gemRobinson_3_2 {GE}

A Robinson Crusoe Economy

Description

Compute the general equilibrium of a Robinson Crusoe economy.

Usage

gemRobinson_3_2(dstl, endowment)

Arguments

dstl

the demand structure tree list.

endowment

the endowment 3-vector. The endowment of the product is a non-negative number. The endowments of labor and land are positive numbers.

Details

A general equilibrium model with 3 commodities (i.e. product, labor, and land) and 2 agents (i.e. a firm and a consumer). The numeraire is labor.

Value

A general equilibrium.

References

http://essentialmicroeconomics.com/ChapterY5/SlideChapter5-1.pdf

http://homepage.ntu.edu.tw/~josephw/MicroTheory_Lecture_11a_RobinsonCrusoeEconomy.pdf

Examples

#### a general equilibrium model with 2 basic commodities (i.e. labor and land)
#### and 1 agent (see the first reference)
dst.Robinson <- node_new("util",
  type = "CD", alpha = 1, beta = c(0.5, 0.5),
  "prod", "lab"
)
node_set(dst.Robinson, "prod",
  type = "CD", alpha = 8, beta = c(0.5, 0.5),
  "lab", "land"
)

node_plot(dst.Robinson)

ge <- sdm2(
  A = list(dst.Robinson),
  names.commodity = c("lab", "land"),
  names.agent = c("Robinson"),
  B = matrix(0, 2, 1),
  S0Exg = matrix(c(
    12,
    1
  ), 2, 1, TRUE),
  numeraire = "lab"
)
ge


## the same economy as above
dst.Robinson <- node_new("util",
  type = "CD", alpha = 1, beta = c(0.5, 0.5),
  "prod", "lab"
)
dst.firm <- node_new("output",
  type = "CD", alpha = 8, beta = c(0.5, 0.5),
  "lab", "land"
)

dstl <- list(dst.firm, dst.Robinson)

ge <- gemRobinson_3_2(dstl, endowment = c(0, 12, 1))
ge

## another example (see the second reference)
dst.firm$alpha <- 1

ge <- gemRobinson_3_2(dstl, endowment = c(3, 144, 1))
ge

#### a Robinson Crusoe economy with labor and two types of land
dst.Robinson <- node_new("util",
  type = "CD", alpha = 1, beta = c(0.5, 0.5),
  "prod1", "prod2"
)
node_set(dst.Robinson, "prod1",
  type = "CD", alpha = 1, beta = c(0.2, 0.8),
  "lab", "land1"
)
node_set(dst.Robinson, "prod2",
  type = "CD", alpha = 1, beta = c(0.8, 0.2),
  "lab", "land2"
)
node_plot(dst.Robinson)

dstl <- list(dst.Robinson)

ge.3_1 <- sdm2(dstl,
  names.commodity = c("lab", "land1", "land2"),
  names.agent = c("Robinson"),
  B = matrix(0, 3, 1),
  S0Exg = matrix(c(
    100,
    100,
    100
  ), 3, 1, TRUE),
  numeraire = "lab"
)
ge.3_1

#### the same economy as above
ge.5_3 <- sdm2(
  A = list(
    dst.firm1 = node_new("output",
                         type = "CD", alpha = 1, beta = c(0.2, 0.8),
                         "lab", "land1"
    ),
    dst.firm2 = node_new("output",
                         type = "CD", alpha = 1, beta = c(0.8, 0.2),
                         "lab", "land2"
    ),
    dst.Robinson = node_new("util",
                            type = "CD", alpha = 1, beta = c(0.5, 0.5),
                            "prod1", "prod2"
    )
  ),
  names.commodity = c("prod1", "prod2", "lab", "land1", "land2"),
  names.agent = c("firm1", "firm2", "Robinson"),
  B = {
    B <- matrix(0, 5, 3)
    B[1, 1] <- B[2, 2] <- 1
    B
  },
  S0Exg = {
    S0Exg <- matrix(NA, 5, 3)
    S0Exg[3:5, 3] <- 100
    S0Exg
  },
  numeraire = "lab"
)
ge.5_3