Dacia and Romalia are two countries with the production function given by the following relationship: f(k) = 6 k^(1/2). Capital to labour ratio in Dacia is twice of that of Romalia. Dacia has a 10% saving rate, 10% population growth rate, and 5% depreciation rate, while Romalia has a 20% saving rate, 10% population growth rate, and 20% depreciation rate.
Compute the following: a) Steady-state capital- labour ratio for each country. Does the initial capital-labour ratio affect the results?
b) Output per worker and consumption per worker for each country.
The given model is solow model .
a) For steady state
sf(k)= (n+ δ) k ...condition for steady state
by putting the values given in the ques , we get
0.1*6 k1/2 = (0.1+0.05)k =(0.15)k
=> k1/2= 4
=> k = 16
sf(k)= (n+ δ) k
0.2*6 k1/2 =(0.2+0.1)k
=> 1.2/0.3 = k1/2
=> k1/2= 4 => k =16
the initial capital ratios have no effect on the steady state capital labour ratios.
b)output per worker is given by Y/L = y =6k1/2= 24
consumption per worker is given by
C/L = (1-s)Y/L which is
c =(1-s)y since consumption is income minus the proportion of income saved.
for Dacia => c= 0.9y
we are given y as 6k1/2 which is 6*4 =24
putting y= 24 , we get
=> c=0.8(24)= 19.2
so output per worker is same while the consumption per worker differs in bothe the countries.
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