antitrust (version 0.99.26)

CMCRCournot-Functions: Compensating Marginal Cost Reductions and Upwards Pricing Pressure (Cournot)

Description

Calculate the marginal cost reductions necessary to restore premerger prices (CMCR), or the net Upwards Pricing Pressure (UPP) in a merger involving firms playing a homogeneous product Cournot pricing game.

Usage

cmcr.cournot(
  shares,
  mktElast,
  party = FALSE,
  rel = c("cost", "price"),
  labels = names(shares)
)
cmcr.cournot2(
  margins,
  rel = c("cost", "price"),
  party = FALSE,
  labels = names(margins)
)
upp.cournot(
  prices,
  margins,
  ownerPre,
  ownerPost = matrix(1, ncol = length(prices), nrow = length(prices)),
  mcDelta = rep(0, length(prices)),
  labels = names(margins)
)

Value

when ‘party’ is FALSE (default), cmcr.cournot, cmcr.cournot2 return a vector with 1 element whose value equals the percentage change in the products' average marginal costs that the merged firms must achieve in order to offset a price increase. When ‘party’ is TRUE, cmcr.cournot, cmcr.cournot2 return a vector with 2 element whose value equals the percentage change in each parties' marginal costs necessary to offset a price increase. When ‘rel’ equals "cost" (default) results are in terms of per-merger marginal costs. Otherwise, results are in terms of pre-merger price.

Arguments

shares

A length-2 vector containing merging party quantity shares.

mktElast

A length-1 containing the industry elasticity.

party

If TRUE calculate a length-2 vector of individial party CMCRs. If FALSE calculate share-weighted CMCR relative to share-weighted pre-merger marginal costs. Default is FALSE

rel

A length 1 character vector indicating whether CMCR should be calculated relative to pre-merger cost (``cost'') or pre-merger price (``price''), Default is ``cost''.

labels

A length-2 vector of product labels.

margins

A length-2 vector of product margins.

prices

A length-2 vector of product prices.

ownerPre

EITHER a vector of length 2 whose values indicate which of the merging parties produced a product pre-merger OR a 2 x 2 matrix of pre-merger ownership shares.

ownerPost

A 2 x 2 matrix of post-merger ownership shares. Default is a 2 x 2 matrix of 1s.

mcDelta

A vector of length 2 where each element equals the proportional change in a product's marginal costs due to the merger. Default is 0, which assumes that the merger does not affect any products' marginal cost.

Author

Charles Taragin

Details

The ‘shares’ (or ‘margins’) vector must have 2 elements, and all ‘shares’ and ‘margins’ elements must be between 0 and 1. The ‘mktElast’ vector must have 1 non-negative element.

References

Froeb, Luke and Werden, Gregory (1998). “A robust test for consumer welfare enhancing mergers among sellers of a homogeneous product.” Economics Letters, 58(3), pp. 367 - 369.

Werden, Gregory and Froeb, Luke (2008). “Unilateral Competitive Effects of Horizontal Mergers”, in Paolo Buccirossi (ed), Handbook of Antitrust Economics (MIT Press).

See Also

cmcr.bertrand for a differentiated products Bertrand version of this measure.

Examples

shares=c(.05,.65)
industryElast = 1.9
margins=shares/industryElast

##  calculate average CMCR as a percentage of pre-merger costs
cmcr.cournot(shares,industryElast, rel="cost")

##  calculate average CMCR as a percentage of pre-merger price
cmcr.cournot(shares,industryElast, rel="price")

##  calculate average CMCR using margins as a percentage of pre-merger costs
cmcr.cournot2(margins, party=TRUE,rel="cost")

##  calculate the average CMCR for various shares and
##  industry elasticities in a two-product merger where both firm
##  products have identical share (see Froeb and
##  Werden, 1998, pg. 369, Table 1)



deltaHHI = c(100, 500, 1000, 2500, 5000) #start with change in HHI
shares = sqrt(deltaHHI/(2*100^2)) #recover shares from change in HHI
industryElast = 1:3

result = matrix(nrow=length(deltaHHI),ncol=length(industryElast),
                dimnames=list(deltaHHI,industryElast))

for(s in 1:length(shares)){
  for(e in 1:length(industryElast)){


    result[s,e] = cmcr.cournot(rep(shares[s],2),industryElast[e])[1]

  }}

print(round(result,1))