Problem 1 Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate, 8, and a population growth rate, n. The production function is given by: Y = AK + BK/3 H1/3 L1/3 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb-Douglas production function. (a) Express output per person, y =Y/L, as a function of capital per person, k =K/L. (b) Write down an expression for y/k as a function of k and graph. (Hint: as k goes to infinity, does the ratio y/k approach zero?) (c) Use the production function in per capita terms to write the fundamental equation of the Solow-Swan model. (d) Suppose first that SA < 8+ n. Draw the savings curve and the depreciation curve. What number does the savings curve approach as k goes to zero? As k goes to infinity, the savings curve approaches a number: what number is that? Is it zero? (e) Under these parameters, will there be positive growth in the long run? (Remember that A and B are constants). Why? (f) What will be the growth rate of consumption and investment under these parameters? (g) Imagine that we have two countries with the same parameters (same A, B, s, 8, and n). One of them is rich and the other is poor. Which one of the two will grow faster? Why? Will those two countries eventually catch up?