Question

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.

Answer 1

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

for Dacia

0.1*6 k^1/2 = (0.1+0.05)k =(0.15)k

=> k^1/2= 4

=> k = 16

for Romalia

sf(k)= (n+ δ) k

0.2*6 k^1/2 =(0.2+0.1)k

=> 1.2/0.3 = k^1/2

=> k^1/2= 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 =6k^1/2= 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 6k^1/2 which is 6*4 =24

putting y= 24 , we get

c=0.9*24= 21.6

for Romalia

c =(1-s)y

=> c=0.8(24)= 19.2

so output per worker is same while the consumption per worker differs in bothe the countries.