solveModel: Function to solve counterfactuals.

Description

Function to solve counterfactuals.

Usage

solveModel(
  N,
  L_i,
  L_j,
  K,
  t_ij,
  a,
  b,
  varphi,
  w_eq,
  u_eq,
  U_eq,
  Q_eq,
  ttheta_eq,
  alpha = 0.7,
  beta = 0.7,
  theta = 7,
  mu = 0.3,
  delta = 0.3585,
  lambda = 0.01,
  rho = 0.9094,
  eta = 0.15,
  epsilon = 0.01,
  zeta = 0.95,
  varrho = 3,
  sh_city = 0.1,
  tol = 10^-10,
  maxiter = 1000
)

Value

A list containing new equilibrium values for the variables of the model. The reported variables are wages (w), residents market access (W_i), endogenous productivities (A), endogenous amenities (B), population (Li), employment (Lj), share of commercial floorspace (ttheta), real income (u), welfare (U), firms market access (FCMA), firms output (Y).

Arguments

N: Integer - Number of locations.
L_i: Nx1 array - Number of residents in each location
L_j: Nx1 array - Number of workers in each location
K: Nx1 array - Land supply
t_ij: NxN matrix - Travel times across locations
a: Nx1 array - Total Factor Productivity in each location
b: Nx1 array - Vector of amenities in each location
varphi: Nx1 array - Density of development
w_eq: Nx1 array - Initial vector of wages
u_eq: Nx1 array - Initial vector of welfare
U_eq: 1x1 array - Initial welfare
Q_eq: Nx1 array - Initial price for floorspace
ttheta_eq: Nx1 array - Share of floorspace used commercially
alpha: Float - Exp. share in consumption, 1-alpha exp. share in housing
beta: Float - Output elasticity with respect to labor
theta: Float - Commuting and migration elasticity.
mu: Float - Floorspace prod function: output elasticity wrt capital
delta: Float - Decay parameter agglomeration force
lambda: Float - agglomeration externality
rho: Float - decay parameter for amenities
eta: Float - amenity externality
epsilon: Float - Parameter that transforms travel times to commuting costs
zeta: Float - convergence parameter
varrho: Float - migration elasticty
sh_city: Share of population living in the city
tol: Float - tolerance factor
maxiter: Integer - Maximum number of iterations for convergence. Default maxiter=1000.