R/MWG_Varian_examples.R

In CGE: Computing General Equilibrium

#' @export

# MWG_exchange_quasiLinear_2_2
Example.MWG.15.B.2 <- function(p0 = c(1, 0.3)) {
  r <- 2^(8 / 9) - 2^(1 / 9)

  MWG_quasi_linear_demand_1 <- function(p, w) { # only for case 'MWG_exchange_quasiLinear_2_2'
    d <- rbind(0, 0)
    w <- w / p[1]
    p <- p / p[1] # normalize wealth and prices
    d[2] <- (1 / p[2])^(1 / 9)
    if (d[2] * p[2] > w) {
      d[2] <- w / p[2]
      d[1] <- 0
    } else {
      d[1] <- w - d[2] * p[2]
    }

    d
  }

  MWG_quasi_linear_demand_2 <- function(p, w) { # only for case 'MWG_exchange_quasiLinear_2_2'
    d <- rbind(0, 0)
    w <- w / p[2]
    p <- p / p[2]
    d[1] <- (1 / p[1])^(1 / 9)
    if (d[1] * p[1] > w) {
      d[1] <- w / p[1]
      d[2] <- 0
    } else {
      d[2] <- w - d[1] * p[1]
    }

    d
  }

  sdm(
    A = function(state) {
      result1 <- MWG_quasi_linear_demand_1(state$p, state$w[1])
      result2 <- MWG_quasi_linear_demand_2(state$p, state$w[2])
      cbind(result1, result2)
    },
    B = diag(2),
    S0Exg = matrix(c(
      2, r,
      r, 2
    ), 2, 2, TRUE), # Exogenous supplies
    GRExg = 0,
    p0 = p0,
    tolCond = 1e-7
  )
}


#' @export

# Varian, H. R.(1992) Microeconomic Analysis... P351-353; (MWG) Mas-Colell, A., Whinston, M. and Green, J. (1995) Microeconomic Theory... P542, 15.C.2.
# case 'CD_3_3'
# column 1: firm (say, wheat producer);
# column 2: firm owner;
# column 3: laborer;
# row 1: wheat;
# row 2: ownership of firm (or land, see Varian (1992, P353));
# row 3: labor (or leisure);
Example.Varian.P352 <- function(agent.number = 3) {
  if (agent.number == 3) {
    sdm(
      A = function(state) {
        a <- 0.5
        alpha <- rep(1, 3)
        Beta <- matrix(c(
          0, a, a,
          0.5, 0, 0,
          0.5, 1 - a, 1 - a
        ), 3, 3, TRUE)

        CD_A(alpha, Beta, state$p) # Demand functions of agents constitute an input coefficient matrx.
      },
      B = diag(3),
      S0Exg = matrix(c(
        NA, NA, NA,
        NA, 1, NA,
        NA, NA, 1
      ), 3, 3, TRUE), # Exogenous supplies,
      GRExg = 0,
      tolCond = 1e-10
    )
  } else {
    sdm(
      A = function(state) {
        a <- 0.5
        alpha <- rep(1, 2)
        Beta <- matrix(c(
          0, a,
          0.5, 0,
          0.5, 1 - a
        ), 3, 2, TRUE)

        CD_A(alpha, Beta, state$p)
      },
      B = matrix(c(
        1, 0,
        0, 1,
        0, 1
      ), 3, 2, TRUE),
      S0Exg = matrix(c(
        NA, NA,
        NA, 1,
        NA, 1
      ), 3, 2, TRUE),
      GRExg = 0,
      tolCond = 1e-10
    )
  }
}


#' @export

# MWG_exchange_CES_2_2, MWG, P541
Example.MWG.Exercise.15.B.6 <- function(p0 = c(1, 2)) {
  sdm(
    A = function(state) {
      alpha <- c(1, 1)
      Beta <- matrix(c(
        1, (12 / 37)^3,
        (12 / 37)^3, 1
      ), 2, 2, TRUE)

      CES_A(c(-2, -2), alpha, Beta, state$p)
    },
    B = diag(2),
    S0Exg = diag(2),
    GRExg = 0,
    p0 = p0,
    priceAdjustmentVelocity = 0.3,
    tolCond = 1e-10
  )
}

#' @export

# MWG_exchange_CD_2_2, MWG, 15.B.1, P519
Example.MWG.15.B.1 <- function(a = 0.1,
                               S0Exg = matrix(c(1, 2, 2, 1), 2, 2, TRUE)) {
  sdm(
    A = function(state) {
      alpha <- c(1, 1)
      Beta <- matrix(c(
        a, a,
        1 - a, 1 - a
      ), 2, 2, TRUE)

      CD_A(alpha, Beta, state$p)
    },
    B = diag(2),
    S0Exg = S0Exg,
    GRExg = 0
  )
}

#' @export

# MWG_exchange_Leontief_Leontief(CD)_2_2, MWG, P541, 15.B.9
Example.MWG.Exercise.15.B.9 <- function(S0Exg = matrix(c(
                                          30, 0,
                                          0, 20
                                        ), 2, 2, TRUE)) {
  sdm(
    A = function(state) {
      result1 <- c(1, 1)
      result2 <- c(1, state$z[2])
      cbind(result1, result2)
    },
    B = diag(2),
    S0Exg = S0Exg,
    GRExg = 0,
    z0 = c(1, 1)
  )
}




#' @export

# labor_CD_3_4, Varian (1992), P357, 18.2.
# column 1: wheat producer;
# column 2: iron producer;
# column 3: laborer 1;
# column 4: laborer 2;
# row 1: wheat;
# row 2: iron;
# row 3: labor;
Example.Varian.Exercise.18.2 <- function() {
  sdm(
    A = function(state) {
      alpha <- c(2, 3, 1, 1)
      Beta <- matrix(c(
        0, 0, 0.4, 0.5,
        0, 0, 0.6, 0.5,
        1, 1, 0, 0
      ), 3, 4, TRUE)

      CD_A(alpha, Beta, state$p)
    },
    B = matrix(c(
      1, 0, 0, 0,
      0, 1, 0, 0,
      0, 0, 1, 1
    ), 3, 4, TRUE),
    S0Exg = {
      S0Exg <- matrix(NA, 3, 4)
      S0Exg[3, 3] <- 10
      S0Exg[3, 4] <- 10
      S0Exg
    },
    GRExg = 0
  )
}