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 a and land grows at a constant rate b (5 points) Compute the average annual growth rates of the Canadian GDP per capita from 1700 to 1830 and the average annual growth rates of the Canadian population from 1700 to 1830. (5 points) Using the equation obtained in question a. and the average annual growth rates found in question b., derive the average annual growth rate of productivity from 1700 to 1830 a under the assumption that the aggregate stock of land used in agriculture remained constant: b = 0. (5 points) Using the equation obtained in question a. and the average annual growth rates found in question b., derive the average annual growth rate of land E from 1700 to 1830 under the assumption that productivity remained constant: a = 0. (5 points) Using the equation obtained in question a. and the average annual growth rates found in question b., derive the average annual growth rate of productivity and land from 1700 to 1830 under the assumption that they both grew at the same rate: a= b. (5 points)

II. Estimating Land and Productivity Growth. (25 points) Let us assume that before 1830 the Canadian output per capita at time t was described by the following aggregate production function: yt = ZtvXt/Nt where Zt stands for the aggregate productivity level at time t, Xt denotes the stock of land used in agriculture at time t and Nt represents the aggregate population at time t. a. Derive a relationship between the growth rate of the output per capita from time tto t+1, an the growth rate of the aggregate population from time t to t+1 under the assumptions that productivity grows at a constant rate a and land grows at a constant rate b. (5 points) Download the historical statistics Angus Maddison's Historical Statistics of the World Economy: 1 2008 AD available from to answer question b.: b. Compute the average annual growth rates of the Canadian GDP per capita from 1700 to 183 and the average annual growth rates of the Canadian population from 1700 to 1830. (5 points) c. Using the equation obtained in question a. and the average annual growth rates found in question b., derive the average annual growth rate of productivity from 1700 to 1830 a unde the assumption that the aggregate stock of land used in agriculture remained constant: b = (5 points) d. Using the equation obtained in question a. and the average annual growth rates found in question b., derive the average annual growth rate of land b from 1700 to 1830 under the assumption that productivity remained constant: a = 0. (5 points) e. Using the equation obtained in question a. and the average annual growth rates found in question b., derive the average annual growth rate of productivity and land from 1700 to 1830 under the assumption that they both grew at the same rate: a = b. (5 points)