peterfoldvari/ssnip

Hypothetical Monopoly Test

ssnip: hypothetical monopoly test

Description

SSNIP stands for the Small but Significant, Non-transitory Increase in Price method to find a set of goods that constitute a market. It is often used to asses the impact of mergers and acquisitions.

ssnip tests for a predefined subset of k goods, sel_ssnip tests for al possible combination of all k goods.

sel_ssnip returns a matrix, with rows sorted in an increasing order of the critalpha value. critalpha is an estmate of the maximum price increase that a hypothetical monopolist could introduce and still have a profit increase. That is, critalpha indirectly measures the possible market power of the monopoly. It is advisable to choose the smallest subset of goods, where critalpha exceeds the predefined limit set by the researcher.

This code is based on a 2002 online manuscript and a 2003 published paper by Ian M. Dobbs (Professor (Emeritus) of Business Economics and Finance, Newcastle University Business School)

Usage

ssnip(P,Q,M,elast,z,R)

sel_ssnip(P,Q,M,elast,z)

Arguments

P: kx1 column vector of unit price

Q: kx1 column vector of quantity sold

M: kx1 column vector of the percentage markup of price above marginal cost (Lerner Index)

elast: kxk matrix of price elasticites

z: scalar, the assumed increase in price (eg: 0.05 stand for 5%)

R: kx1 vector of restrictions selecting a subset of goods

Values

D_0: Change of profit after an infinitesimaly small price increase.

D_profit_z: Change of profit after zx100% increase in prices

critalpha: The maximum rate of change of prices that results in an increase in profit (eg: 1.05 stand for 105%)

Author

Peter Foldvari, Unversity of Amsterdam. email: [email protected]

References

Dobbs, Ian M. (2002) The assessment of market power and market boundaries using the hypothetical monopoly test, manuscript: (http://www.staff.ncl.ac.uk/i.m.dobbs/Files/market%20definition%20ijbe%20n.pdf)

Dobbs, Ian. M. (2003) Demand, Cost Elasticities and Pricing Benchmarks in the Hypothetical Monopoly Test: The Consequences of a Simple SSNIP. Applied Economics Letters 10.9: 545–548.

Examples

Define the input vectors and matrix

P <- c(1.5,1,1.2)

Q <- c(18,20,5)

M <- c(0.2, 0.4, 0.6)

elast <- cbind(c(-3,1,1.1),c(1.1,-4,2.1),c(0.9,0.9,-1.5))

z <- 0.05

Testing for the 1st and 2nd goods:

R <- c(1,1,0)

ssnip(P, Q,M,elast,z,R)

Testing for all possible combinations:

sel_ssnip(P, Q,M,elast,z)

Installation

Intall from R with:

remotes::install_github("peterfoldvari/ssnip")