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Let us assume that all economies were at the steady-state in 1820 and the output per capita at time t was described by the following

Let us assume that all economies were at the steady-state in 1820 and the output per capita at time t was described by the following aggregate production function:

yt = At (X/Nt)

where At stands for the aggregate productivity level at time t, X denotes the fixed stock of land used in agriculture and Nt represents the aggregate population size at time t.

a. Derive a relationship between the growth rate of the output per capita from time t to t+1, and the growth rate of the aggregate population from time t to t+1 under the assumptions that productivity grows at a constant rate .

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