antitrust (version 0.99.26)

BertrandOther-Classes: “Bertrand” Classes

Description

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.

Slots

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)

Objects from the Class

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.

Extends

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.

Author

Charles Taragin

Examples

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