Question

The country of La la land has an agrarian economy and only produces food on a fixed supply of land. The production of food per person hasn’t increased for a very long time even though better fertilizers have become available. Seeing this an economist tries to understand the country’s predicament using a mathematical model. Production in the model is given by a function that combines land and labor in the following way. Y = AL^0.3xN^0.7 Everything that is produced in the economy is consumed. I.e. C = Y . The economist also finds that the growth ratio of population given by N0/N has the following relationship with nutrition levels, measured by consumption per capita. N0/ N = 0.5 (C/N)^0.5 Note that N0 can be written as Nt+1 and N as Nt for notational purpose. (Show Work)

(a) Using equations in the question, write N0 in terms of the parameters A, L and population N.

(b) On a graph with N on the x-axis and N0 on the y-axis, show the country’s level of population in the long-run. Argue using the graph why this is the level of population.

(c) Compute the level of consumption per capita in the long-run.

Answer 1