Consider a Malthusian model in which the equation that relates the population growth rate to income per capita is L

n = y - 100 100 .

Let X be the total quantity of land in the economy, which is fixed. Let x be the quantity of land per capita. The function that relates land per capita and income per capita is y = Ax, where A is a measure of productivity.

a. Suppose that A is constant. What will the steady-state level of income per capita be?

b. Now suppose that A grows at a rate of 10%

per year (that is, Â = 0.1). What will be the steady-state level of income per capita?

Explain what is going on