D
    y
    D
    r
    gyfydyDfydy
    ω
    ω
    ω
    =
    +
    ∫∫
    (equation (11))
- Dividing this equation by ω gives:
  - ()
    0()
    ()( )()  ,
    my
    m
    g
    yf   y  dy    mf   y  dy
    ω
    ω
    ω
    ω
    =
    +
    ∫∫
  - where () r D m ω ω = .
- Differentiating this expression with respect to ω we see that () 0mω ′ <.
- Using () r D r g D m ω ω < ≤ =, it follows that ()()(() ) 0. h m g m ω ω ω ′′ = − >
- The existence of  [,1]ωω ∗ ∈ then follows from the facts that    ()    0hω ∗ < and    (1)    0h >.
  - To establish the first inequality note that since () m y ω ∗ =, we have    ()(  )    0h g E y ω ∗ = −  <.
  - The second inequality follows from equation (11), which for 1 ω = reduces to:
    - 0
      (1) ( )()(  )()0.
      r
      r
      D y
      r
      D
      hg   y f ydyD   gf ydy
      = −   = − >
      ∫∫

### Corner equilibrium with r-debt (r-debt only)
- Since r dP must be positive in a corner equilibrium with r-debt, it follows that such an equilibrium exists if and only if  ω ω ≤, as stated in the Proposition.

### Corner equilibrium with n-debt (n-debt only)
- Let nP and nD respectively denote the price and quantity of n-debt in this equilibrium.
- Replace an infinitesimal amount of n-debt, n dD, by an infinitesimal amount of r-debt, r dD. The price of the new r-debt is equal to nP to a first-order of approximation (since selective default occurs with an infinitesimal probability).
- Differentiating (4) and using (6) and nr PP =, we have:
  - 23
    2
    11
    () ()()    .
    rr
    nn
    nn
    dDdD
    DD
    r
    n
    DD
    rrr
    dP
    yD  f ydyf ydy
    dDdDdD
    ω ω
    ω
    ++
    ⎛⎞
    = − − −
    ⎜⎟
    ⎝⎠
    ∫∫
- Using L'Hospital rule we can show that
  - 0
    22
    0
    ()
    1
    lim(  ) and
    ()
    1
    lim()   (  ),
    2
    r
    n
    n
    r
    r
    n
    n
    r
    dD
    D
    n
    D
    dD
    r
    dD
    D
    n
    n
    D
    dD
    r
    fD
    fydy
    dD
    fD
    yDfydy
    dD
    ω
    ω
    ω
    ω
    +
    →
    +
    →
    =
    − =
    ∫
    ∫
- from which it follows that
  - 0
    1
    lim()1  .
    2
    r
    r
    n
    dD
    r
    dP
    fD
    dD
    ω
    →
    ⎛⎞
    = − −
    ⎜⎟
    ⎝⎠
- This limit is positive (as it must be if n-debt is a corner equilibrium) if and only if 1/ 2. ω >

### Figure 1: model specification and parameter values
- The figure is based on the following specification of the model: y is uniformly distributed in [0,2] and g = 0.4.
- The figure shows "Share of n-debt : optimum" and "Share of n-debt: laissez-faire" plotted against omega with multiplicity regions labeled "pure n-debt" and "pure r-debt".

*Source: _wp07192 - 6. We show that there*

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