The Golden Rule level of capital is the level of capital that maximizes consumption in the steady state. It is determined by setting the change in capital (investment minus depreciation) equal to zero and solving for k.

Given the production function y = 2k^1/2 and the depreciation rate δ = 0.1, we can find the Golden Rule level of capital as follows:

1. Set up the equation for the change in capital: Δk = investment - depreciation = s*y - δ*k, where s is the saving rate and y is the output. At the Golden Rule level, Δk = 0.

2. Substitute the production function into the equation: 0 = s*2k^1/2 - 0.1*k.

3. To maximize consumption, we set s = 1 (all output is saved). So the equation becomes: 0 = 2k^1/2 - 0.1*k.

4. Solve for k: 0 = 2k^1/2 - 0.1*k = 2k^1/2 = 0.1*k = 20 = k^1/2 = k = 400.

So, the Golden Rule level of capital is reached when k is 400. None of the options provided (200, 150, 120, 100) are correct.

Question

The Golden Rule level of capital is the level of capital that maximizes consumption in the steady state. It is determined by setting the change in capital (investment minus depreciation) equal to zero and solving for k.

Given the production function y = 2k^1/2 and the depreciation rate δ = 0.1, we can find the Golden Rule level of capital as follows:

1. Set up the equation for the change in capital: Δk = investment - depreciation = s*y - δ*k, where s is the saving rate and y is the output. At the Golden Rule level, Δk = 0.

2. Substitute the production function into the equation: 0 = s*2k^1/2 - 0.1*k.

3. To maximize consumption, we set s = 1 (all output is saved). So the equation becomes: 0 = 2k^1/2 - 0.1*k.

4. Solve for k: 0 = 2k^1/2 - 0.1*k => 2k^1/2 = 0.1*k => 20 = k^1/2 => k = 400.

So, the Golden Rule level of capital is reached when k is 400. None of the options provided (200, 150, 120, 100) are correct.

Knowee AI · Accepted Answer

The Golden Rule level of capital is the level of capital that maximizes consumption in the steady state. It is determined by setting the change in capital (investment minus depreciation) equal to zero and solving for k.

Given the production function y = 2k^1/2 and the depreciation rate δ = 0.1, we can find the Golden Rule level of capital as follows:

1. Set up the equation for the change in capital: Δk = investment - depreciation = s*y - δ*k, where s is the saving rate and y is the output. At the Golden Rule level, Δk = 0.

2. Substitute the production function into the equation: 0 = s*2k^1/2 - 0.1*k.

3. To maximize consumption, we set s = 1 (all output is saved). So the equation becomes: 0 = 2k^1/2 - 0.1*k.

4. Solve for k: 0 = 2k^1/2 - 0.1*k => 2k^1/2 = 0.1*k => 20 = k^1/2 => k = 400.

So, the Golden Rule level of capital is reached when k is 400. None of the options provided (200, 150, 120, 100) are correct.

If the production function is y = 2k1/2 and δ = 0.1, then the Golden Rule level is reached when k is:200.150.120.100.

Question

If the production function is $y = 2k^{1/2}$ and $\delta = 0.1$ , then the Golden Rule level is reached when $k$ is:

Solution

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