| Diversion-Methods {antitrust} | R Documentation |
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{-\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.
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{\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.
Value
returns a k x k matrix of diversion ratios, where the i,jth element is the diversion from i to j.