Relaxing the Malthusian Assumptions (24 points) Let us consider a simple Malthusian model with no productivity growth in which Assumption 1 holds but Assumption 2 is reversed in the sense that the income per capita has a negative effect on population growth. Under which condition a steady-state solution still exists? What would happen over time to such an economy with an initial level of income per capita below its steady-state value? What would happen over time to such an economy with an initial level of income per capita above its steady-state value? What would happen over time to such an economy initially located at its steady-state solution and experiencing a one-time increase in productivity? If Assumption 1 is also reversed in the sense that a larger population raises the income per capita, then what would happen in the short-run and in the long-run to an economy (with Assumption 2 reversed) initially located at its steady-state solution and experiencing a one-time increase in productivity? Explain and use graphs. (24 points)