Compensating Marginal Cost Reductions and Upwards Pricing Pressure (Cournot)

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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

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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.

Author(s)

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.

See Also

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

Examples

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    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))

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