Laws and Norms: Bénabou & Tirole (2025)

What this is. The paper’s core propositions, the image-concern model with its equations, and the signaling-game analysis of expressive law: enough to understand what it proved and how, without reading all 42 pages. To extend or replicate the formal results, read the original at doi.org/10.1086/738343.

TL;DR

Bénabou and Tirole (2006a) introduced the image-concern model; this paper completes that program by deriving optimal taxation and the expressive role of law. A continuum of agents with heterogeneous intrinsic motivation v choose a prosocial action, earn reputational returns from peers who infer their type from their choice (honor if they act, stigma if they do not), and respond to material incentives y set by a principal. Under symmetric information, the optimal first-best incentive departs from the standard Pigouvian subsidy by subtracting the reputational rent that the marginal contributor extracts, and is hump-shaped in society’s overall prosociality and in the compliance cost: norms substitute for incentives at both extremes of compliance. Under asymmetric information, where the principal knows the social environment θ but agents do not, the law becomes expressive. The principal uses her choice of y to signal θ, leading to softer law when she wants to signal norm strength, and tougher law when she signals the magnitude of the social externality. Extensions cover societies’ resistance to economists’ prescriptions (“commodification”), zero-tolerance policies, broken-windows theory, norm-based interventions, and the avoidance of cruel punishments.

Core results

All locators refer to the version with DOI 10.1086/738343 (HAL preprint hal-05577272, 35 pp.).

#	Result	Locator	Content as stated
R1	First-best optimal incentive subtracts the reputational rent from the standard Pigouvian subsidy	Prop. 1(i), eq. (14), p. 14	$y^{FB}_\theta = \epsilon_\theta - \Delta_\theta\!\left(\tfrac{c_\theta - \epsilon_\theta}{e_\theta}\right)$; the second term is the reputational rent extracted by the marginal contributor
R2	Second-best optimal incentive is always strictly below the first-best and decreases with the shadow cost of funds	Prop. 1(ii), eq. (15), p. 14	$y^{SI}_\theta < y^{FB}_\theta$ for all λ > 0; prosocial behavior is always underprovided; social multiplier amplifies but does not fully replace y
R3	Optimal incentive is hump-shaped (bell-shaped) in the overall prosociality of society θ and in the compliance cost c	Prop. 2, Fig. 2, pp. 14-15	When f_θ is strictly unimodal, y^{FB}_θ is single-peaked at θ₀ = (c − ε)/e; high prosociality (respectable act) and low prosociality (admirable act) both reduce the optimal incentive relative to the modal case
R4	Soft law results when the principal’s private information (M⁺, P⁻) or (M⁻, P⁺); tough law when (M⁺, P⁺) or (M⁻, P⁻)	Prop. 5, Fig. 3, pp. 20-21	y^{AI}_θ < y^{SI}_θ on the off-diagonal of Table 1; y^{AI}_θ > y^{SI}_θ on the diagonal; always underprovision of prosocial behavior
R5	A separating equilibrium (expressive law) exists when θ shifts societal values with a norm, operates a right truncation, affects the externality ε, or affects compliance cost under an anti-norm	Prop. 7, p. 22	SOC₁ and SOC₂ hold strictly; existence is proved in the Online Appendix for cases (a)-(d)
R6	Full pooling can prevail when θ indexes social monitoring intensity or performs a left truncation; no separating equilibrium exists when θ is a distributional-shift parameter under an anti-norm or a cost parameter under a norm	Props. 8-9, p. 23	Prop. 8: A = B = 0 when θ = μ (social monitoring) or θ is a left-truncation parameter. A full-pooling equilibrium exists and is preferred to any other equilibrium by all principal types in the social-vigilance case, and in the left-truncation case when F(v) is uniform. Prop. 9: A < 0 under a distributional shift with an anti-norm (Δ’ > 0) or cost uncertainty with a norm (Δ’ < 0), ruling out separation
R7	A principal with private information about θ selectively discloses: reveals good news, withholds bad; in any stable equilibrium more disclosure occurs when the probability of obtaining information is higher	Prop. 10, p. 24	Disclosure iff θ ≥ θ̃ (under M⁺) or θ ≤ θ̃ (under M⁻); in any stable equilibrium, threshold θ̃ decreases as the probability q of observing θ rises
R8	Commodification spillovers make soft law optimal when strong incentives on a formally-controlled activity would signal low prosociality and erode the norm in a non-incentivized activity	Prop. 11, p. 27	For λ small enough, the high-type principal sets y^{AI}{θ_H} < y^{SI}{θ_H}; the least-cost separating equilibrium is D1-robust
R9	The shape of the preference distribution determines whether reputational pressure creates norms or anti-norms	Lemma 1(ii)-(iv), p. 9	If f_θ is unimodal, Δ_θ is strictly quasi-convex and has an interior minimum when endpoint densities are sufficiently small; if f_θ is U-shaped, Δ_θ is strictly quasi-concave and has an interior maximum when endpoint densities are sufficiently large
R10	Costless incentives preserve first-best policy under private information when the policy is monotonic	Prop. 3, p. 19	For λ = 0, monotonic y^{FB}_θ remains an asymmetric-information equilibrium; if neither P+ nor P- holds, an announcement of θ with y = y^{FB}_θ implements the first best
R11	With costly incentives, the asymmetric-information first-order condition has a unique boundary-undistorted, comonotonic solution	Prop. 4, p. 20	For λ > 0 small enough, under P+ or P- for the symmetric-information incentive, (19) has a unique y^{AI}_θ satisfying NDB and (y^{AI}_θ)‘(y^{SI}_θ)’ > 0
R12	Separating equilibrium requires on-path incentive compatibility and an endpoint single-crossing condition	Prop. 6, p. 22	SOC₁ at θ̂ = θ is necessary; SOC₁ for all θ̂, θ plus SOC₂ at θ̂ ∈ {θ₁, θ₂} for all y is sufficient

Overall. Optimal policy corrects the Pigouvian subsidy in two directions: subtract the reputational rent (norms already motivate, so over-incentivizing is wasteful and crowds out esteem), and use the signal sent by incentive choice itself to harness agents’ intrinsic motivation and image concerns. The expressive content of law is soft when signaling social norms and tough when signaling social costs.

Theory / model

The core model (Section II, pp. 6-9) has a continuum of agents of mass 1, each choosing a ∈ {0,1}. Choosing a = 1 costs c_θ, creates externality ε_θ, and earns a material incentive y from the principal. Agent types v are private information, distributed with continuous density f_θ(v) > 0 on V_θ = [v^min_θ, v^max_θ]. Intrinsic motivation for compliance is e_θ ≡ γε_θ + 1 − γ, capturing both consequentialist concern (weight γ on externalities) and warm glow. The utility function (eq. 1, p. 6) is:

$$U = (ve_\theta - c_\theta + y)\,a + \epsilon_\theta\,\bar{a}_\theta + \mu_\theta\!\left(E_\theta[\tilde{v} \mid a, y] - \bar{v}_\theta\right). \tag{1}$$

Here ā_θ is aggregate participation, μ_θ is the weight on reputational concerns, and $E_\theta[\tilde{v} \mid a, y]$ is others’ posterior mean belief about the agent’s type. The third term captures image concerns: the agent values being perceived as high-v by peers (or, via self-signaling, by himself). Reputation is a positional good.

The two conditional moments that generate honor and stigma (eqs. 2-3, pp. 7-8) are:

$$E^+_\theta(v) = E_\theta[\tilde{v} \mid \tilde{v} \geq v], \quad E^-_\theta(v) = E_\theta[\tilde{v} \mid \tilde{v} < v], \tag{2}$$ $$\Delta_\theta(v^*) \equiv \mu_\theta\!\left[E^+_\theta(v^*) - E^-_\theta(v^*)\right]. \tag{3}$$

$E^+_\theta(v^*)$ is the honor conferred on those who contribute when v* is the cutoff, and $E^-_\theta(v^*)$ is the stigma borne by abstainers. An agent chooses a = 1 iff $ve_\theta \geq c_\theta - y - \Delta_\theta(v^*)$, so the equilibrium cutoff $v^*_\theta(y)$ satisfies (eq. 4, p. 8):

$$v^*_\theta(y)\,e_\theta - c_\theta + y + \Delta_\theta(v^*_\theta(y)) = 0. \tag{4}$$

Average utility integrates intrinsic motivation, the private cost and incentive, plus the externality from aggregate participation (equation 5, p. 8):

$$\bar{U}_\theta = \int_{v^*_\theta(y)}^{+\infty} (v e_\theta - c_\theta + y)\,dF_\theta(v) + \epsilon_\theta \bar{a}_\theta = \int_{v^*_\theta(y)}^{+\infty} (v e_\theta + \epsilon_\theta - c_\theta + y)\,dF_\theta(v). \tag{5}$$

The non-extrinsic motivation at a candidate cutoff is (equation 7, p. 10):

$$m_\theta(v,v^*) \equiv v e_\theta - c_\theta + \Delta_\theta(v^*). \tag{7}$$

Differentiating the equilibrium cutoff with respect to the environment parameter gives (equation 8, p. 10):

$$\frac{\partial v^*_\theta(y)}{\partial \theta} = -\frac{v^*_\theta(y)\gamma\frac{\partial \epsilon_\theta}{\partial \theta} - \frac{\partial c_\theta}{\partial \theta} + \frac{\partial \Delta_\theta}{\partial \theta}(v^*_\theta(y))}{e_\theta + \Delta'_\theta(v^*_\theta(y))}. \tag{8}$$

For a uniform shift in societal preferences, equation 9 states the equivalence between a shift in θ and an incentive increase of θe:

$$v^*_\theta(y) - \theta = v^*_0(y + \theta e) \quad \text{for all } (y,\theta). \tag{9}$$

Lemma 1 (attributed to Jewitt; Harbaugh and Rasmusen; Adriani and Sonderegger; p. 9) characterizes Δ_θ: when f_θ is unimodal, Δ_θ is strictly quasi-convex. The equilibrium then exhibits a norm (strategic complements, Δ’_θ < 0) for respectable behaviors and an anti-norm (strategic substitutes, Δ’_θ > 0) for admirable, rare behaviors. Multiple equilibria can arise when complementarity is strong; uniqueness is ensured by $e_\theta + \Delta'_\theta(v) > 0$ for all v. The social multiplier (eq. 6, p. 8),

$$s_\theta(y) \equiv -\frac{\partial v^*_\theta}{\partial y} = \frac{1}{e_\theta + \Delta'_\theta(v^*_\theta(y))}, \tag{6}$$

amplifies the compliance response to a unit increase in y through the reputational feedback. It exceeds $1/e_\theta$ for respectable (norm-driven) behaviors and falls below $1/e_\theta$ for admirable ones.

Under asymmetric information (Sections IV-VI), θ ∈ [θ₁, θ₂] is privately known to the principal. Agents infer θ from y and form long-run reputations. The informational multiplier (Section IV.B, pp. 18-19) captures the additional channel: the policy signals θ, shifting agents’ beliefs about ε, c, or the distribution of values, and hence their intrinsic motivation and reputational incentives. The principal’s objective under asymmetric information is (eq. 18, p. 19):

$$W^{AI}_\theta(y) = \int_{v^*_{\hat\theta(y)}(y)}^{+\infty} \!\left[ve_\theta + \epsilon_\theta - c_\theta - \lambda y\right] f_\theta(v)\,dv, \tag{18}$$

where $\hat\theta(y)$ is agents’ belief about θ on the equilibrium path.

Building on Bénabou and Tirole (2006a) and Bénabou and Tirole (2003), the paper also extends the framework in Section V to direct communication: a principal who can selectively disclose hard information about θ will reveal good news and conceal bad news (Proposition 10), with credibility limited by the sender’s incentives. Besley and Ghatak (2005) provide related background on motivated-agent settings that informs the optimal-policy analysis.

Method

The paper derives optimal policy in two settings and establishes the existence of separating equilibria for expressive law. It builds on signaling-game-pbe, principal-agent, and mechanism-design.

The principal’s symmetric-information welfare objective (equation 10, p. 12) is

$$W^{SI}_\theta(y) \equiv \int_{v^*_\theta(y)}^{+\infty} [v e_\theta + \epsilon_\theta - c_\theta - \lambda y] f_\theta(v)\,dv. \tag{10}$$

The maintained interior-cutoff condition is (equation 11, p. 13):

$$v^{\min}_\theta e_\theta + \varepsilon < c_\theta - \epsilon_\theta < v^{\max}_\theta e_\theta - \varepsilon. \tag{11}$$

The displayed externality condition used in Proposition 1 is (equation 13, p. 13):

$$\epsilon_\theta > \max\{\Delta_\theta(v^{\min}_\theta),\Delta_\theta(v^{\max}_\theta)\} = \mu_\theta \max\{\bar{v}_\theta-v^{\min}_\theta, v^{\max}_\theta-\bar{v}_\theta\}. \tag{13}$$

The first-best and second-best policy formulas in Proposition 1 are (equations 14-15, p. 14):

$$y^{FB}_\theta = \epsilon_\theta - \Delta_\theta\!\left(\frac{c_\theta-\epsilon_\theta}{e_\theta}\right). \tag{14}$$ $$y^{SI}_\theta = \frac{\epsilon_\theta-\Delta_\theta(v^*_\theta(y^{SI}_\theta))}{1+\lambda} - \frac{\lambda}{(1+\lambda)h_\theta(v^*_\theta(y^{SI}_\theta))s_\theta(v^*_\theta(y^{SI}_\theta))}. \tag{15}$$

Costly incentives imply underprovision of prosocial behavior at the second-best optimum (equation 16, p. 15):

$$\epsilon_\theta + v^*_\theta(y^{SI}_\theta)e_\theta - c_\theta - \lambda y^{SI}_\theta > 0. \tag{16}$$

Symmetric information: modified Pigou-Ramsey (Section III). The principal maximizes social welfare $W^{SI}_\theta(y)$ subject to eq. (4). The first-order condition (eq. 12, p. 13) equates the net social marginal benefit to the deadweight loss from paying all inframarginal agents:

$$\frac{\epsilon_\theta + v^*_{\hat\theta(y)}(y)e_\theta - c_\theta - \lambda y}{e_\theta + \Delta'_{\hat\theta(y)}(v^*_{\hat\theta(y)}(y))} = \frac{\lambda}{h_\theta(v^*_{\hat\theta(y)}(y))}, \tag{12}$$

where $h_\theta(v) = f_\theta(v)/[1-F_\theta(v)]$ is the monotone hazard rate. The first-best formula (eq. 14, p. 14) subtracts from the standard Pigouvian subsidy ε_θ the reputational rent $\Delta_\theta((c_\theta - \epsilon_\theta)/e_\theta)$ that the marginal contributor extracts. The second-best (eq. 15) further discounts for fiscal cost.

Asymmetric information: the expressive-law signaling problem (Section IV). In a separating equilibrium, the principal of type θ chooses $y^{AI}_\theta$ and agents invert y to learn θ exactly. The first-order condition (eq. 19, p. 19) adds an informational multiplier to eq. (12):

$$\left(\frac{\epsilon_\theta + v^*_{\hat\theta(y)}(y)e_\theta - c_\theta - \lambda y}{e_\theta + \Delta'_{\hat\theta(y)}(v^*_{\hat\theta(y)}(y))}\right)\!\!\left(1 + \left(v^*_{\hat\theta(y)}(y)\gamma\frac{\partial\epsilon_\theta}{\partial\theta} - \frac{\partial c_\theta}{\partial\theta} + \frac{\partial\Delta_\theta}{\partial\theta}(v^*_{\hat\theta(y)}(y))\right)\hat\theta'(y)\right) = \frac{\lambda}{h_\theta(v^*_{\hat\theta(y)}(y))}. \tag{19}$$

The second bracket is the informational multiplier: $\hat\theta'(y) = 1/(y^{AI}_\theta)'$ is the inverse slope of the separating schedule; the term in parentheses captures how a belief shift about θ changes motivation (via M⁺ or M⁻) and reputational pressure (via P⁺ or P⁻). When these signs align (diagonal of Table 1), the multiplier exceeds 1 and calls for tougher law; when they oppose (off-diagonal), it falls below 1 and calls for softer law.

The comparative static of the first-best policy with respect to θ is (equation 17, p. 16):

$$\frac{d y^{FB}_\theta}{d\theta} = \left(1 + (\gamma c_\theta + 1 - \gamma)\frac{\Delta'_\theta}{e_\theta^2}\right)\frac{\partial \epsilon_\theta}{\partial \theta} - \frac{\Delta'_\theta}{e_\theta}\frac{\partial c_\theta}{\partial \theta} - \frac{\partial \Delta_\theta}{\partial \theta}. \tag{17}$$

The paper extends Mailath (1987)‘s classic analysis to non-monotone payoffs. The key second-order condition for a separating equilibrium (Proposition 6, SOC₁, p. 22) is:

\mathcal{A}(\theta, \hat\theta) \equiv y'(\hat\theta)\,b(\theta,\hat\theta,y(\hat\theta))\,\frac{\partial\!\left[b(\theta,\hat\theta,y(\hat\theta))\,h_\theta(v^*_{\hat\theta}(y(\hat\theta)))\right]}{\partial\theta} \geq 0, \tag{SOC_1}

where $b(\theta,\hat\theta,y)$ is the social benefit of a marginal contribution. A ≥ 0 ensures no principal type wants to mimic another. For a type-θ principal believed to be type θ̂, the payoff and the marginal social benefit are (equations 20-21, p. 21):

$$W(\theta,\hat{\theta},y) \equiv \int_{v^*_{\hat{\theta}}(y)}^{+\infty} [v e_\theta + \epsilon_\theta - c_\theta - \lambda y]f_\theta(v)\,dv. \tag{20}$$ $$b(\theta,\hat{\theta},y) = v^*_{\hat{\theta}}(y)e_\theta + \epsilon_\theta - c_\theta - \lambda y. \tag{21}$$

The endpoint single-crossing condition required with SOC₁ is (SOC₂, p. 22):

\mathcal{B}(\theta,\hat{\theta},y) \equiv y'(\hat{\theta})\frac{\partial^2 W(\theta,\hat{\theta},y)}{\partial \theta\partial y} \geq 0. \tag{SOC_2}

Proposition 7 (p. 23) then identifies the four cases where SOC₁ and a complementary SOC₂ hold strictly, establishing existence of a separating equilibrium. Propositions 8-9 (p. 23) characterize knife-edge (full pooling) and impossible (no separating equilibrium) cases.

Empirical specifications

This paper contains no empirical analysis or estimating regression of its own, so there are no fixed effects, standard errors, or empirical sample. All results are propositions with formal proofs in the Online Appendix. Section II.E (pp. 11-12) surveys empirical applications by other researchers that test the model’s comparative-statics predictions: Besley, Jensen and Persson (2023) use eq. (4) to study tax evasion in local British and Welsh councils 1980-2009 and document persistence of social-multiplier effects; Jia and Persson (2021) exploit Chinese affirmative-action policy changes to test predictions on ethnic-identity choice; Chen (2016) studies deterrence effects of WWI executions on Irish vs British soldiers to test the social-multiplier comparative static.

Datasets used

This paper uses no datasets. All results are mathematical propositions.

Dataset	Role in paper	Wiki page
(none)	Theory paper	none

When to read the full paper

Read the original at doi.org/10.1086/738343 if you are: (1) working through the formal proofs, all of which are in the Online Appendix; (2) studying the extension sections (Section VI on spillovers, zero-tolerance policies, broken-windows theory, and cruel punishments; the Online Appendix on reciprocity, conformity, and status); (3) applying the framework to specific policies, where Table 1 (p. 16) and Figure 2 (p. 14) summarize the comparative statics; or (4) building on the expressive-law signaling equilibrium, where Propositions 6-9 and their appendix proofs are the required inputs.

Attribution and rights

Source: peer-reviewed, Journal of Political Economy 134(2), pp. 731-772. This distillation was extracted by an LLM on 2026-06-26 and is not human-verified or independently reproduced. Paywalled; extract-only. An accepted-manuscript version is available on HAL at hal.science/hal-05577272v1.

Bénabou, Roland, and Jean Tirole. “Laws and Norms.” Journal of Political Economy 134, no. 2 (2025): 731-772. DOI: 10.1086/738343.