gemNonrivalry_Uncongestiblity {GE}

Some Examples Illustrating Uncongestible Non-rival Goods

Description

Some examples illustrating (uncongestible) non-rival goods (or services), Lindahl prices and the uniform price. In general equilibrium models, non-rival services can be regarded as personalized services, which are joint products of a production process (see Mas-Colell, Whinston, and Green, 1995, section 16.G).

Usage

gemNonrivalry_Uncongestiblity(...)

Arguments

...

arguments to be passed to the function sdm2.

References

Mas-Colell, Andreu and Whinston, Michael Dennis and Green, Jerry R. (1995, ISBN: 0195073401) Microeconomic Theory. Oxford University Press (New York).

Examples

## The firm supplies non-rival services.
dst.firm <- 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"
)

ge <- sdm2(
  A = list(dst.firm, 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"
)

ge$p # Lindahl prices
ge$z
addmargins(ge$D, 2)
addmargins(ge$S, 2)
addmargins(ge$DV)

## Computing the uniform price of the non-rival services
## by transfer payment between consumers.
ge <- sdm2(
  A = list(dst.firm, 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 = function(A, state) {
    # A[[1]]$last.s is the previous labor supply of consumer1.
    if (is.null(A[[1]]$last.s)) A[[1]]$last.s <- 60

    p <- state$p / state$p[3]
    last.DV <- dg(p) %*% state$last.A %*% dg(state$last.z)
    transfer.payment <- last.DV[1, 2] - mean(c(last.DV[1, 2], last.DV[2, 3]))

    A[[1]]$last.s <- state$S[3, 2] <- A[[1]]$last.s *
      ratio_adjust((60 + transfer.payment) / A[[1]]$last.s, 0.2)
    state$S[3, 3] <- 120 - state$S[3, 2]

    state
  }
)

# Taking transfer payment into account, the uniform price of the non-rival services is 0.5.
ge$p
addmargins(ge$D, 2)
addmargins(ge$S, 2)
addmargins(ge$DV)

ge2 <- sdm2(
  A = list(dst.firm, 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, 80, 40
  ), 3, 3, TRUE),
  names.commodity = c("serv1", "serv2", "labor"),
  names.agent = c("firm", "consumer1", "consumer2"),
  numeraire = "labor"
)

ge2$p
addmargins(ge2$D, 2)
addmargins(ge2$S, 2)
addmargins(ge2$DV)

## Calculate a stationary state with price regulation.
## Both services have the same price and service 2 is oversupplied.
pcss <- sdm2(
  A = list(dst.firm, 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 = function(state) {
    state$p[2] <- state$p[1]
    state
  },
  maxIteration = 1,
  numberOfPeriods = 200,
  depreciationCoef = 0,
  ts = TRUE
)

pcss$p
addmargins(pcss$D, 2)
addmargins(pcss$S, 2)
matplot(pcss$ts.q, type = "l")
matplot(pcss$ts.z, type = "l")
matplot(pcss$ts.p, type = "l")

##
pcss <- sdm2(
  A = list(dst.firm, 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, 50, 50
  ), 3, 3, TRUE),
  names.commodity = c("serv1", "serv2", "labor"),
  names.agent = c("firm", "consumer1", "consumer2"),
  numeraire = "labor",
  policy = list(
    function(state) {
      state$p[1:2] <- sum(state$p[1:2] * c(0.8, 0.2))
      state
    },
    makePolicyMeanValue()
  ),
  maxIteration = 1,
  numberOfPeriods = 1000,
  ts = TRUE
)

pcss$p
addmargins(pcss$D, 2)
addmargins(pcss$S, 2)
addmargins(pcss$DV)
addmargins(pcss$SV)
matplot(pcss$ts.q, type = "l")
matplot(pcss$ts.z, type = "l")
matplot(pcss$ts.p, type = "l")