- 1 Consider An Economy Described By The Following Cobb Douglas Aggregate Production Function Y F K L K 1 3 2 1 (190.89 KiB) Viewed 110 times
1.) Consider an economy described by the following Cobb- Douglas aggregate production function: Y = F (K, L) =K(1/3)/(2/3) i.) Does this Cobb-Douglas aggregate production function exhibit constant returns to scale? Explain why. ii.) Derive the per-capita Cobb-Douglas production function. iii.) Assuming that the depreciation rate (d) is 4 percent, the population growth (n) is 5 percent, exogenous technological growth (g) is 1 percent, and the savings rate (s) is 18 percent- derive the fundamental Solow growth equation, the steady-state per-capita capital stock (k*) [take out to 3 decimal places in this case), steady-state per-capita output (y*)[take out to 4 decimal places in this case), steady-state per-capita consumption (c*)[take out to 4 decimal places in this case), and finally the golden-rule level of capital accumulation that maximizes consumption (kgold*) [throughout this figure's derivation, again, anytime your intermediary- and final-answers are large decimals, round out to four decimal places] ; all of which-except the golden-rule level of capital-are derived from the convergent steady-state condition of the fundamental Solow growth equation: sf(k) = (d + n)k = iv.) Assume in one year, this economy's savings rate (s) rises to 22 percent-while all else remains equal-and recalculate the steady- state per-capita capital stock (k*), steady-state per-capita output (y*), and steady-state per-capita consumption (c*) (again, for each of your separate calculations; if necessary, round to four decimal places). What do you notice when you compare steady- state per-capita capital (k) and output (y), from the second derivation-where savings (s) equals 22%, to that of the first derivation, when savings (s) equaled 18%?