Sim-Functions {trade}

Tariff Simulation With User-Supplied Demand Parameters

Description

Simulates the price effects of an ad valorem tariff with user-supplied demand parameters under the assumption that all firms in the market are playing either a differentiated products Bertrand pricing game, 2nd price auction, or bargaining game.

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

Usage

sim(
  prices,
  supply = c("moncom", "bertrand", "auction", "bargaining"),
  demand = c("logit", "ces"),
  demand.param,
  owner,
  tariffPre = rep(0, length(prices)),
  tariffPost,
  subset = rep(TRUE, length(prices)),
  insideSize = 1,
  priceOutside,
  priceStart,
  bargpowerPre = rep(0.5, length(prices)),
  bargpowerPost = bargpowerPre,
  labels = paste("Prod", 1:length(prices), sep = ""),
  ...
)

Arguments

prices

A length k vector of product prices.

supply

A character string indicating how firms compete with one another. Valid values are "moncom" (monopolistic competition), "bertrand" (Nash Bertrand), "auction2nd" (2nd score auction), or "bargaining".

demand

A character string indicating the type of demand system to be used in the merger simulation. Supported demand systems are logit (‘Logit’) or ces (‘CES’).

demand.param

See Below.

owner

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

tariffPre

A vector of length k where each element equals the current ad valorem tariff (expressed as a proportion of the consumer price) imposed on each product. Default is 0, which assumes no tariff.

tariffPost

A vector of length k where each element equals the new ad valorem tariff (expressed as a proportion of the consumer price) imposed on each product. Default is 0, which assumes no tariff.

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.

insideSize

A length 1 vector equal to total units sold if ‘demand’ equals "logit", or total revenues if ‘demand’ equals "ces".

priceOutside

A length 1 vector indicating the price of the outside good. This option only applies to the ‘Logit’ class and its child classes Default for ‘Logit’,‘LogitNests’, and ‘LogitCap’ is 0, and for ‘CES’ and ‘CesNests’ is 1.

priceStart

A length k vector of starting values used to solve for equilibrium price. Default is the ‘prices’ vector for all values of demand except for ‘AIDS’, which is set equal to a vector of 0s.

bargpowerPre

A length k vector of pre-merger bargaining power parameters. Values must be between 0 (sellers have the power) and 1 (buyers the power). Ignored if ‘supply’ not equal to "bargaining".

bargpowerPost

A length k vector of post-merger bargaining power parameters. Values must be between 0 (sellers have the power) and 1 (buyers the power). Default is ‘bargpowerPre’. Ignored if ‘supply’ not equal to "bargaining".

labels

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

...

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

Details

Using user-supplied demand parameters, sim simulates the effects of a merger in a market where firms are playing a differentiated products pricing game.

If ‘demand’ equals ‘Logit’ then ‘demand.param’ must equal a list containing

• alphaThe price coefficient.

• meanvalA length-k vector of mean valuations ‘meanval’. If none of the values of ‘meanval’ are zero, an outside good is assumed to exist.

If demand equals ‘CES’ then ‘demand.param’ must equal a list containing

• gamma The price coefficient,

• alphaThe coefficient on the numeraire good. May instead be calibrated using ‘shareInside’,

• meanvalA length-k vector of mean valuations ‘meanval’. If none of the values of ‘meanval’ are zero, an outside good is assumed to exist,

• shareInside The budget share of all products in the market. Default is 1, meaning that all consumer wealth is spent on products in the market. May instead be specified using ‘alpha’.

Value

sim returns an instance of the class specified by the ‘demand’ argument.

Author(s)

Charles Taragin [e-mail]

See Also

The S4 class documentation for: Logit and CES,

Examples

## Calibration and simulation results from a merger between Budweiser and
## Old Style. Note that the in the following model there is no outside
## good; BUD's mean value has been normalized to zero.

## 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")
tariff <- c(0,0,0,0,.1,.1)

price    <- c(.0441,.0328,.0409,.0396,.0387,.0497)

# a list containing price coefficient and mean valuations
demand.param=list(alpha=-48.0457,
                  meanval=c(0,0.4149233,1.1899885,0.8252482,0.1460183,1.4865730)
)

sim.logit <- sim(price,demand="logit",supply="bertrand", demand.param,
                 owner=owner,tariffPost=tariff,labels=prodNames)



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

elast(sim.logit,TRUE)      # returns premerger elasticities
elast(sim.logit,FALSE)     # returns postmerger elasticities

diversion(sim.logit,TRUE)  # return premerger diversion ratios
diversion(sim.logit,FALSE) # return postmerger diversion ratios


cmcr(sim.logit)            #calculate compensating marginal cost reduction
upp(sim.logit)             #calculate Upwards Pricing Pressure Index

CV(sim.logit)              #calculate representative agent compensating variation