v52\"! " m' new.\" Problem 1 Consider the Solow-Swan growth model, with a savings rate, 5, a depreciation rate, 5, and a population growth rate, n. The production function is given by: Y = AK + BK1/3H1/3L1/3 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. 0 (a) Express output per person, y =Y/L, as a function of capital per person, k =K/L. 0 (b) Write down an expression for y/ k as a function of k and graph. (Hint: as k goes to innity, does the ratio y/ k approach zero?) 0 (c) Use the production function in per capita terms to write the fundamental equation of the Solow-Swan model. 0 ((1) Suppose rst that SA 8+ n. Draw the savings and depreciation curves. Under these circumstances, will there be positive growth in the long run? Why? 0 (i) If s = 0.32, A = 2, B = 2, 5: 0.22, h*= 50,000 and n = 0.1, the growth rate converges to some value as time goes to infinity. What is this value? 0 (i) For these specific parameters, say that this country has a GDP (Y) value of $ 531 billion. What is the level of consumption? 0 (k) What will be the GDP next year