Question

1, A country has the production function Y=L1/2K1/2 a. This production function has returns to scale. marginal product of capital and 2. The United States has been at or near the steady state for quite some time and yet the economy still grows. What might account for this? 3. If a country has a natural disaster which destroys much of its physical capital what do you expect to happen to the level of output and what do you expect to happen to the rate of economic growth? 79개 단어 ! [e 영어(미국)

Answer 1

1. Y = L^1/2 K^1/2

(a) Marginal product of capital =>  $\frac{\partial Y}{\partial K} = 1/2 [L^{1/2} K^{-1/2}]$

$\frac{\partial Y}{\partial K} = 1/2 (L/K)^{1/2}$

As and when a unit of capital is increased, the marginal product of capital falls (since the denominator increases). Thus, the marginal product of capital is decreasing.

(b) Returns to scale can be determined by adding up the power of labour and capital in the Cobb Douglas production function.

Suppose Y = L^a K^b

If a + b > 1, there will be increasing returns to scale.

If a + b < 1, there will be decreasing returns to scale.

If a + b = 1, there will be constant returns to scale.

In the function given, 1/2 + 1/2 = 1.

That is, there are constant returns to scale.

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