# Class “Logit”

### Description

The “Logit” class contains all the information needed to calibrate a Logit demand system and perform a merger analysis under the assumption that firms are playing a differentiated products Bertrand pricing game.

### Objects from the Class

Objects can be created by using the constructor function `logit`

.

### Slots

Let k denote the number of products produced by all firms.

`prices`

:A length k vector of product prices.

`margins`

:A length k vector of product margins, some of which may equal NA.

`pricePre`

:A length k vector of simulated pre-merger prices.

`pricePost`

:A length k vector of simulated post-merger prices.

`priceStart`

:A length k vector of starting values used to solve for equilibrium price.

`normIndex`

:An integer specifying the product index against which the mean values of all other products are normalized.

`shareInside`

:The share of customers that purchase any of the products included in the ‘prices’ vector.

`priceOutside`

:The price of the outside good. Default is 0.

`slopes`

:A list containing the coefficient on price (‘alpha’) and the vector of mean valuations (‘meanval’)

### Extends

Class `Bertrand`

, directly.
Class `Antitrust`

, by class `Bertrand`

, distance 2.

### Methods

For all of methods containing the ‘preMerger’ argument, ‘preMerger’ takes on a value of TRUE or FALSE, where TRUE invokes the method using the pre-merger ownership structure, while FALSE invokes the method using the post-merger ownership structure.

`calcPrices`

`signature(object = Logit, preMerger = TRUE,isMax=FALSE,...)`

Compute either pre-merger or post-merger equilibrium
prices under the assumptions that consumer demand is Logit and firms play a differentiated product
Bertrand Nash pricing game. When isMax equals TRUE, a check is run
to determine if the calculated equilibrium price vector locally maximizes
profits. ‘...’ may be used to change the
default values of `BBsolve`

, the non-linear equation solver.

`calcPriceDeltaHypoMon`

`signature(object = Logit,prodIndex,...)`

Calculates the price changes that a Hypothetical Monopolist would impose on its products relative to pre-merger prices.

`calcShares`

`signature(object = Logit, preMerger = TRUE,revenue = FALSE)`

Compute either pre-merger or post-merger equilibrium shares under the assumptions that consumer demand is Logit and firms play a differentiated product Bertrand Nash pricing game. ‘revenue’ takes on a value of TRUE or FALSE, where TRUE calculates revenue shares, while FALSE calculates quantity shares.

`calcSlopes`

`signature(object = Logit)`

Uncover Logit demand parameters. Assumes that firms are currently at equilibrium in a differentiated product Bertrand Nash pricing game.

`CV`

`signature(object = Logit)`

Calculate the amount of money a representative consumer would need to be paid to be just as well off as they were before the merger.

`elast`

`signature(object = Logit, preMerger = TRUE)`

Computes a k x k matrix of own and cross-price elasticities.

### Author(s)

Charles Taragin charles.taragin@usdoj.gov

### Examples

1 2 | ```
showClass("Logit") # get a detailed description of the class
showMethods(classes="Logit") # show all methods defined for the class
``` |