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by Erel Segal Halevi (Submitted: 04/11/2012)

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This is an elaboration of the [land-random model](, that takes differences in income into account.

Citizens gain income from several sources - some depend on land while others do not. Citizens buy land with probability that is directly proportional to their wealth - the rich are more probable to buy land than the poor. Can the Jubilee still help the poor get some land?

Freedom, in Biblical economy, means that every citizen owns a land-plot. Originally, this was achieved by two means:

* Initially, all land was divided into equal plots, and each citizen got a plot;
* Once in 50 years, in the year of Jubilee, all lands returned to the original owners.

This model checks whether it is possible to achieve the goal of Freedom (meaning, every citizen owns a land) even when the initial division is not equal.


There are **num-of-citizens** citizens, and **num-of-lands** land-plots.

Initially, land is divided in a way defined by the **initial-land-division** menu. There are several options:

* random land division - each land goes to a citizen selected at random. This means that some citizens will have no land, while others will have many plots.
* equal land division - each citizen gets a single land plot in turn, until there are no more lands left.
* give all lands to a single citizen (n citizens, where n=1).

At each period, each citizen gains some income. The income comes from several sources:

* A. Work - each citizen gets some salary per period, regardless of land ownership. The salary of a citizen is chosen in the beginning from a log-normal probability distribution (cf. F. Clementi and M. Gallegati, "Pareto's law of income distribution: Evidence for germany, the united kingdom, and the united states," EconWPA, 2005). The parameters of the lognormal distribution are calculated from **income-from-work-mean**, and from **income-from-work-equality**, which is defined as median/mean. Additionally, each period there is a chance that a citizen's income will change - this chance is **income-from-work-mobility**. In case a citizen's income changes, the system will select a new income at random, from the same log-normal distribution.
* B. Agriculture - each land gives its owner a constant income per period.
* C. Rent - each land gives its owner an income that depends on its position - central lands get more rent than peripheral lands. Specifically, the rent from each land is A M (1 - 0.5 ((x / xmax)2 - (y / ymax )2)), where M is **income-from-rent-mean**, and A is a normalization constant.
* D. Welfare - optionally, the government may decide to give a flat income to every citizen (cf. "Citizen's dividend" in Wikipedia).

At each period, each land has some probability of being sold: the **probability-of-deal-per-period** slider. If a land is sold, it is transferred to a citizen picked at random, where the probability of each citizen to be the buyer is proportional to his/her wealth.

After 50 periods (or a different number, set by the **periods-per-jubilee** slider), a Jubilee procedure is performed, as defined by the **jubilee-procedure** menu. There are 3 options:

* no-jubilee - nothing is done;
* jubilee-to-landless - each citizen with no land picks one of the lands that he had in the previous Jubilee (if any), and gets it back.
* jubilee-from-landowners - each citizen with more than one land picks one of the lands that he wants to keep, and returns all other lands to their owners in the previous Jubilee.
* jubilee-to-landless-from-landowners - each land, whose current owner has more than oen land, and whose previous owner has no land, is returned from the current owner to the previous owner.
* jubilee-for-all - each citizen gets all lands that he had in the previous Jubilee.

After the Jubilee, the trade goes on as before. The simulation stops after **last-period** periods. A

lternatively, you can use the **num-of-runs** slider to run the simulation several times, and calculate the mean and std of the number of landless citizens at the last-period. These values will be printed in the output window, as a tab-seperated line.


Choose the number of citizens and lands, the probability of deal per period, the number of periods per Jubilee, the Jubilee procedure, and the value of each income component. Then click **setup**.

Pressing the **go once** button will run a single period.

The wealth of the citizens changes. The color of the citizens changes according to their wealth - wealthier citizens will have brighter colors.

The wealth distribution is shown in the "wealth distribution" plot.

Some lands will be sold to new owners. A directed link points from the original owner to the new owner. The brightness of each land will match the brightness of its new owner.

The land distribution is shown in the "land distribution" histogram and the "landless" plot.

As the model runs, there are more and more links. But at the Jubilee year, some or all lands return to their original owner, so some or all links are removed.

The percentage of deals canceled is shown in the "deals canceled" plot.


When the Jubilee procedure is "jubilee-for-landless", the number of landless citizens decreases in each Jubilee, relative to the previous Jubilee. Over time, all citizens will have land. The land distribution approaches the state of a single land per citizen.

To see this more clearly, set the probability-of-deal to 1.0, and the periods-per-jubilee to 1.

This does not happen for "no-jubilee" or for "jubilee-for-all".


Change the **income-from-work** to 0, and restart. Is it still true that all citizens eventually have land?

Increase the income-from-work gradually. How does this affect the speed in which the system converges?

After convergence, decrease the income-from-work to 0 again. Does this affect the land distribution?

Play with the other income components - **income-from-agriculture**, **income-from-rent** and **income-from-welfare**. Do they have any effect?


Perhaps the model should also include subjective prerefences: some citizens prefer to live in the east, while others prefer to live in the west. etc.

Currently, the land price is ignored - land is just transfered from the seller to the buyer for free. In Biblical times, the land price was calculated as the annual income from the land, times the number of years remaining until the coming Jubilee.


Citizens are turtles. Land-plots are patches. However, since there are usually more patches then turtles, only some of the patches are considered for the model. They are called "land-patches" in the code.

Links are used to link the original owner of a land with its current owner. A cycle, in that graph, means that the relevant owners switched their lands.

A utility function, "one-of-biased", is used to select a buyer: it gets as input an agentset and a reporter, and selects one agent at random, with probability proportional to the value that the reporter reports for it. In our model, the reporter simply returns the wealth of the citizen, so that probability of buying land is proportional to wealth.


If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:
- Segal-the-Levite, Erel (2012). NetLogo Land-Income model.
- Wilensky, U. (1999). NetLogo. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.


Copyright 2012 Erel Segal the Levite.

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