ISI 2010

[s]

Consider a Solow model with the production function Y = K^1/2L^1/2, where Y ,
K and L are levels of output, capital and labour, respectively. Suppose, 20% of
income is saved and invested. Assume that the rate of growth of labour force,
that is,(dL/dt/L)= 0.05.
(a) Find the capital-labour ratio, rate of growth of output, rate of growth of
savings and the wage rate, in the steady state growth equilibrium.
(b) Suppose that the proportion of income saved goes up from 20% to 40%.
What will be the new steady state growth rate of output?
(c) Is the rate of growth of output in the new steady state equilibrium different
from that obtained just before attaining the new steady state (after
deviating from the old steady state)? Explain.

(a)capital labour ratio=k=16
rate of growth of output=.05
rate of growth of savings=.05
wage rate=2

(b)new steady state growth rate of output doesnt change as dY/dt/Y doesnt depend on s but for part (c) after deviation from steady state and before attaining new one rate of growth of output rises...but eventually becomes 0.05 at new steady state
can someone please confirm the answers..

[ritu]

hi s:)
i am also getting the same answers as yours....just tell me one thing that how u calculated savings rate.....m confused that whether it should be 0.20 itself or .05 as u said?????????

[s]

hi ritu

savings rate is 0.20 but they hav asked for rate of growth of savings which is (dS/dt)/S...Note S=savings amount whereas s=savings rate...
so S=sY=0.2Y
dS/dt=0.2dY/dt

Y=K^1/2L^1/2=K(t)^1/2L(t)^1/2
so dY/dt=[1/2*(K/L)^1/2*dL/dt + 1/2*(L/K)^1/2*dK/dt ].....(check for urself)

now find out (dY/dt)/Y u'l get it as equal to n = 0.05 this is because at steady state all variables in model grow at the same rate which is n

thus (dS/dt)/S = 0.2 (dY/dt)/0.2Y = (dY/dt)/Y = 0.05
thats how i got it

:)

[Ram]

Hi,
 
   I am from non economics background and now I am preparing for the MA Economics entrance entrance exams. can you plz explain the answers how you get those??Thanks in advance...

[s]

hi Ram,

first find out from the production function the rate at which per capita capital accumulates, ie dk/dt= 0.2k^1/2-0.05k

at steady state dk/dt=0 so K/L=16

next find out dY/dt/Y which is n=0.05 (shown in my previous post)

for parts (b) and (c) u should read solow growth model from any good macroeconomics book (you may read Mathematical Economics by chiang wainwright)

[Rajat]

Can someone please explain how capital labour ratio is 16 ?
I got the ratio as 16 but only by assuming that depreciation is zero.

Is there a better method ?

[Rajat]

Can Someone please help here

[dhruv]

No, we have to assume depreciation = 0. Here, capital/capita depreciates by the rate of growth of labour force which should be equal to rate of growth of capital/capita, i.e., savings rate or investment.

What we have to keep in mind is that at steady state something should remain constant. Here, it is per capita output and capital.

If depreciation is not given, then it implies that capital itself doesn't depreciates which corresponds to the theory of growth where we were trying to find how economies maintain constant growth of output, but here instead of technology we have zero depreciation and labour growth rate to maintain constant growth. Maybe, technology growth rate just offsets the depreciation rate.