################################################################################
##  Function:     x0 <- rand.x(p, x)
##  Parameters:   k [number of goods]
##                n [number of observations]
##  Inputs:       p [(n by t) matrix of prices]
##                x [(n by t) matrix of consumption amounts]
##  Outputs:      x0 [(n by t) matrix of consumption amounts, with bundles at
##                    each observation chosen uniformly randomly]
##  Libraries:    gtools
##  Calls:        none
##  Description:  returns a matrix of consumption amounts, with bundles at each
##                observation chosen uniformly randomly from budgets given by
##                the data input of prices and consumption amounts
################################################################################

rand.x <- function(p, x) {
  
  #  number of goods
  k <- dim(p)[1]
  
  #  number of observations
  n <- dim(p)[2]
  
  #  generate uniformly random budget shares
  w0 <- t(rdirichlet(n, 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, n, p, p.x, x, x0, w0)
  return(result)
  
}