# Class “CES”

### Description

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

### Objects from the Class

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

.

### Slots

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

`slopes`

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

`priceOutside`

:The price of the outside good. Default is 1.

### Extends

Class `Logit`

, directly.
Class `Bertrand`

, by class `Logit`

, distance 2.
Class `Antitrust`

, by class `Bertrand`

, distance 3.

### 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.

`calcShares`

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

Compute either pre-merger or post-merger equilibrium revenue shares under the assumptions that consumer demand is CES 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)`

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

`CV`

`signature(object, revenueInside)`

Calculates compensating variation. If ‘revenueInside’ is missing, then CV returns compensating variation as a percent of the representative consumer's income. If ‘revenueInside’ equals the total expenditure on all products inside the market, then CV returns compensating variation in levels.

`elast`

`signature(object, 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("CES") # get a detailed description of the class
showMethods(classes="CES") # show all methods defined for the class
``` |