bertrand_quota {trade}

quota Simulation With A Bertrand Pricing Game

Description

Simulate the effect of quotas when firms play a Bertrand pricing game and consumer demand is either Logit, CES, or AIDS

Usage

bertrand_quota(
  demand = c("logit"),
  prices,
  quantities,
  margins,
  owner = NULL,
  mktElast = NA_real_,
  diversions,
  quotaPre = rep(Inf, length(quantities)),
  quotaPost,
  priceOutside = ifelse(demand == "logit", 0, 1),
  priceStart,
  isMax = FALSE,
  parmStart,
  control.slopes,
  control.equ,
  labels = paste("Prod", 1:length(quantities), sep = ""),
  ...
)

Arguments

demand

A character vector indicating which demand system to use. Currently allows logit (default), ces, or aids.

prices

A length k vector product prices. Default is missing, in which case demand intercepts are not calibrated.

quantities

A length k vector of product quantities.

margins

A length k vector of product margins. All margins must be either be between 0 and 1, or NA.

owner

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

mktElast

A negative number equal to the industry pre-merger price elasticity. Default is NA .

diversions

A k x k matrix of diversion ratios with diagonal elements equal to -1. Default is missing, in which case diversion according to revenue share is assumed.

quotaPre

A vector of length k where each element equals the current quota (expressed as a proportion of pre-merger quantities) imposed on each product. Default is Inf, which assumes no quota.

quotaPost

A vector of length k where each element equals the new quota (expressed as a proportion of pre-merger quantities) imposed on each product. Default is Inf, which assumes no quota.

priceOutside

price of the outside good. Equals 0 for logit and 1 for ces. Not used for aids.

priceStart

For aids, a vector of length k who elements equal to an initial guess of the proportional change in price caused by the merger. The default is to draw k random elements from a [0,1] uniform distribution. For ces and logit, the default is prices.

isMax

If TRUE, checks to see whether computed price equilibrium locally maximizes firm profits and returns a warning if not. Default is FALSE.

parmStart

aids only. A vector of length 2 who elements equal to an initial guess for "known" element of the diagonal of the demand matrix and the market elasticity.

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.

...

Additional options to feed to the BBsolve optimizer used to solve for equilibrium prices.

Details

Let k denote the number of products produced by all firms. Using price, and quantity, information for all products in each market, as well as margin information for at least one products in each market, bertrand_quota is able to recover the slopes and intercepts of the Logit, demand system. These parameters are then used to simulate the price effects of a quota under the assumption that the firms are playing a simultaneous price setting game.

Value

bertrand_quota returns an instance of class QuotaLogit.

References

Simon P. Anderson, Andre de Palma, Brent Kreider, Tax incidence in differentiated product oligopoly, Journal of Public Economics, Volume 81, Issue 2, 2001, Pages 173-192.

Examples

## Calibration and simulation results from a 80% quota on non-US beers "OTHER-LITE"
## and "OTHER-REG"
## Source: Epstein/Rubenfeld 2004, pg 80

prodNames <- c("BUD","OLD STYLE","MILLER","MILLER-LITE","OTHER-LITE","OTHER-REG")
owner <-c("BUD","OLD STYLE","MILLER","MILLER","OTHER-LITE","OTHER-REG")
price    <- c(.0441,.0328,.0409,.0396,.0387,.0497)
quantities   <- c(.066,.172,.253,.187,.099,.223)*100
margins <- c(.3830,.5515,.5421,.5557,.4453,.3769)
quota <- c(Inf,Inf,Inf,Inf,.8,.8)

names(price) <-
 names(quantities) <-
 names(margins) <-
 prodNames


result.logit <- bertrand_quota(demand = "logit",prices=price,quantities=quantities,
                                margins = margins,owner=owner, quotaPost = quota, labels=prodNames)

print(result.logit)           # return predicted price change
summary(result.logit)         # summarize merger simulation