gemOLG_Land_4_3: An Overlapping Generations Model with Land

Description

Some examples of an overlapping generations model with land.

Usage

gemOLG_Land_4_3(...)

Arguments

...: arguments to be passed to the function sdm2.

Details

In this model, consumers live for two periods. Age2 owns a unit of land and age1 owns a unit of labor. Here the land use rights and land ownership are regarded as two commodities. Age2 gets land rent by selling land use rights to the firm. Then land ownership is sold to age1. Age1 saves by purchasing land ownership.

Here, the ratio of land rent to wage (denoted as xi) is determined by the production function. No matter what the saving rate of age1 is, and at what price the land ownership is transferred to age1, the consumption ratio of age2 and age1 will not be less than xi.

When the consumer's intertemporal utility function is min(c1, c2), the intertemporal substitution elasticity is 0, and each consumer desires the same amount of consumption in the two periods. It can also be assumed that the consumer's intertemporal substitution elasticity is close to 0 rather than exactly zero.

If xi>1, then this economy will inevitably have efficiency loss (dynamic inefficiency). In this case, in order to achieve the optimal allocation, not only age2 should give land to age1 for free, but age2 also needs to distribute part of the land rent to age1. However, age2 has no incentive to do so.

References

Rhee, Changyong (1991) Dynamic Inefficiency in an Economy with Land. Review of Economic Studies. 58(4), pp:791-797.

Examples

Run this code

# \donttest{
saving.rate <- 0.001
ratio.saving.consumption <- saving.rate / (1 - saving.rate)

dst.firm <- node_new(
  "prod",
  type = "CD", alpha = 5,
  beta = c(1 / 6, 2 / 6, 3 / 6),
  "lab", "prod", "land.use.rights"
)

dst.age1 <- node_new(
  "util",
  type = "FIN",
  rate = c(1, ratio.saving.consumption),
  "prod", "land.ownership"
)

dst.age2 <- node_new(
  "util",
  type = "Leontief", a = 1,
  "prod"
)

ge <- sdm2(
  A = list(
    dst.firm, dst.age1, dst.age2
  ),
  B = matrix(c(
    1, 0, 0,
    0, 0, 0,
    0, 0, 0,
    0, 0, 0
  ), 4, 3, TRUE),
  S0Exg = matrix(c(
    NA, NA, NA,
    NA, 1, NA,
    NA, NA, 1,
    NA, NA, 1
  ), 4, 3, TRUE),
  names.commodity = c("prod", "lab", "land.use.rights", "land.ownership"),
  names.agent = c("firm", "age1", "age2"),
  numeraire = "lab"
)

ge$p
ge$D
ge$DV
ge$S
ge$SV

## Change the saving-consumption ratio.
dst.age1$rate <- c(1, ratio.saving.consumption = 99)

ge <- sdm2(
  A = list(
    dst.firm, dst.age1, dst.age2
  ),
  B = matrix(c(
    1, 0, 0,
    0, 0, 0,
    0, 0, 0,
    0, 0, 0
  ), 4, 3, TRUE),
  S0Exg = matrix(c(
    NA, NA, NA,
    NA, 1, NA,
    NA, NA, 1,
    NA, NA, 1
  ), 4, 3, TRUE),
  names.commodity = c("prod", "lab", "land.use.rights", "land.ownership"),
  names.agent = c("firm", "age1", "age2"),
  numeraire = "lab"
)

ge$p
ge$D
ge$DV
ge$S
ge$SV
# }