gemNonexcludability {GE}

Some Examples Illustrating Non-excludability

Description

Some examples illustrating non-rival goods with non-excludability.

Usage

gemNonexcludability(...)

Arguments

...

arguments to be passed to the function sdm2.

See Also

gemNonrivalry_Uncongestiblity

Examples

dst.firm0 <- node_new(
  "non-rival services",
  type = "Leontief", a = 1,
  "labor"
)

dst.consumer1 <- node_new(
  "util",
  type = "SCES", es = 1, # es = 0
  alpha = 1, beta = c(0.75, 0.25),
  "serv1", "labor"
)

dst.consumer2 <- node_new(
  "util",
  type = "SCES", es = 1, # es = 0
  alpha = 1, beta = c(0.5, 0.5),
  "serv2", "labor"
)

f.CD <- function(policy = NULL) {
  ge <- sdm2(
    A = list(dst.firm0, dst.consumer1, dst.consumer2),
    B = matrix(c(
      1, 0, 0,
      1, 0, 0,
      0, 0, 0
    ), 3, 3, TRUE),
    S0Exg = matrix(c(
      NA, NA, NA,
      NA, NA, NA,
      NA, 60, 60
    ), 3, 3, TRUE),
    names.commodity = c("serv1", "serv2", "labor"),
    names.agent = c("firm", "consumer1", "consumer2"),
    numeraire = "labor",
    policy = policy
  )

  cat("ge$p:\n")
  print(round(ge$p, 5))
  cat("ge$z:\n")
  print(round(ge$z, 5))
  cat("ge$D:\n")
  print(addmargins(round(ge$D, 5), 2))
  cat("ge$S:\n")
  print(addmargins(round(ge$S, 5), 2))
}

f.CD()

# Suppose consumer 2 is a free rider.
policy.nonexcludability <- function(state) {
  state$S[2, 3] <- state$S[2, 1]
  state$S[2, 1] <- 0
  state
}
f.CD(policy.nonexcludability)

## Assume that both consumers have the same linear utility
# function x1 + 1.25 * x2, wherein x1 is the quantity
# of service and x2 is the quantity of labor.

dst.firm1 <- node_new(
  "serv1",
  type = "Leontief", a = 0.8,
  "labor"
)

dst.firm2 <- node_new(
  "serv2",
  type = "Leontief", a = 0.8,
  "labor"
)

dst.consumer1 <- node_new(
  "util",
  type = "Leontief", a = 1,
  "serv1"
)

dst.consumer2 <- node_new(
  "util",
  type = "Leontief", a = 1,
  "serv2"
)

f.linear <- function(policy = NULL) {
  ge <- sdm2(
    A = list(
      dst.firm0, dst.consumer1, dst.consumer2,
      dst.firm1, dst.firm2
    ),
    B = matrix(c(
      1, 0, 0, 1, 0,
      1, 0, 0, 0, 1,
      0, 0, 0, 0, 0
    ), 3, 5, TRUE),
    S0Exg = matrix(c(
      NA, NA, NA, NA, NA,
      NA, NA, NA, NA, NA,
      NA, 60, 60, NA, NA
    ), 3, 5, TRUE),
    names.commodity = c("serv1", "serv2", "labor"),
    names.agent = c("firm.public", "consumer1", "consumer2", "firm1", "firm2"),
    numeraire = "labor",
    policy = policy
  )

  cat("ge$p:\n")
  print(round(ge$p, 5))
  cat("ge$z:\n")
  print(round(ge$z, 5))
  cat("ge$D:\n")
  print(addmargins(round(ge$D, 5), 2))
  cat("ge$S:\n")
  print(addmargins(round(ge$S, 5), 2))
}

f.linear()

# Suppose consumer 2 is a free rider.
f.linear(policy.nonexcludability)