Simulates the price effects of a merger between two firms with usersupplied demand parameters under the assumption that all firms in the market are playing a differentiated products Bertrand pricing game.
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Let k denote the number of products produced by all firms. 
prices 
A length k vector of product prices. 
demand 
A character string indicating the type of demand system to be used in the merger simulation. Supported demand systems are linear (‘Linear’), loglinear(‘LogLin’), logit (‘Logit’), nested logit (‘LogitNests’), ces (‘CES’), nested CES (‘CESNests’) and capacity constrained Logit (‘LogitCap’). 
demand.param 
See Below. 
ownerPre 
EITHER a vector of length k whose values indicate which firm produced a product premerger OR a k x k matrix of premerger 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 postmerger ownership shares. 
nests 
A length k vector identifying the nest that each product belongs to. Must be supplied when ‘demand’ equals ‘CESNests’ and ‘LogitNests’. 
capacities 
A length k vector of product capacities. Must be supplied when ‘demand’ equals ‘LogitCap’. 
mcDelta 
A vector of length k where each element equals the proportional 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 postmerger simulation and FALSE if it should be excluded.Default is a length k vector of TRUE. 
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. 
labels 
A klength 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. 
Using usersupplied demand parameters,
sim
simulates the effects of a merger in a market where
firms are playing a differentiated products pricing game.
If ‘demand’ equals ‘Linear’, ‘LogLin’, or ‘AIDS’, then ‘demand.param’ must be a
list containing ‘slopes’, a k x k matrix of slope coefficients, and
‘intercepts’, a lengthk vector of intercepts. Additionally, if
‘demand’ equals ‘AIDS’, ‘demand.param’ must contain ‘mktElast’, an
estimate of aggregate market elasticity. For ‘Linear’
demand models, sim
returns an error if any intercepts are
negative, and for both ‘Linear’, ‘LogLin’, and ‘AIDS’ models, sim
returns an error if not all diagonal elements of the slopes matrix are
negative.
If ‘demand’ equals ‘Logit’ or ‘LogitNests’, then ‘demand.param’ must equal a list containing
alphaThe price coefficient.
meanvalA lengthk 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’ or ‘CESNests’, 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 lengthk 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’.
sim
returns an instance of the class specified by the
‘demand’ argument.
Charles Taragin charles.taragin@usdoj.gov
The S4 class documentation for: Linear
,
AIDS
, LogLin
, Logit
,
LogitNests
, CES
, CESNests
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36  ## 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","MILLERLITE","OTHERLITE","OTHERREG")
ownerPre <c("BUD","OLD STYLE","MILLER","MILLER","OTHERLITE","OTHERREG")
ownerPost <c("BUD","BUD","MILLER","MILLER","OTHERLITE","OTHERREG")
nests < c("Reg","Reg","Reg","Light","Light","Reg")
price < c(.0441,.0328,.0409,.0396,.0387,.0497)
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",demand.param,ownerPre=ownerPre,ownerPost=ownerPost)
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

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