# cmcr.cournot: Compensating Marginal Cost Reductions and Upwards Pricing... In antitrust: Tools for Antitrust Practitioners

## Description

Calculate the average marginal cost reduction necessary to restore pre-merger prices, or the net Upwards Pricing Pressure in a two-product merger involving firms playing a homogeneous product Cournot pricing game.

## Usage

 ```1 2 3 4 5 6``` ```cmcr.cournot(shares,mktElast) upp.cournot(prices, margins, ownerPre, ownerPost=matrix(1,ncol=length(prices), nrow=length(prices)), mcDelta=rep(0,length(prices)), labels=paste("Prod",1:length(prices),sep="")) ```

## Arguments

 `shares` A length-2 vector containing merging party quantity shares. `mktElast` A length-1 containing the industry elasticity. `prices` A length-2 vector of product prices. `margins` A length-2 vector of product margins. `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. `labels` A length-2 vector of product labels.

## Details

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

## Value

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.

Charles Taragin

## 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.

`cmcr.bertrand` for a differentiated products Bertrand version of this measure.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30``` ``` shares=c(.05,.65) industryElast = 1.9 cmcr.cournot(shares,industryElast) ## Calculate the necessary percentage cost reductions 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)) ```