Intermittent Collusive Agreements: Antitrust Policy and Business Cycles

Emilie Dargaud; Armel Jacques

doi:10.1515/rle-2022-0017

Article

Intermittent Collusive Agreements: Antitrust Policy and Business Cycles

Emilie Dargaud and Armel Jacques

Published/Copyright: September 12, 2023

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From the journal Review of Law & Economics Volume 19 Issue 3

Abstract

In this article we study collusive strategies and the optimal level of fines when firms face random demand fluctuations. Collusive firms can choose to alternate collusive periods with more competitive periods: such an intermittent strategy can be implemented particularly if demand variability is high. Firms then set competitive prices during recessions to cancel the risk of cartel detection and keep the ability to cartelize for the future. If the maximum fine is too low to fully deter cartels, the antitrust authority can influence the choice of collusive agreement by varying the level of fines according to demand states. If the demand is highly variable, the antitrust authority may induce firms to collude in all demand states (by decreasing the fine during recessions), in order to detect and break up cartels more easily. On the other hand, if the demand variability is low the optimal policy may be to reduce the fine when demand is high.

Keywords: collusion; antitrust policy; business cycles

JEL Classification: K42; L22; L41

Corresponding author: Emilie Dargaud, Univ Lyon, Université Lumière Lyon 2, GATE, UMR 5824, F-69130 Ecully, France, E-mail: dargaud@gate.cnrs.fr

Appendix A

A.1 Computations of δ l C and δ h C

Low demand: Collusion on the monopoly price is sustainable iff:

π m θ l n − ρ f l + δ 1 − ρ Π C ≥ π m θ l − ρ f l

⇔ δ ≥ δ l C ≡ n − 1 π m θ l 1 − ρ μ + n − 1 π m θ l − n μ ρ f l + 1 − μ π m θ h − n ρ f h .

High demand: The collusion sustainability condition is:

π m θ h n − ρ f h + δ 1 − ρ Π C ≥ π m θ h − ρ f h

⇔ δ ≥ δ h C ≡ n − 1 π m θ h 1 − ρ μ π m θ l − n ρ f l − 1 − μ n ρ f h + n − μ π m θ h .

A.2 Deviating Firms are Not Fined

Throughout this article, we consider that collusive firms can be fined independently of whether a defection from the agreement occurs. We explore the alternative assumption in this appendix: a deviating firm is not fined (this assumption could be supported if we introduced leniency programs for instance).^[42]

The discounted profits of the C strategy remain the same:

Π C = μ π m θ l n − ρ f l + 1 − μ π m θ h n − ρ f h 1 − δ 1 − ρ .

However deviation profits increase and the no-deviation constraints are therefore as follows.

If demand is low,

π m θ l n − ρ f l + δ 1 − ρ Π C ≥ π m θ l

⇔ δ ≥ δ l C = n − 1 π m θ l + n ρ f l 1 − ρ n + μ − 1 π m θ l + 1 − μ π m θ h − n 1 − μ ρ f h + n 1 − μ ρ f l .

If demand is high,

π m θ h n − ρ f h + δ 1 − ρ Π C ≥ π m θ h

⇔ δ ≥ δ h C = n − 1 π m θ h + n ρ f h 1 − ρ μ π m θ l − n μ ρ f l + n − μ π m θ h + n μ ρ f h .

Comparing these two thresholds is more complex than under the other assumption and much depends on the parameter values. We analyze the case: n = 2 and μ = 1/2.

In this case the following comparison applies:

δ h C ≥ δ l C ⇔ π m θ h − π m θ l ≥ 2 ρ f l − f h .

The LHS of the above expression is positive. If the level of fine during booms is higher than during recessions, the above inequality is achieved and we find again the same result as in RS. However if f _l is significantly higher than f _h we may find the opposite result: collusion is less sustainable during recessions.

A.3 Computations of π*

Expected discounted profit is equal to:

Π C * = μ π m θ l n − ρ f l + 1 − μ π * n − ρ f h 1 − δ 1 − ρ .

Firms should choose the highest value for π*. However, they must respect the no-deviation constraint when demand is high. π* is computed by binding this constraint:

π * n − ρ f h + δ 1 − ρ Π C * = π * − ρ f h .

Then we obtain:

π * = δ 1 − ρ μ π m θ l − n ρ μ f l + 1 − μ f h n − 1 − δ 1 − ρ n − μ .

A.4 Non-sustainability of the Intermittent Collusive Strategies for Intermediate Values of δ

H strategy (collusion during booms): Firms charge the marginal cost if demand is low. During booms the individual collusive profit is: π * n . Firms only have the incentive to deviate during booms. Collusion is sustainable iff:

π * n − ρ f h + δ 1 − ρ Π * ≥ π * − ρ f h + δ × 0 ,

with:

Π * = μ 0 + δ Π * + 1 − μ π * n − ρ f h + δ 1 − ρ Π * ⇔ Π * = 1 − μ 1 − δ + 1 − μ δ ρ π * n − ρ f h .

Replacing for Π* in the previous condition allows us to re-write the no-deviation condition during booms as:

π * n − ρ f h + δ 1 − ρ 1 − μ 1 − δ + 1 − μ δ ρ π * n − ρ f h ≥ n π * n − ρ f h

⇔ δ ≥ δ H * ≡ n − 1 n 1 − ρ + μ ρ − μ − n 1 − ρ 1 − μ ρ f h π * .

f h π * decreases in π*. Then n 1 − ρ + μ ρ − μ − n 1 − ρ 1 − μ ρ f h π * increases and δ ^H* decreases in π*. The minimum value of δ H * is therefore reached for the monopoly price.

The H strategy is easier to sustain when firms set the monopoly price rather than a lower price. If δ < δ ^H the H strategy is not sustainable.

L strategy (collusion during recessions): Firms charge the marginal cost if demand is high. During recessions firms the individual collusive profit is: π * n . Firms have incentives to deviate only during recessions. Collusion is sustainable iff:

π * n − ρ f l + δ 1 − ρ Π L * ≥ π * − ρ f l + δ × 0 ⇔ δ ≥ δ L * ≡ n − 1 1 − μ ρ n − 1 − μ − n 1 − ρ μ ρ f l π * .

The minimum value of δ L * is reached for the monopoly price. Then the L strategy is easier to sustain when firms set the monopoly price rather than a lower price. If δ < δ ^L the L strategy is not sustainable.

A.5 Comparison of Sustainability Thresholds

If demand is high, the collusive strategy i ∈ {C, H} is sustainable iff:

π m θ h n − ρ f h + δ 1 − ρ Π i ≥ π m θ h − ρ f h .

Deviation and current collusive profits are the same with the C and H strategies. But the discounted expected collusive profit is different, and the following inequality applies:

δ H ≥ δ h C ⇔ Π C ≥ Π H .

If demand is low, the collusive strategy i ∈ {C, L} is sustainable iff:

π m θ l n − ρ f l + δ 1 − ρ Π i ≥ π m θ l − ρ f l .

From which we deduce:

δ L ≥ δ l C ⇔ Π C ≥ Π L .

A.6 Computations of Expected Consumer Surplus

C strategy: Consumer surplus is c s m θ k throughout the collusive period and c s n c θ k afterwards, k ∈ {l, h}.

C S C = μ c s m θ l + 1 − μ c s m θ h + δ 1 − ρ C S C + ρ C S ⇔ C S C = μ c s m θ l + 1 − μ c s m θ h + δ ρ C S 1 − δ 1 − ρ .

H strategy: Consumer surplus is c s m θ h or c s n c θ l throughout the collusive period and c s n c θ k afterwards, k ∈ {l, h}.

C S H = μ c s n c θ l + δ C S H + 1 − μ s c m θ h + δ 1 − ρ C S H + ρ C S ⇔ C S H = μ c s n c θ l + 1 − μ c s m θ h + 1 − μ δ ρ C S 1 − δ + 1 − μ δ ρ .

L strategy: Consumer surplus is s c n c θ h or s c m θ l throughout the collusive period and s c n c θ k afterwards, k ∈ {l, h}.

C S L = μ c s m θ l + δ 1 − ρ C S L + ρ C S + 1 − μ c s n c θ h + δ C S L ⇔ C S L = μ c s m θ l + 1 − μ c s n c θ h + μ δ ρ C S 1 − δ + μ δ ρ .

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Received: 2022-03-21

Accepted: 2023-05-30

Published Online: 2023-09-12

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https://doi.org/10.1515/rle-2022-0017

Keywords for this article

collusion; antitrust policy; business cycles