antitrust (version 0.99.10)

Linear-class: Class “Linear”

Description

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

Objects from the Class

Objects can be created by using the constructor function linear.

Slots

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

intercepts:

A length k vector of demand intercepts.

prices:

A length k vector product prices.

quantities:

A length k vector of product quantities.

margins:

A length k vector of product margins. All margins must be between 0 and 1.

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.

symmetry:

If TRUE, requires the matrix of demand slope coefficients to be consistent with utility maximization theory.

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, preMerger = TRUE,...)

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. ‘...’ may be used to change the default values of constrOptim, the non-linear equation solver used to enforce non-negative equilibrium quantities.

calcPriceDeltaHypoMon

signature(object,prodIndex,...)

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

calcQuantities

signature(object, preMerger = TRUE)

Compute either pre-merger or post-merger equilibrium quantities under the assumptions that consumer demand is Linear and firms play a differentiated product Bertrand Nash pricing game.

calcShares

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

Compute either pre-merger or post-merger equilibrium quantity shares under the assumptions that consumer demand is Linear and firms play a differentiated product Bertrand Nash pricing game.

calcSlopes

signature(object)

Uncover slopes and intercept from a Linear demand system. Assumes that firms are currently at equilibrium in a differentiated product Bertrand Nash pricing game.

CV

signature(object = "Linear")

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, preMerger = TRUE)

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

Examples

# NOT RUN {
showClass("Linear")           # get a detailed description of the class
showMethods(classes="Linear") # show all methods defined for the class
# }