antitrust (version 0.99.10)

auction2nd.logit: 2nd Score Procurement Auction Model

Description

Calibrates consumer demand using Logit and then simulates the price effect of a merger between two firms under the assumption that all firms in the market are playing a differentiated products 2nd score auction game.

Usage

auction2nd.logit(prices,shares,margins,
                  ownerPre,ownerPost,
                  normIndex=ifelse(isTRUE(all.equal(sum(shares), 
                            1, check.names=FALSE)), 1, NA),
                  mcDelta=rep(0,length(prices)),
                  subset=rep(TRUE,length(prices)),
                  mcDeltaOutside=0,
                  control.slopes,
                  labels=paste("Prod",1:length(prices),sep="")
                  )

             
auction2nd.logit.alm(prices,shares,margins,
                             ownerPre,ownerPost,
                             mktElast = NA_real_,
                             insideSize = NA_real_,
                             mcDelta=rep(0,length(prices)),
                             subset=rep(TRUE,length(prices)),
                             mcDeltaOutside=0,
                             parmsStart,
                             control.slopes,
                             control.equ,
                             labels=paste("Prod",1:length(prices),sep="")
)

Arguments

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

prices

A length k vector of product prices.

shares

A length k vector of product (quantity) shares. Values must be between 0 and 1.

margins

A length k vector of product margins (in levels, not percents), some of which may equal NA.

normIndex

An integer equalling the index (position) of the inside product whose mean valuation will be normalized to 1. Default is 1, unless ‘shares’ sum to less than 1, in which case the default is NA and an outside good is assumed to exist.

ownerPre

EITHER a vector of length k whose values indicate which firm produced a product pre-merger OR a k x k matrix of pre-merger ownership shares.

ownerPost

EITHER a vector of length k whose values indicate which firm produced a product after the merger OR a k x k matrix of post-merger ownership shares.

mktElast

a negative value indicating market elasticity. Default is NA.

insideSize

An integer equal to total pre-merger units sold. If shares sum to one, this also equals the size of the market.

mcDelta

A vector of length k where each element equals the (level) change in a product's marginal costs due to the merger. Default is 0, which assumes that the merger does not affect any products' marginal cost.

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.Default is a length k vector of TRUE.

mcDeltaOutside

A length 1 vector indicating the change in the marginal cost of the outside good. Default is 0.

parmsStart

A length 2 vector of starting values used to solve for price coefficient and the share of the outside good. The first element should always be the price coefficient and the second should be the outside good.

control.slopes

A list of optim control parameters passed to the calibration routine optimizer (typically the calcSlopes method).

control.equ

A list of BBsolve control parameters passed to the non-linear equation solver (typically the calcPrices method).

labels

A k-length vector of labels. Default is "Prod#", where ‘#’ is a number between 1 and the length of ‘prices’.

Value

auction2nd.logit returns an instance of '>Auction2ndLogit, a child class of '>Logit..

Details

Using product prices, quantity shares and all of the product margins from at least one firm, auction2nd.logit is able to recover the price coefficient and product mean valuations in a Logit demand model. auction2nd.logit then uses these calibrated parameters to simulate a merger between two firms, under the assumption that firms are particpating in a 2nd score procurement auction.

auction2nd.logit.alm is identical to auction2nd.logit except that it assumes that an outside product exists and uses additional margin information to estimate the share of the outside good.

References

Miller, Nathan (2014). “Modeling the effects of mergers in procurement” International Journal of Industrial Organization , 37, pp. 201-208.

See Also

logit

Examples

# NOT RUN {
## Calibration and simulation results from a merger between firms 2 and 3 
## of a 4-firm market
## Source: Miller 2014 backup materials http://www.nathanhmiller.org/research

share = c(0.29,0.40,0.28,0.03)

price = c(35.53,  154, 84.08, 53.16)
cost  =  c(NA, 101, NA, NA)

ownerPre <- ownerPost <- diag(length(share))

#Suppose products 2 and 3 merge
ownerPost[2,3] <- ownerPost[3,2] <- 1 

margin = price - cost

result <- auction2nd.logit(price,share,margin,
ownerPre=ownerPre,ownerPost=ownerPost,normIndex=2)


print(result)
summary(result,revenue=FALSE)

##re-run without any price information except Firm 2

price <- rep(NA_real_, length(price))

result.noprice <- auction2nd.logit(price,share,margin,
ownerPre=ownerPre,ownerPost=ownerPost,normIndex=2)

print(result.noprice)
summary(result.noprice,revenue=FALSE)

## Get a detailed description of the 'Auction2ndLogit' class slots
showClass("Auction2ndLogit")

## Show all methods attached to the 'Auction2ndLogit' Class
showMethods(classes="Auction2ndLogit")

# }