gemResearchDevelopmentIntensity {GE}

Some Examples of Spot Market Clearing Paths Illustrating Research and Development Intensity

Description

Some examples of spot market clearing paths (alias instantaneous equilibrium 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(...)

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.

Value

A spot market clearing path.

Examples

#### 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