PS-methods: Producer Surplus Methods

In antitrust: Tools for Antitrust Practitioners

Producer Surplus Methods

Description

In the following methods, calcProducerSurplus computes the expected profits of each supplier with the game depending on the class. The available classes are: Bertrand, Cournot, and Auction2ndCap.

calcProducerSurplusGrimTrigger is a method that may be used to explore how a merger affects firms' incentives to collude.

Usage

## S4 method for signature 'Bertrand'
calcProducerSurplus(object, preMerger = TRUE)

## S4 method for signature 'VertBargBertLogit'
calcProducerSurplus(object, preMerger = TRUE)

## S4 method for signature 'Auction2ndCap'
calcProducerSurplus(object, preMerger = TRUE, exAnte = TRUE)

## S4 method for signature 'Cournot'
calcProducerSurplus(object, preMerger = TRUE)

## S4 method for signature 'Bertrand'
calcProducerSurplusGrimTrigger(
  object,
  coalition,
  discount,
  preMerger = TRUE,
  isCollusion = FALSE,
  ...
)

Arguments

object	An instance of one of the classes listed above.
preMerger	If TRUE, returns pre-merger outcome. If FALSE, returns post-merger outcome. Default is TRUE.
exAnte	If ‘exAnte’ equals TRUE then the ex ante expected result for each firm is produced, while FALSE produces the expected result conditional on each firm winning the auction. Default is TRUE.
coalition	A length c vector of integers indicating the index of the products participating in the coalition.
discount	A length k vector of values between 0 and 1 that represent the product-specific discount rate for all products produced by firms particiapting in the coalition. NAs are allowed.
isCollusion	TRUE recalculates demand and cost parameters under the assumption that the coalition specified in ‘coalition’ is operating pre-merger. FALSE (the default) uses demand and cost parameters calculated from the ‘ownerPre’ matrix.
...	Additional argument to pass to calcPrices (for calcProducerSurplusGrimTrigger)

Details

calcProducerSurplusGrimTrigger calculates ‘preMerger’ product producer surplus (as well as other statistics – see below), under the assumption that firms are playing an N-player iterated Prisoner's Dilemma where in each period a coalition of firms decides whether to cooperate with one another by setting the joint surplus maximizing price on some ‘coalition’ of their products, or defect from the coalition by setting all of their products' prices to optimally undercut the prices of the coalition's products. Moreover, firms are assumed to play Grim Trigger strategies where each firm cooperates in the current period so long as every firm in the coalition cooperated last period and defects otherwise. product level ‘discount’ rates are then employed to determine whether a firm's discounted surplus from remaining in the coalition are greater than its surplus from optimally undercutting the coalition prices' for one period plus its discounted surplus when all firms set Nash-Bertrand prices in all subsequent periods.

Value

calcProducerSurplusGrimTrigger returns a data frame with rows equal to the number of products produced by any firm participating in the coalition and the following 5 columns

• Discount:The user-supplied discount rate

• Coord:Single period producer surplus from coordinating

• Defect:Single period producer surplus from defecting

• Punish:Single period producer surplus from punishing using Bertrand price

• IC:TRUE if the discounted producer surplus from coordinating across all firm products are greater than the surplus from defecting across all firm products for one period and receiving discounted Bertrand surplus for all subsequent periods under Grim Trigger.

antitrust documentation built on Aug. 24, 2022, 9:05 a.m.