Consider the continuous time Solow growth model with population growth but without technological progress, i.e. n > 0 and g = 0. Looking at economic data we nd a negative correlation between income and population growth, that is higher income is associated with lower population growth rates. This problem will ask you to analyze how this affects our model in a simple way. Suppose there is a threshold of capital per effective worker for, below which a country has a population growth of H1 and above which its population grows at rate n2. Mathematically, the following conditions hold: 111 > R2 'n.='n.1 for k ((5 + n2)kT Note that the last two conditions represent inequalities that hold at the threshold level and do NOT represent conditions that hold for every k. (a) Show graphically how the above conditions aect the Solow model. Specically, draw the savings function, the production function and the depreciation and dilution function (the latter includes population growth) all in per-e'iciency-unitsoflabor terms. Also identify clearly all possible steady states (b) For each of the steady states identify if it is (locally) stable or unstable. (c) If the economy starts with a capital stock per worker that is smaller than by, in which steady state will the economy end up? 2 (d) Suppose the country is in the steady state that you identied in (c). What can the country do to reach the steady state with the highest capital stock per worker among those steady states you found in (a)? (e) What is the growth rate of output per worker in the steady state from part (c)? What is it for the steady state the country tries to reach in part (d)