The Golden Rule level of capital is the level of capital that maximizes consumption in the steady state. It is found by setting the marginal product of capital (MPK) equal to the depreciation rate (δ).

The production function given is y = 2k^1/2.

First, we need to find the marginal product of capital (MPK). The MPK is the derivative of the production function with respect to k.

The derivative of y = 2k^1/2 with respect to k is MPK = (1/2) * 2k^(-1/2) = k^(-1/2).

Setting this equal to the depreciation rate (δ = 0.5), we get:

k^(-1/2) = 0.5.

To solve for k, we can square both sides of the equation to get rid of the square root:

k = 1/(0.5)^2 = 1/0.25 = 4.

So, the Golden Rule level is reached when k is 4.

Question

The Golden Rule level of capital is the level of capital that maximizes consumption in the steady state. It is found by setting the marginal product of capital (MPK) equal to the depreciation rate (δ).

The production function given is y = 2k^1/2.

First, we need to find the marginal product of capital (MPK). The MPK is the derivative of the production function with respect to k.

The derivative of y = 2k^1/2 with respect to k is MPK = (1/2) * 2k^(-1/2) = k^(-1/2).

Setting this equal to the depreciation rate (δ = 0.5), we get:

k^(-1/2) = 0.5.

To solve for k, we can square both sides of the equation to get rid of the square root:

k = 1/(0.5)^2 = 1/0.25 = 4.

So, the Golden Rule level is reached when k is 4.

Knowee AI · Accepted Answer

The Golden Rule level of capital is the level of capital that maximizes consumption in the steady state. It is found by setting the marginal product of capital (MPK) equal to the depreciation rate (δ).

The production function given is y = 2k^1/2.

First, we need to find the marginal product of capital (MPK). The MPK is the derivative of the production function with respect to k.

The derivative of y = 2k^1/2 with respect to k is MPK = (1/2) * 2k^(-1/2) = k^(-1/2).

Setting this equal to the depreciation rate (δ = 0.5), we get:

k^(-1/2) = 0.5.

To solve for k, we can square both sides of the equation to get rid of the square root:

k = 1/(0.5)^2 = 1/0.25 = 4.

So, the Golden Rule level is reached when k is 4.

If the production function is y = 2k1/2 and δ = 0.5, then the Golden Rule level is reached when k is:6.10.4.1.

Question

If the production function is `y = 2k^{1/2}` and `δ = 0.5`, then the Golden Rule level is reached when `k` is:

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