R/util_ces.R

In UchidaMizuki/econutil:

#' @export
util_ces <- function(substitution) {
  f <- function(substitution, efficiency, weights, quantities) {
    efficiency * sum(weights * quantities ^ substitution) ^ (1 / substitution)
  }

  new_util_homothetic(f,
                      substitution = substitution,
                      efficiency = NA_real_,
                      weights = double(),
                      class = "util_ces")
}

#' @export
util_calibrate.util_ces <- function(x, prices, quantities, ...) {
  substitution <- x$substitution

  weights <- prices * quantities ^ (1 - substitution)
  weights <- weights / sum(weights)

  x$weights <- weights
  x$efficiency <- sum(prices * quantities) / sum(weights * quantities ^ substitution) ^ (1 / substitution)
  x
}

#' @export
util_demand_marshall.util_ces <- function(x, prices, income, ...) {
  substitution <- x$substitution

  weights <- x$weights
  income *
    weights ^ (1 / (1 - substitution)) * prices ^ (1 / (substitution - 1)) /
    sum(weights ^ (1 / (1 - substitution)) * prices ^ (substitution / (substitution - 1)))
}

#' @export
type_sum.util_ces <- function(x, ...) {
  "CES"
}

#' @export
obj_sum.util_ces <- function(x, ...) {
  paste0(type_sum(x), "(", big_mark(x$substitution), "): ", big_mark(x$efficiency))
}