In the Solow model with labor-augmenting technological change, if the saving rate is 60%, population growth is 2%, the depreciation rate is 2%, the growth of efficiency workers is 1%, and the capital share is 50%, then in the steady state capital per effective worker is:

A. 100 and at the golden rule capital per effective worker is 100
B. 144 and at the golden rule capital per effective worker is 144
C. 100 and at the golden rule capital per effective worker is 144
D. 144 and at the golden rule capital per effective worker is 100

In the Solow model with labor-augmenting technological change, the steady state capital per effective worker is 6 and at the golden rule, the capital per effective worker is also 6.

Explanation:

In the Solow model with labor-augmenting technological change, the steady state capital per effective worker can be calculated using the following formula:

Capital per effective worker = (Saving rate / (Depreciation rate + Population growth + Efficiency growth)) * Capital share

Plugging in the given values:

Capital per effective worker = (0.60 / (0.02 + 0.02 + 0.01)) * 0.50

Capital per effective worker = (0.60 / 0.05) * 0.50

Capital per effective worker = 12 * 0.50

Capital per effective worker = 6

Therefore, in the steady state, the capital per effective worker is 6.

The golden rule capital per effective worker can be calculated using the following formula:

Golden rule capital per effective worker = (Saving rate / (Depreciation rate + Population growth + Efficiency growth)) * (1 - Capital share)

Plugging in the given values:

Golden rule capital per effective worker = (0.60 / (0.02 + 0.02 + 0.01)) * (1 - 0.50)

Golden rule capital per effective worker = (0.60 / 0.05) * 0.50

Golden rule capital per effective worker = 12 * 0.50

Golden rule capital per effective worker = 6

Therefore, at the golden rule, the capital per effective worker is also 6.

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