CGE (version 0.3.3)

CES_A: CES Demand Coefficient Matrix

Description

This function computes the CES demand coefficient matrix.

Usage

CES_A(sigma, alpha, Beta, p, Theta = NULL)

Arguments

sigma

a numeric m-vector or m-by-1 matrix.

alpha

a nonnegative numeric m-vector or m-by-1 matrix.

Beta

a nonnegative numeric n-by-m matrix.

p

a nonnegative numeric n-vector or n-by-1 matrix.

Theta

null or a positive numeric n-by-m matrix.

Value

A demand coefficient n-by-m matrix is computed which indicates the demands of agents (firms or consumers) for obtaining unit product or utility with CES production functions or utility functions (e.g. alpha*(beta1*x1^sigma+beta2*x2^sigma)^(1/sigma) or alpha*(beta1*(x1/theta1)^sigma+beta2*(x2/theta2)^sigma)^(1/sigma)) under the price vector p.

References

LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)

Examples

# NOT RUN {
CES_A(-1, 2, c(0.2, 0.1), c(1, 2))

#####
sigma <- c(-1, -1, -1)
alpha <- c(1, 1, 1)
Beta <- matrix(c(
  0, 1, 1,
  1, 0, 0,
  1, 0, 0
), 3, 3, TRUE)
p <- 1:3
CES_A(sigma, alpha, Beta, p)

#####
sigma <- -1e-10
alpha <- 1
Beta <- c(0.8, 0.2)
Theta <- c(2, 1)
p <- c(1, 1)
CES_A(sigma, alpha, Beta, p, Theta)
CD_A(alpha * prod(Theta^(-Beta)), Beta, p)

CES_A(sigma, alpha, Beta, p, Beta)
CD_A(alpha * prod(Beta^(-Beta)), Beta, p)

CES_A(-1e5, alpha, Beta, p, Theta)
# }