4 Mathematical Malthusian Model This question is about determining if the Malthusian trap still exists when the production function has increasing returns to scale. Consider a slightly different production function from the one we had in the Malthusian model in class. Y, = F(AX, L) = (AX)* (L,)? where A > () is the technological level, X > 0 is the amount of land, @ > 0 and 1 > > 0. (In the slides' model, 3 =1 . In this question, we only impose that 1 > # > 0 and a > 0.) 1. For what values of 3 does the production function have decreasing, constant, and increasing returns to scale? (your answer can be a function of any other parameter A, X, if needed) (5 points) For what values of 5 does the production have decreasing, constant, and increasing marginal product of labor? (your answer can be a function of any other parameter A, X, if needed) (5 points) With this production function, the evolution of income per capita in the Malthusian model B1 would be given by yi:1 = w(y) = (%) (y;)?. Draw the function w(y;) together with a 45-degree line. Show graphically that there is a unique stable steady-state where income per capita is constant. hint: remember that 5