Consider a small open economy whose demand and domestic supply of capital relationships are R = 30 - (1/2)K and K = 7R,respectively (where K and R denote capital and its marginal product).Capital is perfectly mobile internationally,and the yield on capital (R)in the rest of the world is 6.Starting from this situation,suppose that an increase in national savings changes the domestic supply of capital relationship to K = 8R.
I: This country's GNP increases by 36.
II: Labour's share of GNP falls.
A) I is true; II is not.
B) II is true; I is not.
C) Both I and II are true.
D) Neither I nor II is true.

Question

Quizplus · Accepted Answer

We can start by finding the equilibrium level of capital and output in the initial situation:
K = 7R
R = 30 - (1/2)K
Substituting the first equation into the second equation, we get:
R = 30 - (1/2)(7R) = 26.5
K = 7(26.5) = 185.5
GNP = R*K = 4,917.25

Next, we can find the new equilibrium level of capital and output after the increase in national savings, which changes the domestic supply of capital relationship to K = 8R:
K = 8R
R = 30 - (1/2)K
Substituting the first equation into the second equation, we get:
R = 30 - (1/2)(8R) = 26
K = 8(26) = 208
GNP = R*K = 5,408

Therefore, the increase in national savings leads to an increase in GNP by:
5,408 - 4,917.25 = 490.75

As for the second statement, we can use the Cobb-Douglas production function to see whether labor's share of GNP falls or not:
GNP = A(K^α)(L^(1-α))
where A is a constant, α is the share of capital in output, and (1-α) is the share of labor in output.

In the initial situation, we have:
GNP = (185.5^(1/2))(L^(1/2))
Taking the derivative of GNP with respect to L, we get:
dGNP/dL = 0.5*(185.5^(1/2))*(L^(-1/2))
This means that labor's marginal productivity is decreasing as L increases, i.e., diminishing returns to labor. Therefore, labor's share of GNP is falling.

In the new situation, we have:
GNP = (208^(1/2))(L^(1/2))
Taking the derivative of GNP with respect to L, we get:
dGNP/dL = 0.5*(208^(1/2))*(L^(-1/2))
Once again, labor's marginal productivity is decreasing as L increases, and therefore labor's share of GNP is falling.

Hence, both statements I and II are true.

Consider a Small Open Economy Whose Demand and Domestic Supply