GE (version 0.3.9)

gemResearchDevelopmentIntensity: Some Examples of Market-Clearing Paths Illustrating Research and Development Intensity

Description

Some examples of market-clearing paths illustrating R&D intensity. R&D intensity of a firm is the ratio of expenditures by the firm on R&D to the firm's sales.

Usage

gemResearchDevelopmentIntensity(...)

Value

A market-clearing path.

Arguments

...

arguments to be passed to the function sdm2.

Details

The first example contains two kinds of commodities (namely product and labor) and three economic agents (namely a firm, a R&D center of the firm and a laborer). Since the R&D center does not produce products, the R&D center is regarded as a consumer-type agent in the model. The utility level of the R&D center (that is, the R&D level) will affect the technological progress rate of the firm. In the model, the firm allocates part of its output to the R&D centers for sale according to a given R&D intensity, which is equivalent to allocating part of the firm's sales revenue to the R&D center. At first, the economy is set in steady-state equilibrium without R&D activity. R&D activities begin in the fifth period.

Examples

# \donttest{
#### a 2-by-3 example.
RDIntensity <- 0.3
RDEffectivenessCoefficient <- 0.001

dst.firm <- node_new(
  "prod",
  type = "CD",
  alpha = 2, beta = c(0.5, 0.5),
  "prod", "cc1"
)
node_set(dst.firm, "cc1",
  type = "Leontief", a = 1,
  "lab"
)

dst.RDCenter <- node_new(
  "util",
  type = "CD",
  alpha = 1, beta = c(0.5, 0.5),
  "prod", "lab"
)

dst.laborer <- node_new(
  "util",
  type = "Leontief",
  a = 1,
  "prod"
)

# a function calculating the rate of technological progress according to the level of R&D.
f.TPR <- function(RDLevel) RDEffectivenessCoefficient * RDLevel

f <- function() {
  sdm2(
    A = list(dst.firm, dst.RDCenter, dst.laborer),
    B = matrix(c(
      1, 0, 0,
      0, 0, 0
    ), 2, 3, TRUE),
    S0Exg = matrix(c(
      NA, NA, NA,
      NA, NA, 100
    ), 2, 3, TRUE),
    names.commodity = c("prod", "lab"),
    names.agent = c("firm", "RDCenter", "laborer"),
    numeraire = "prod",
    z0 = c(200, 0, 100),
    policy = list(
      function(time, A, state) {
        if (time >= 5) {
          state$S[1, 2] <- state$S[1, 1] * RDIntensity
          state$S[1, 1] <- state$S[1, 1] * (1 - RDIntensity)
          last.a <- node_set(A[[1]], "cc1")$a
          last.RDLevel <- state$last.z[2]
          technology.progress.rate <- f.TPR(last.RDLevel)
          node_set(A[[1]], "cc1", a = last.a / (1 + technology.progress.rate))
        }

        state
      },
      policyMarketClearingPrice
    ),
    maxIteration = 1,
    numberOfPeriods = 50,
    ts = TRUE
  )
}

ge <- f()
matplot((ge$ts.z), type = "o", pch = 20)
ge$z

## change the R&D intensity.
node_set(dst.firm, "cc1", a = 1)
RDIntensity <- 0.8
ge <- f()
matplot((ge$ts.z), type = "o", pch = 20)
ge$z

## random rate of technological progress.
set.seed(1)
RDIntensity <- 0.3
node_set(dst.firm, "cc1", a = 1)
f.TPR <- function(RDLevel) max(0, rnorm(1, RDEffectivenessCoefficient * RDLevel,
  sqrt(RDEffectivenessCoefficient * RDLevel)))
ge <- f()
matplot((ge$ts.z), type = "o", pch = 20)
ge$z

## two firms with different R&D intensity.
node_set(dst.firm, "cc1", a = 1)
RDIntensity1 <- 0.1
RDIntensity2 <- 0.05
RDEffectivenessCoefficient <- 0.002

dst.firm2 <- Clone(dst.firm)
dst.RDCenter2 <- Clone(dst.RDCenter)
ge <- sdm2(
  A = list(dst.firm, dst.RDCenter, dst.laborer, dst.firm2, dst.RDCenter2),
  B = matrix(c(
    1, 0, 0, 1, 0,
    0, 0, 0, 0, 0
  ), 2, 5, TRUE),
  S0Exg = matrix(c(
    NA, NA, NA, NA, NA,
    NA, NA, 200, NA, NA
  ), 2, 5, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm1", "RDCenter1", "laborer", "firm2", "RDCenter2"),
  numeraire = "prod",
  z0 = c(200, 0, 200, 200, 0),
  policy = list(
    function(time, A, state) {
      if (time >= 5) {
        state$S[1, 2] <- state$S[1, 1] * RDIntensity1
        state$S[1, 1] <- state$S[1, 1] * (1 - RDIntensity1)
        last.a1 <- node_set(A[[1]], "cc1")$a
        last.RDLevel1 <- state$last.z[2]
        technology.progress.rate1 <- RDEffectivenessCoefficient * last.RDLevel1
        node_set(A[[1]], "cc1", a = last.a1 / (1 + technology.progress.rate1))

        state$S[1, 5] <- state$S[1, 4] * RDIntensity2
        state$S[1, 4] <- state$S[1, 4] * (1 - RDIntensity2)
        last.a2 <- node_set(A[[4]], "cc1")$a
        last.RDLevel2 <- state$last.z[5]
        technology.progress.rate2 <- RDEffectivenessCoefficient * last.RDLevel2
        node_set(A[[4]], "cc1", a = last.a2 / (1 + technology.progress.rate2))
      }

      state
    },
    policyMarketClearingPrice
  ),
  maxIteration = 1,
  numberOfPeriods = 50,
  ts = TRUE
)

matplot((ge$ts.z), type = "o", pch = 20)
ge$z

## Assume that the R&D center is owned by the government and
## receives revenue through taxation on firms.
## The technologies developed by the R&D center are public goods.
node_set(dst.firm, "cc1", a = 1)
RDIntensity <- 0.1
RDEffectivenessCoefficient <- 0.002

dst.firm2 <- Clone(dst.firm)

ge <- sdm2(
  A = list(dst.firm, dst.RDCenter, dst.laborer, dst.firm2),
  B = matrix(c(
    1, 0, 0, 1,
    0, 0, 0, 0
  ), 2, 4, TRUE),
  S0Exg = matrix(c(
    NA, NA, NA, NA,
    NA, NA, 200, NA
  ), 2, 4, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm1", "RDCenter", "laborer", "firm2"),
  numeraire = "prod",
  z0 = c(200, 0, 200, 200),
  policy = list(
    function(time, A, state) {
      if (time >= 5) {
        last.RDLevel <- state$last.z[2]
        technology.progress.rate <- RDEffectivenessCoefficient * last.RDLevel

        state$S[1, 2] <- (state$S[1, 1] + state$S[1, 4]) * RDIntensity
        state$S[1, 1] <- state$S[1, 1] * (1 - RDIntensity)
        state$S[1, 4] <- state$S[1, 4] * (1 - RDIntensity)
        last.a1 <- node_set(A[[1]], "cc1")$a
        node_set(A[[1]], "cc1", a = last.a1 / (1 + technology.progress.rate))

        last.a2 <- node_set(A[[4]], "cc1")$a
        node_set(A[[4]], "cc1", a = last.a2 / (1 + technology.progress.rate))
      }

      state
    },
    policyMarketClearingPrice
  ),
  maxIteration = 1,
  numberOfPeriods = 30,
  ts = TRUE
)

matplot((ge$ts.z), type = "o", pch = 20)
ge$z
# }