04 Jun Question Malthusian Model Imagine you are the ruler of a kingdom
Question
Malthusian Model
Imagine you are the ruler of a kingdom in the middle ages. Using some census data that the scholars of your kingdom
collected, you found out that the births and deaths rates depend in the individual consumption in the following way
1
gB (c) = 2c 2
and
1
gD (c) = c 2 .
Also, the scholars inform you that the population of tomorrow and today ratio follows the pattern
N
= H(c) = gB (c) + gD (c).
N
In addition, the scholars were able to nd the production function that depends only in the land of the kingdom and the
population in it
1
1
Y = zF (K, L) = zK 2 L 2 .
a) Write the dynamic Malthusian key formula of the model that links the population of today with the population of
tomorrow. This is, write a function of N depending only in N , taking as given parameters technology z and land K.
b) You acknowledge that your lineage has ruled that kingdom almost an eternity with the same land and the same
technology. Studying old manuscripts of your kingdom, you nd out that the amount of land in the kingdom is about
100 units and the technology factor is 1. Find the population, the aggregate production, the aggregate consumption,
the land-per-capita, and the consumption-per-capita of your kingdom. Graph also the dynamic Malthusian key formula
and explain how to nd the population of your kingdom.
c) An empire across the mountains is plotting the slow downfall of your kingdom. In order to do this, they poured salt
all over your agricultural lands for months. This contracted the productivity of your lands in half ( =
z
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