antitrust (version 0.99.10)

Auction2ndCap-class: Class “Auction2ndCap”

Description

The “Auction2ndCap” class contains all the information needed to calibrate a 2nd price auction with capacity constraints

Objects from the Class

Objects can be created by using the constructor function auction2nd.cap.

Slots

Let k denote the number of firms.

capacities:

A length k vector of firm capacities.

margins:

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

prices:

A length k vector of product prices.

reserve:

A length 1 vector equal to observed buyer's reserve price. May equal NA.

shareInside:

A length 1 vector equal to the probability that a buyer does not select the outside option. May equal NA.

sellerCostCDF:

A length 1 character vector equal to the name of the function that calculates the Cumulative Distribution (CDF) of SellerCosts.

sellerCostCDFLowerTail:

A length 1 logical vector equal to TRUE if the probabilities are P[X <= x], otherwise, P[X > x].

sellerCostPDF:

A function returning the Probability Density of Seller Costs.

sellerCostBounds:

The bounds on the seller's CDF.

sellerCostParms:

The parameters of the seller's CDF.

buyerValuation:

Buyer's self-supply cost.

reservePre:

Buyer's optimal pre-merger reservation price.

reservePost:

Buyer's optimal post-merger reservation price.

mcDelta:

A length k vector equal to the proportional change in a firm's capacity following the merger.

parmsStart:

A vector of starting values.

Extends

Class '>Antitrust, directly.

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. Likewise, for all methods containing the ‘exAnte’ argument, if ‘exAnte’ equals TRUE then the ex ante expected result for each firm is produced, while FALSE produces the expected result conditional on each firm winning the auction.

calcBuyerExpectedCost

signature(object = Auction2ndCap, preMerger = TRUE)

Computes the expected amount that the buyer will pay to the auction winner.

calcBuyerValuation

signature(object = Auction2ndCap)

Computes the value to the buyer of the outside option.

calcExpectedLowestCost

signature(object = Auction2ndCap, preMerger = TRUE)

Computes the expected lowest cost of the winning bid.

calcExpectedPrice

signature(object = Auction2ndCap, preMerger = TRUE)

Computes the expected price paid by the buyer.

calcProducerSurplus

signature(object = Auction2ndCap, preMerger = TRUE,exAnte=TRUE)

Computes the expected profits of each supplier

calcMC

signature(object = Auction2ndCap, t, preMerger = TRUE,exAnte=TRUE)

Computes the expected marginal cost of each supplier for a given capacity profile ‘t’. Default is ‘preMerger’ capacities.

calcMargins

signature(object = Auction2ndCap, preMerger = TRUE,exAnte=TRUE)

Compute each firm's expected margin.

calcOptimalReserve

signature(object = Auction2ndCap, preMerger = TRUE,lower,upper)

Computes the bidder's optimal reserve price.

calcPrices

signature(object = Auction2ndCap, preMerger = TRUE,exAnte=TRUE)

Computes the expected price that the buyer pays, conditional on the buyer purchasing from a particular firm.

calcSellerCostParms

signature(object = Auction2ndCap)

Calibrate the parameters of the Seller Cost CDF, as well as the reserve price, if not supplied.

calcShares

signature(object = Auction2ndCap, preMerger = TRUE,exAnte=TRUE)

Compute the probability that a firm wins.

cdfG

signature(object = Auction2ndCap,c,preMerger=TRUE)

Calculates the probability that a cost draw less than or equal to ‘c’ is realized for each firm. If ‘c’ is not supplied, the buyer reserve and total capacity is used.

summary

signature(object = Auction2ndCap,exAnte=FALSE, parameters=FALSE,digits=2)

Summarize the results of the calibration and simulation.

Examples

# NOT RUN {
showClass("Auction2ndCap")           # get a detailed description of the class
showMethods(classes="Auction2ndCap") # show all methods defined for the class
# }