Question

3)- Consider an economy with the production function: Y=4K0.6 No.4, in the framework of the Solow Model, with usual definitions. Suppose, the labor force is growing at 1% a year, depreciation rate is 4%, and saving rate is 20%. (Total 17 points) a)- Find the steady state equilibrium of per worker levels of capital, output, and consumption. (4) b)- Find the golden rule saving rate, and golden rule per worker levels of output, capital, and consumption. (4) c)- How much are the growth rates of total output and total capital, in the steady state equilibrium. Why? (2) d)- Explain why or why not it is advisable to promote more saving in this economy. (1) e)- Suppose the economy is initially in the steady state equilibrium, draw a graph showing the original equilibrium and the impact of a sudden exit of a big portion of the population out of the country. Explain the changes. Draw the time line for per worker out to show the impacts over time. (6)

Answer 1

at steady k= (16) Y = 4K 6 No 4 narol, 8=:of S=2 a) State sy= (Sth) k y = YIN = 4 •6 80 •2 (4) Ro6= .05 ² •87.05 = 804 Ve4 = 1024 y = 4 ߺ6 64 C = (-S) 4 = + 8 x6 = 6] 25 mg donuod b) at Golden Rule MPK = nto MPK = aylak 2.4 k-4 = 105 d=31-6 ka= (4.4/.05)4 4 (06) ko4

80 at Steady state sy= (8+n) k SG=_oš Ro4 4. SQ = (05/4) (204/05) •4/04 204/4 = .6 SG = 60 % Ang K 9= 15962.58 YG = 4 kg 6 = 13 30 15 CG (1-59) 992 4 YG 532 And

-) gy= n = 49. 1% gk = n = d) as current saving rate < Golden Rule level 80 gt is advisable to promote more swing, Bir consn per worker is Max in Golden state.

It's mandatory to solve first Four parts mainly