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Assume that the production function in the Solow model is Y = K1/2L1/2, with 30% of output being saved, 10% of the capital stock depreciating every year, and the economy starting off with 4 units of capital per worker. Which of the following is true:

Question

Assume that the production function in the Solow model is Y = K1/2L1/2, with 30% of output being saved, 10% of the capital stock depreciating every year, and the economy starting off with 4 units of capital per worker. Which of the following is true:

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Solution 1

The Solow model is

Solution 2

To answer this question, we need more specific options to choose from. However, I can provide a general analysis based on the given information.

In the Solow model, the steady-state level of capital per worker (k*) is determined by the equation sY = δK, where s is the saving rate, Y is output, δ is the depreciation rate, and K is the capital stock.

Given the production function Y = K^1/2L^1/2, the output per worker (y) is k^1/2, where k = K/L is capital per worker.

Substituting y = k^1/2 into the steady-state equation gives sk^1/2 = δk. Solving for k gives k* = (s/δ)^2.

Substituting the given values s = 0.3 and δ = 0.1 gives k* = (0.3/0.1)^2 = 9.

Therefore, in the long run, the economy will converge to a steady-state level of 9 units of capital per worker.

However, the economy starts off with 4 units of capital per worker, which is less than the steady

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