antitrust (version 0.99.10)

diversion-methods: Methods For Calculating Diversion

Description

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

Usage

# S4 method for ANY
diversion(object,preMerger=TRUE,revenue=FALSE)

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’.

Value

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

Methods

diversion

signature(object=Bertrand,preMerger=TRUE,revenue=FALSE)

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 \(\frac{-\epsilon_{ji}share_j}{\epsilon_{ii}share_i}\), where \(\epsilon_{ij}\) 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 \(-\frac{\epsilon_{ji}(\epsilon_{jj}-1)r_j}{\epsilon_{jj}(\epsilon_{ii}-1)r_j}\) 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.

diversion

signature(object=AIDS,preMerger=TRUE,revenue=TRUE)

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 \(\frac{\beta_{ji}}{\beta_ij}\), where \(\beta_{ij}\) 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.