Question

Suppose an economy described by the Solow model has the following production function:

1/2 1/2 Y=K (LE) .

a. For this economy, what is f(k)?

b. Use your answer to part (a) to solve for the steady-state value of y as a function of s, n, g, and ?.

c. Two neighboring economies have the above production function, but they have different parameter values. Atlantis has a saving rate of 28 percent and a population growth rate of
1 percent per year. Xanadu has a saving rate of 10 percent and a population growth rate of 4 percent per year. In both countries, g = 0.02 and ? = 0.04. Find the steady-state value of

d. y for each country.

Answer 1

solution: The given production function is as follows: Y= k 1/2 LE 1/2 (a) To calculate fCk) divide the production function by LE Y= killa LE/ K'la Ell .. Y LE LE Ya fck) = 12 Lella = f(K) = kila Here, fck) is output for worker and Kis capital for worker, (6) At the steady state Akzo The steady state is calculatod as follows: Bk = sy=Cotnag k. O=sk 1/2 = (8thtg]k, 'sk'l2 - (OthigJk. k cornto) kih S - cs Scanned with CamScanner

S The steady state value of xin Atlantis k'la (athtg) +979) Y is! Cd tntg) 0.28 conut (-0025 tool 17- 9.33 The steady state value of y=xander is: Y=S cdtntg) 010 Toout '2002) + 0.04) Y- ly- lido CS Scanned with CamScanner