Recent Developments in the Theory of Regulation Mark Armstrong and David E.M. Sappington Presented by : Bruno Martins Phillip Ross Arthur Smith November 10, 2014 Armstrong & Sappington Theory of Regulation November 10, 2014 1 / 64
Optimal Monopoly Regulation Motivation How do we characterize optimal monopoly regulatory policy? What is the objective? What are we maximizing? What policies are feasible in ideal settings? What policies are feasible in practical settings? What happens when the setting is changed to include multiple firms? Armstrong & Sappington Theory of Regulation November 10, 2014 2 / 64
Optimal Monopoly Regulation Outline Optimal regulation in stylized settings Practical regulatory policies Optimal regulation with multiple firms Armstrong & Sappington Theory of Regulation November 10, 2014 3 / 64
Optimal Monopoly Regulation Optimal Regulation Regulator’s objective Regulation under complete information Perturbations to the model Adverse selection Moral hazard Partially informed regulators (audits) Dynamic interactions Armstrong & Sappington Theory of Regulation November 10, 2014 4 / 64
Optimal Monopoly Regulation Optimal Regulation - Regulator’s Objective Maximize S + α R subject to the cost of raising funds, Λ S : Consumer surplus R : Monopoly rents α ∈ [0 , 1]: Weight regulator places on monopoly rents Λ ≥ 0: Taxpayer welfare declines by 1 + Λ for every dollar raised in funds Armstrong & Sappington Theory of Regulation November 10, 2014 5 / 64
Optimal Monopoly Regulation Optimal Regulation - Complete information Case 1 (Baron and Myerson): ( α ∈ (0 , 1) , Λ = 0) Regulator compensates monopolist for fixed cost and sets price equal to marginal cost: used as the benchmark for other models here Case 2 (Laffont and Tirole): ( α = 1 , Λ > 0) Ramsey prices: rents contribute to tax reduction Total welfare: v ( p ) + (1 + Λ) π ( p ) Maximizing over p yields: ( p − c ) Λ 1 = [ 1+Λ ] η ( p ) where η ( p ) is the p elasticity of demand for product p Armstrong & Sappington Theory of Regulation November 10, 2014 6 / 64
Optimal Monopoly Regulation Adverse Selection - Standard Framework Benchmark example (as seen in class) Firm MC, c i ∈ { c L , c H } c L with probability φ ; ∆ c = c H − c L > 0 Rent reporting truthfully: R i = Q ( p i )( p i − c i ) − F + T i Rent reporting falsely: Q ( p j )( p j − c i ) − F + T j = R j + Q ( p j )( c j − c i ) IR H : R H ≥ 0 binds IC L : R L ≥ ∆ c Q ( p H ) binds Armstrong & Sappington Theory of Regulation November 10, 2014 7 / 64
Optimal Monopoly Regulation Adverse Selection - Standard Framework Policy in standard case p L = c L φ 1 − φ (1 − α )∆ c p H = c H + R L = ∆ c Q ( p H ) R H = 0 Armstrong & Sappington Theory of Regulation November 10, 2014 8 / 64
Optimal Monopoly Regulation Adverse Selection - Countervailing Incentives Let fixed costs be such that ∆ F = F L − F H ≥ 0 Proposition If a firm is informed about both fixed and marginal cost then: If ∆ F ∈ [∆ c Q ( c H ) , ∆ c Q ( c L )] then the full information outcome is feasible and optimal If ∆ F < ∆ c Q ( c H ) then p H > c H and p L = c L If ∆ F > ∆ c Q ( c L ) then p L < c L and p H = c H Regulator can gain from firm’s increase in information! Armstrong & Sappington Theory of Regulation November 10, 2014 9 / 64
Optimal Monopoly Regulation Adverse Selection - other results Unknown scope for cost reduction (observed MC, unobserved FC) p L = c L ; p H = c H ; R L = F H ( c H ) − F L ( c L ) > 0 = R H Q ( c L ) + F ′ L ( c L ) = 0 φ Q ( c H ) + F ′ 1 − φ (1 − α )( F ′ L ( c H ) − F ′ L ( c H ) = − L ( c L )) > 0 Asymmetric demand information If C ′′ ( q ) ≥ 0 the full-information outcome is feasible If C ′′ ( q ) < 0 it is often optimal to set a single price and transfer payment for all demand realizations Armstrong & Sappington Theory of Regulation November 10, 2014 10 / 64
Optimal Monopoly Regulation Unified Result If IC constraint for firm of type i does not bind, the price for firm j is not distorted, that is p j = p ∗ j Welfare expression: W = φ [ w L ( p L ) − (1 − α ) R L ] + (1 − φ )[ w H ( p H ) − (1 − α ) R H ] Reduces to: W = φ [ w L ( p L ) + (1 − α )∆ π ( p H )] + (1 − φ ) w H ( p H ) ∆ π ( p ) = π H ( p ) − π L ( p ) Armstrong & Sappington Theory of Regulation November 10, 2014 11 / 64
Optimal Monopoly Regulation Unified Result Armstrong & Sappington Theory of Regulation November 10, 2014 12 / 64
Optimal Monopoly Regulation Moral Hazard - Framework Model Firm chooses effort φ ∈ (0 , 1); disutility of effort D ( φ ) Regulator delivers utilities { U L , U H } based on the observed realized state Key Results If firms are risk neutral, full information outcome is possible If firms are risk adverse, incentives are weakened so rents are extracted Under limited liability, the low type can also extract rents (even at maximum punishment, the low type firm needs incentives for IC) Armstrong & Sappington Theory of Regulation November 10, 2014 13 / 64
Optimal Monopoly Regulation Partially Informed Regulator - Audits Firm’s private marginal cost information: c ∈ { c L , c H } After contracting, a public signal is observed: s ∈ { s L , s H } Probability of observing a low signal: φ i : φ L > φ H Under limited liability, the low-cost firm attains rents (otherwise full-information outcome is feasible) If audits are costly, it becomes another choice variable (in the reported high cost case) assuming limited liability Armstrong & Sappington Theory of Regulation November 10, 2014 14 / 64
Optimal Monopoly Regulation Partially Informed Regulator - Regulatory Capture Probability regulator informed of low cost: ψ = φζ Probability of low-cost, given uninformed regulator: φ U = φ (1 − ζ ) 1 − φζ < 0 Extra cost of “bribing” regulator: θ Weight given to regulator’s surplus: α R Maximize W = φ [ w L ( c L ) − (1 − α )∆ c Q ( p H )] + (1 − φ ) w H ( p H ) φ U ψ 1 − φ U (1 − α )∆ c (1 − ψ )(1 + θ )(1 − φ U )(1 − α R )∆ c p H = c h + + � �� � � �� � Baron-Myerson price Distortion to reduce firm stake in collusion Firm is worse off when regulatory capture is possible! ( R L lower and p H higher) Armstrong & Sappington Theory of Regulation November 10, 2014 15 / 64
Optimal Monopoly Regulation Multi-dimensional private information Consider two goods with different production costs (types { LL , LH , HL , HH } ) R ij = Q ( p 1 ij )( p 1 ij − c i ) + Q ( p 2 ij )( p 2 ij − c j ) − F − T ij Only R HH = 0 will bind - all other types can get rents from pretending to be that type R A ≥ R HH + ∆ c Q ( p HH ) R LL ≥ R HH + 2∆ c Q ( p HH ) and R LL ≥ R A + ∆ c Q ( p A H ) Armstrong & Sappington Theory of Regulation November 10, 2014 16 / 64
Optimal Monopoly Regulation Multi-dimensional private information - Results Let φ L ( φ H ) be the probability of low cost given the cost of good one is L ( H ) Then maximization problem yields the following proposition Proposition The optimal policy in the symmetric multi-dimensional setting has the features: There are no price distortions for low-cost products p LL = p A L = c L When correlations are strong ( φ L ≥ 2 φ H ) then (p HH = p A H ) and the regulatory policy for each product is independent (the IC constraint discouraging reporting type c HH when the true type is c LL dominates) When correlations are weak ( φ L ≤ 2 φ H ) then (p HH > p A H ) and the regulatory policy the two products are dependent (the IC constraint discouraging reporting type c LH or c HL when the true type is c LL dominates) Armstrong & Sappington Theory of Regulation November 10, 2014 17 / 64
Optimal Monopoly Regulation Dynamic interactions - Commitment and Renegotiation Under full commitment (and shared discount factor) Prices and rents are the same each period as in the single period problem When there is the potential for renegotiation Separating equilibrium requires a high allocation of rents (in a two period model) If the discount factor is high, a pooling payment in the first period is optimal (increases the regulator’s commitment power) Armstrong & Sappington Theory of Regulation November 10, 2014 18 / 64
Optimal Monopoly Regulation Dynamic interactions - Short term contracts Regulator cannot credibly commit to delivering second period payments When discount δ is small, standard adverse selection implemented in the first period, full information pricing in the second For intermediate values of δ separation is induced in the first period and full information in the second When δ is large enough, a partial pooling equilibrium is introduced in the first period Armstrong & Sappington Theory of Regulation November 10, 2014 19 / 64
Practical Regulatory Policies Practicality of Optimal Policies Normative Approach has limitations: Information asymmetries are difficult to characterize precisely Optimal policy is unknown when information asymmetries are large and multi-dimensional Difficult to know complete specification of all relevant constraints Some optimal instruments are not available in practice (e.g., transfers) Goals of regulators are not always clear in all situations Armstrong & Sappington Theory of Regulation November 10, 2014 20 / 64
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