Question

c. Assume that neither country experiences population growth or technological progress and that 6 percent of capital depreciates each year. Assume further that country A saves 15 percent of output each year and country B saves 23 percent of output each year. Using your answer from part b and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker (k∗) , income per worker (y∗) , and consumption per worker (c∗) for each country.

Answer 1

Check Explanation.

Step-by-step explanation:

Note that the production function of bother country = Y=F(K,L) = K L c : k^1/2 L^1/2.

Thus Y/L = b; b = k^1/2 L^1/2/ L.

b = k^1/2.

From the question we are given that L = 6% = 0.06.

Country A saves 15% = 15/100 = 0.15 and country B saves 23% = 23/100 = 0.23.

For country A,

(a). the steady state;

∆k = 0 = y - dk.

0 = 0.15 × k^1/2 - 0.06k.

K^1/2 = 2.5, k* = 6.25

(b). y = K^1/2 = (6.25)^1/2.

y* = 2.5

(c). C = 2.5 - (0.15 × 2.5) = 2.5 - 0.375.

C* = 2.125.

Then, for COUNTRY B.

(a). ∆k = 0 = y - dk.

0 = 0.25 × k^1/2 - 0.06k.

K^1/2 = 4.167, k* = 17.36

(b). y = K^1/2 = (17.36)^1/2.

y* = 4.167.

(c). C = 4.167 - (0.25 × 4.167) = 2.5 - 0.375.

C* = 3.127.

C* = 2.125.