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In an economy where consumption, savings and output is dictated by the basic Solow model, the per worker production function is given as: y= . Capital depreciates at a rate of 0.2. The savings rate is currently 0.4. What is the golden rule level of output per worker?A.6.25B.2.5C.0.5D.2

Question

In an economy where consumption, savings and output is dictated by the basic Solow model, the per worker production function is given as: y= . Capital depreciates at a rate of 0.2. The savings rate is currently 0.4. What is the golden rule level of output per worker?A.6.25B.2.5C.0.5D.2

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Solution

The golden rule level of output per worker in the Solow model is the level of output per worker that maximizes consumption per worker in the steady state. It is determined by the equation:

s = δ / (δ + n + g)

where: s = savings rate δ = depreciation rate n = population growth rate g = technological progress rate

However, in your question, you've only provided the depreciation rate (δ = 0.2) and the savings rate (s = 0.4). To calculate the golden rule level of output per worker, we would also need to know the values for n and g.

Assuming that n and g are both 0 (which is a simplifying assumption and may not reflect the reality of most economies), we can proceed with the calculation:

s = δ / (δ + n + g) 0.4 = 0.2 / (0.2 + 0 + 0) 0.4 = 0.2 / 0.2 0.4 = 1

This implies that the economy is already at the golden rule level of savings. However, without the per worker production function, we cannot calculate the golden rule level of output per worker. The options provided (A. 6.25, B. 2.5, C. 0.5, D. 2) cannot be determined with the given information.

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