Goods and services are produced in this economy using the following Cobb-Douglas production function, Y, = KF(HL)" % a (0,1) H is the measure of the average level of human capital (e.g., average years of schooling in the workforce. For the Cobb-Douglas case as given above: (i) write down Solow's Fundamental Equation (as defined in class), (ii) using a diagram, show how we obtain the steady state per worker capital stock, and (ii1) derive an expression for the steady state per worker capital stock. C. The South African Health Ministry has become increasingly worried about the growing AIDS epidemic in that country. You have been rushed in to provide the Ministry with advice on the likely impact of AIDS on South Africa's long-run economic performance. After careful study, you conclude that AIDS will impact the Conomy in fwo ways: (1) South Africa will experience a dramatic reduction in the population growth rate due mainly to higher child mortality rates and shorter average life expectancy. (i1) South Africa will experience over time a decrease in the average number of years of schooling in the population. There are at least two reasons for this: a. There is likely to be a significant increase in the number of orphans {whose parents have died of AIDS). These orphans are unlikely to be given access to much schooling opportunities. b. Because of the mode of transmission and long gestation period, AIDS tends to kill off the segment of the adult population that is relatively yvoung and which in recent times has had the most access to educational opportunities. Using a diagram to support vour analysis, present the Health Ministry with a coherent explanation of the likely impact of AIDS on South Africa's steady state per capita income. d. A prominent Economist interjects in the middle of your presentation. He offers the following comments: \"l don't think we need to do anything about the AIDS epidemic at all! In fact, my own research finds that AIDS will raise the long-run level of per worker income in South Africa.\" Is it possible that the AIDS epidemic could actually raise South Africa's long-run level of per worker income? Explain vour answer using a diagram. Suppose you concluded that his analysis of the situation could be correct (note: this should not be taken as a hint! It could well be a red herring!), do you agree nevertheless with his policy recommendation (1.., the part about us having no need to do anything about the epidemic)? Explain