################################################################################
##  Function: x0 <- rand.x (p, x)
##  Inputs: p >> 0 is a (k by t) matrix of prices, x >= 0 is a (k by t) matrix
##  of consumption bundles, k >= 2 is the number of goods, t >= 1 is the number
##  of observations
##  Outputs: x0 >= 0 is a matrix of uniformly random consumption bundles
##  Libraries: gtools
##  Description: returns a matrix of consumption bundles chosen uniformly
##  randomly from the budgets corresponding to a given data set of prices and
##  consumption bundles
################################################################################

rand.x <- function (p, x) {
  
  #  number of goods
  k <- dim (p)[1]
  
  #  number of observations
  t <- dim (p)[2]
  
  #  generate uniformly random budget shares
  w0 <- t (rdirichlet (t, rep (1, k)))
  
  #  generate uniformly random consumption bundles
  p.x <- apply (p * x, 2, sum)
  p.x <- matrix (p.x, k, t, byrow = TRUE)
  x0 <- w0 * p.x / p
  
  #  clean and return result  
  result <- x0
  remove (k, p, p.x, t, x, x0, w0)
  return (result)
  
}