bertrand_foc_vert_gnl: Downstream Bertrand first-order conditions

In mergersim: Merger Simulation and Calibration

Downstream Bertrand first-order conditions

Description

Downstream Bertrand first-order conditions

Usage

bertrand_foc_vert_gnl(
  price_r,
  own_down,
  own_up,
  alpha,
  delta,
  cost_r,
  price_w,
  cost_w,
  nest_allocation = NA,
  mu = NA,
  sumFOC = FALSE
)

Arguments

price_r	Downstream or retail prices
own_down	Ownership matrix for downstream firms
own_up	Ownership matrix for upstream firms
alpha	Price coefficient
delta	Mean values
cost_r	Marginal costs for downstream firm for each product
price_w	Upstream or wholesale prices, treated as costs by downstream firms
cost_w	Marginal costs for upstream firm for each product
nest_allocation	For generalized nested logit demand, a J-by-K matrix where each element (j,k) designates the membership of good j in nest k. Rows should sum to 1.
mu	Nesting parameters for each nest
sumFOC	logical; whether to return the sum of squares of the first-order conditions. Defaults to FALSE, in which case it returns each product first-order condition as a vector.

Details

This function calculates the first-order conditions from a Bertrand price-setting model of competition as the downstream market of a vertical supply chain. This version allows for generalized nested logit demand.

Value

The first-order conditions

mergersim documentation built on July 21, 2026, 5:09 p.m.