Diversion-Methods: Methods For Calculating Diversion

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Methods For Calculating Diversion

Description

Calculate the diversion matrix between any two products in the market.

Usage

## S4 method for signature 'Bertrand'
diversion(object, preMerger = TRUE, revenue = FALSE)

## S4 method for signature 'AIDS'
diversion(object, preMerger = TRUE, revenue = TRUE)

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

Arguments

object	An instance of one of the classes listed above.
preMerger	If TRUE, calculates pre-merger price elasticities. If FALSE, calculates post-merger price elasticities. Default is TRUE.
revenue	If TRUE, calculates revenue diversion. If FALSE, calculates quantity diversion. Default is TRUE for ‘Bertrand’ and FALSE for ‘AIDS’.

Details

For Bertrand, when ‘revenue’ is FALSE (the default), this method uses the results from the merger calibration and simulation to compute the quantity diversion matrix between any two products in the market. Element i,j of this matrix is the quantity diversion from product i to product j, or the proportion of product i's sales that leave (go to) i for (from) j due to a increase (decrease) in i's price. Mathematically, quantity diversion is \frac{-ε_{ji}share_j}{ε_{ii}share_i}, where ε_{ij} is the cross-price elasticity from i to j.

When ‘revenue’ is TRUE, this method computes the revenue diversion matrix between any two products in the market. Element i,j of this matrix is the revenue diversion from product i to product j, or the proportion of product i's revenues that leave (go to) i for (from) j due to a increase (decrease) in i's price. Mathematically, revenue diversion is -\frac{ε_{ji}(ε_{jj}-1)r_j}{ε_{jj}(ε_{ii}-1)r_j} where r_i is the revenue share of product i.

When ‘preMerger’ is TRUE, diversions are calculated at pre-merger equilibrium prices, and when ‘preMerger’ is FALSE, they are calculated at post-merger equilibrium prices.

For AIDS, when ‘revenue’ is TRUE (the default), this method computes the revenue diversion matrix between any two products in the market. For AIDS, the revenue diversion from i to j is \frac{β_{ji}}{β_ij}, where β_{ij} is the percentage change in product i's revenue due to a change in j's price.

When ‘revenue’ is FALSE, this callNextMethod is invoked. Will yield a matrix of NAs if the user did not supply prices.

When ‘preMerger’ is TRUE, diversions are calculated at pre-merger equilibrium prices, and when ‘preMerger’ is FALSE, they are calculated at post-merger equilibrium prices.

Value

returns a k x k matrix of diversion ratios, where the i,jth element is the diversion from i to j.

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