Consider the following Malthusian model.

Suppose that the relationship between income per capita (y) and the growth rate of the population (L n) is given by the equation:

Ln = y - 100.

Suppose that output is produced using labor and land, according to the equation Y = L 1/2 X1/2, where X is the quantity of land. Assume that X = 1,000,000.

a. Draw a graph with y on the horizontal axis and L n on the vertical axis, showing the relationship between income per capita and population growth.

b. Derive the relationship between population, L, and income per capita, y. (Hint:

Remember that y = Y/L.) Sketch this relationship on a graph with L on the vertical axis and y on the horizontal axis.

c. Use the equations you have derived to compute the steady-state values of L and y.