Consider the Solow-Swan growth model, with a savings rate, 5, a depreciation rate, 6, and a population growth rate, in. The production function is given by Y = AK + BK3/4L1/4 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. - {i} Does this production function exhibit constant returns to scale? Explain why. - {ii} Does it exhibit diminishing returns to physical capital? Explain why. - {iii} Express output per person, y = E, as a function of capital per person, it = f. - {iv} Write down an expression fory/k as a function of k and graph. (Hint: as k goes to infinity, does the ratio y/k approach zero?) - {v} Use the production function in per capita terms to write the fundamental equation of the Solow-Swan model. - {vi} Suppose first that 5A 6 + :1. Draw the savings and depreciation curves, making sure to label the steady state level of capitallif it exists}. Under these circumstances, will there be positive growth in the long run? Why? - {x} lfs =0.4, A =2, 3 =1, 6: .25, and :1 =0.10, the growth rate converges to some value as time goes to innity. What is this value