A. Consider a Malthusian economy. Suppose that: . The production technology is: yt = [(AX)/L(]"' ; a E (0, 1). . The utility function of an adult of generation t is: ut = yln n, + (1 - y)Inc; ye (0, 1). . The cost of raising a child isp in term of the consumption good 1. Derive the dynamical system of population, Le, and income per capita, y: Lt+1 = $(L.; A); yt+1 = 2 (yt ) . 2. What is the steady-state equilibrium of population and income per capita as a function of the level of technology, A? Consider two economies, A and B in a Malthusian steady state equilibrium 3. If the level of technology in economy B is higher, would its income per capita be higher? 4. Suppose that due to larger body size in countryB the cost of raising children in country B, pB > p4. Would country B be poorer (in the steady-state) than country A, due to this larger cost of raising