Homework answers / question archive / Consider an economy described by the following CobbDouglas aggregate production function: Y = F (K, L) = ^( / ) ^( / ) i

Consider an economy described by the following CobbDouglas aggregate production function: Y = F (K, L) = ^( / ) ^( / ) i

Business

Share With

---

Consider an economy described by the following CobbDouglas aggregate production function:

Y = F (K, L) = ^( / ) ^( / )

i.) Does this Cobb-Douglas aggregate production function exhibit constant returns to scale? Explain why.

ii.) Derive the per-capita (per-worker) Cobb-Douglas production function

iii.) Assuming that the depreciation rate (?) is 9.5 percent, the population growth (n) is 6 percent, exogenous technological growth (g) is 1.5 percent, and the savings rate (s) is 12 percent derive the fundamental Solow growth equation, the steady-state per-capita capital stock (k*) [take out to 3 decimal places in this case], and steady-state per-capita output (y*)[take out to 4 decimal places in this case] 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 20 percent-while all else remains equal-and recalculate the steadystate per-capita capital stock (k*) and steady-state per-capita output (y*). What do you notice when you compare steady-state per-capita capital (k) and output (y), from the second derivation-where savings (s) equals 20%, to that of the first derivation, when savings (s) equaled 12%?