defineMarketTools-methods {antitrust}

Methods For Implementing The Hypothetical Monopolist Test

Description

An Implementation of the Hypothetical Monopolist Test described in the 2010 Horizontal Merger Guidelines.

HypoMonTest implements the Hypothetical Monopolist Test for a given ‘ssnip’.

calcPricesHypoMon computes prices for a subset of firms under the control of a hypothetical monopolist under the specified demand function or auction.

diversionHypoMon calculates the matrix of revenue diversions between all products included in the merger simulation, irrespective of whether or not they are also included in ‘prodIndex’.

calcPriceDeltaHypoMon computes the proportional difference in product prices between the prices of products in ‘prodIndex’ (i.e. prices set by the Hypothetical Monopolist) and prices set in the pre-merger equilibrium. ‘...’ may be used to pass arguments to the optimizer.

Usage

## S4 method for signature 'Bertrand'
HypoMonTest(object, prodIndex, ssnip = 0.05, ...)

## S4 method for signature 'Cournot'
HypoMonTest(object, plantIndex, prodIndex, ssnip = 0.05, ...)

## S4 method for signature 'Cournot'
calcPricesHypoMon(object, plantIndex, prodIndex)

## S4 method for signature 'Linear'
calcPricesHypoMon(object, prodIndex)

## S4 method for signature 'Logit'
calcPricesHypoMon(object, prodIndex)

## S4 method for signature 'LogLin'
calcPricesHypoMon(object, prodIndex)

## S4 method for signature 'AIDS'
calcPricesHypoMon(object, prodIndex, ...)

## S4 method for signature 'LogitCap'
calcPricesHypoMon(object, prodIndex, ...)

## S4 method for signature 'Auction2ndLogit'
calcPricesHypoMon(object, prodIndex)

## S4 method for signature 'Bertrand'
diversionHypoMon(object, prodIndex, ...)

## S4 method for signature 'AIDS'
diversionHypoMon(object)

## S4 method for signature 'Bertrand'
calcPriceDeltaHypoMon(object, prodIndex, ...)

## S4 method for signature 'Cournot'
calcPriceDeltaHypoMon(object, prodIndex, plantIndex, ...)

## S4 method for signature 'AIDS'
calcPriceDeltaHypoMon(object, prodIndex, ...)

Arguments

object

An instance of one of the classes listed above.

prodIndex

A vector of product indices that are to be placed under the control of the Hypothetical Monopolist.

ssnip

A number between 0 and 1 that equals the threshold for a “Small but Significant and Non-transitory Increase in Price” (SSNIP). Default is .05, or 5%.

...

Pass options to the optimizer used to solve for equilibrium prices.

plantIndex

A vector of plant indices that are to be placed under the control of the Hypothetical Monopolist (Cournot).

Details

Let k denote the number of products produced by all firms playing the Bertrand pricing game above.

HypoMonTest is an implementation of the Hypothetical Monopolist Test on the products indexed by ‘prodIndex’ for a ‘ssnip’. The Hypothetical Monopolist Test determines whether a profit-maximizing Hypothetical Monopolist who controls the products indexed by ‘prodIndex’ would increase the price of at least one of the merging parties' products in ‘prodIndex’ by a small, significant, and non-transitory amount (i.e. impose a SSNIP).

calcPriceDeltaHypoMon calculates the price changes relative to (predicted) pre-merger prices that a Hypothetical Monopolist would impose on the products indexed by ‘prodIndex’, holding the prices of products not controlled by the Hypothetical Monopolist fixed at pre-merger levels. With the exception of ‘AIDS’, the calcPriceDeltaHypoMon for all the classes listed above calls calcPricesHypoMon to compute price levels. calcPriceDeltaHypoMon is in turn called by HypoMonTest.

diversionHypoMon calculates the matrix of revenue diversions between all products included in the merger simulation, irrespective of whether or not they are also included in ‘prodIndex’. This matrix is useful for diagnosing whether or not a product not included in ‘prodIndex’ may have a higher revenue diversion either to or from a product included in ‘prodIndex’. Note that the ‘AIDS’ diversionHypoMon method does not contain the ‘prodIndex’ argument, as AIDS revenue diversions are only a function of demand parameters.

Value

HypoMonTest returns TRUE if a profit-maximizing Hypothetical Monopolist who controls the products indexed by ‘prodIndex’ would increase the price of at least one of the merging parties' products in ‘prodIndex’ by a ‘ssnip’, and FALSE otherwise. HypoMonTest returns an error if ‘prodIndex’ does not contain at least one of the merging parties products.

calcPriceDeltaHypoMon returns a vector of proportional price changes for all products placed under the control of the Hypothetical Monopolist (i.e. all products indexed by ‘prodIndex’).

calcPricesHypoMon is identical, but for price levels.

diversionHypoMon returns a k x k matrix of diversions, where element i,j is the diversion from product i to product j.

References

U.S. Department of Justice and Federal Trade Commission, Horizontal Merger Guidelines. Washington DC: U.S. Department of Justice, 2010. https://www.justice.gov/atr/horizontal-merger-guidelines-08192010 (accessed May 5, 2021).