Recon (version 0.3.0.0)

stackelberg_solver: Stackelberg Duopoly with numeric solution

Description

This function numerically finds the equilibrium in a Stackelberg duopoly model with linear functions. For guaranteed existence of equilibrium, cost parameters should be non-negative. The general functional form for a function of argument x is \(f(x) = p_0 + p_1 x\). Parameters p refer to the inverse demand function. The firm indexed by "l" is the leader, and the one indexed by "f" is the follower.

Usage

stackelberg_solver(leader = c(0, 1), follower = c(0, 1),
  demand = c(0, -1), l0 = 0, f0 = 0)

Arguments

leader

vector of coefficients of the leader's cost function which in order must be: intercept of leader's cost function and linear term's parameter of leader's cost function

follower

vector of coefficients of the follower's cost function which in order must be: intercept of intercept of follower's cost function linear term's parameter of follower's cost function

demand

vector of coefficients of the market demand curve. Must be, in order, intercept and linear coefficient.

l0

Initial guess for leader's output. Defaults to 0. Strongly advised not to set this parameter unless you are very aware of what you're doing.

f0

Initial guess for follower's output. Defaults to 0. Strongly advised not to set this parameter unless you are very aware of what you're doing.

Value

A list with market price, firm output, profits and market share

Examples

# NOT RUN {
l = c(100, 4)
f = c(120, 5)
p = c(300, -10)
stackelberg_solver(leader = l, follower = f, demand = p)

# }