# Compensating Marginal Cost Reductions and Upwards Pricing Pressure (Cournot)

### 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 |

### 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

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))
``` |