Let us the Malthusian model to describe the situation in Avataria. In particular, the relationship between its income per capita (y) and the growth rate of the population (AL) is given by equation ALIL = y 15. Suppose its output is produced using labor and capital according to equation Y = 6*{K)m(L)m. (a) Draw a graph with y on the horizontal axis and ALIL on the vertical axis, showing the relationship between income per capita (y) and population growth in Avataria. (b) Assume K = 625. Using the formula for the total output, derive the relationship between population (L) and income per capita (y). (Hint: remember that y = YIL and k = KIL.) Sketch this relationship on a graph with L on the vertical axis and y on the horizontal axis. (c) Use the equations you derived to compute the steady-state values ofL and y. (d) Suppose that due to increased love for kids, the population growth accelerates so that its new relationship with the income per capita becomes ALIL = y 10. Calculate new values of the steady-state values of L and y