BertrandOther-Classes {antitrust} | R Documentation |

The “Bertrand” class is a building block used to create other classes in this package. As such, it is most likely to be useful for developers who wish to code their own merger calibration/simulation routines.

Each class below contains all the information needed to calibrate a specific type of demand system and perform a merger simulation analysis under the assumption that firms are playing a differentiated products Bertrand pricing game.

The “Linear” class has the information for a Linear demand system.

The “LogLin” class has the information for a Log-Linear demand system.

The “AIDS” class has the information for a AIDS demand system.

The “PCAIDS” class has the information for a PCAIDS demand system

The “PCAIDSNests” class has the information for a nested PCAIDS demand system

Below, let k denote the number of products produced by all firms.

`shares`

A length k vector containing observed output. Depending upon the model, output will be measured in units sold, quantity shares, or revenue shares.

`mcDelta`

A length k vector where each element equals the proportional change in a product's marginal costs due to the merger.

`slopes`

A k x (k+1) matrix of linear demand intercepts and slope coefficients

`subset`

A vector of length k where each element equals TRUE if the product indexed by that element should be included in the post-merger simulation and FALSE if it should be excluded.

`intercepts`

A length k vector of demand intercepts. (Linear only)

`prices`

A length k vector product prices. (Linear only)

`quantities`

A length k vector of product quantities. (Linear only)

`margins`

A length k vector of product margins. All margins must be between 0 and 1. (Linear only)

`diversion`

A k x k matrix of diversion ratios with diagonal elements equal to -1.

`priceStart`

A length k vector of prices used as the initial guess in the nonlinear equation solver. (Linear and AIDS only)

`symmetry`

If TRUE, requires the matrix of demand slope coefficients to be consistent with utility maximization theory. Default is false. (Linear and LogLin only)

`insideSize`

A positive number equal to total pre-merger revenues for all products included in the simulation. (AIDS only)

`mktElast`

A negative number equal to the industry pre-merger price elasticity. (AIDS only)

`parmStart`

A length 2 vector who elements equal to an initial of a single diagonal element of the matrix of slope coefficients, as well as the market elasticity. (AIDS only)

`priceDelta`

A length k vector containing the simulated price effects from the merger. (AIDS only)

`knownElast`

A negative number equal to the pre-merger own-price elasticity for any of the k products. (PCAIDS only)

`knownElastIndex`

An integer equal to the position of the ‘knownElast’ product in the ‘shares’ vector. (PCAIDS only)

`nests`

A length k vector identifying which nest a product belongs to. (Nested PCAIDS only)

`nestsParms`

A length k vector containing nesting parameters. (Nested PCAIDS only)

For Bertrand, objects can be created by calls of the form `new("Bertrand", ...)`

.

For Linear, objects can be created by using the constructor function `linear`

.

For LogLin, objects can be created by using the constructor function `loglin`

.

For AIDS, objects can be created by using the constructor function `aids`

.

For PCAIDS, objects can be created by using the constructor `pcaids`

.

For nested PCAIDS, objects can be created by using the constructor `pcaids.nests`

.

Bertrand: Class `Antitrust`

, directly.

Linear: Class `Bertrand`

, directly.
Class `Antitrust`

, by class `Bertrand`

, distance 2.

LogLin: Class `Linear`

, directly.
Class `Bertrand`

, by class `Linear`

, distance 2.
Class `Antitrust`

, by class `Bertrand`

, distance 3.

AIDS: Class `Linear`

, directly. Class `Bertrand`

, by class “Linear”, distance 2.

PCAIDS: Class `AIDS`

, directly. Class `Linear`

, by class `AIDS`

, distance 2.
Class `Bertrand`

, by class `Linear`

, distance 3. Class `Antitrust`

, by class `Bertrand`

, distance 4.

Nested PCAIDS: Class `PCAIDS`

, directly. Class `AIDS`

, by class `PCAIDS`

, distance 2.
Class `Linear`

, by class `AIDS`

, distance 3. Class `Bertrand`

, by class `Linear`

, distance 4.
Class `Antitrust`

, by class `Bertrand`

, distance 5.

Charles Taragin ctaragin@ftc.gov

showClass("Bertrand") # get a detailed description of the class showClass("Linear") # get a detailed description of the class showClass("LogLin") # get a detailed description of the class showClass("AIDS") # get a detailed description of the class showClass("PCAIDS") # get a detailed description of the class showClass("PCAIDSNests") # get a detailed description of the class

[Package *antitrust* version 0.99.25 Index]