stackelberg_solver function

Stackelberg Duopoly with numeric solution

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.

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.

Returns

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

Examples

l = c(100, 4)
f = c(120, 5)
p = c(300, -10)
stackelberg_solver(leader = l, follower = f, demand = p)

Author(s)

Pedro Cavalcante Oliveira, Department of Economics, Fluminense Federal University pedrocolrj@gmail.com