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Consider a basic Solow–Swan model. Suppose the aggregate production function is 𝑌=𝐴𝐾12𝐿12 and that A=1 , the depreciation rate is 𝛿=0.06  and the saving rate is 𝑠=0.12. In steady state, which of the following is TRUE?Group of answer choicesOutput per worker is 2.00 and consumption per worker is 0.24Output per worker is 2.00 and consumption per worker is 1.76Output per worker is 1.68 and consumption per worker is 1.48Output per worker is 1.68 and consumption per worker is 1.12

Question

Consider a basic Solow–Swan model. Suppose the aggregate production function is 𝑌=𝐴𝐾12𝐿12 and that A=1 , the depreciation rate is 𝛿=0.06  and the saving rate is 𝑠=0.12. In steady state, which of the following is TRUE?Group of answer choicesOutput per worker is 2.00 and consumption per worker is 0.24Output per worker is 2.00 and consumption per worker is 1.76Output per worker is 1.68 and consumption per worker is 1.48Output per worker is 1.68 and consumption per worker is 1.12

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Solution

In the Solow-Swan model, the steady state level of output per worker (y*) and consumption per worker (c*) can be calculated using the given parameters.

First, we need to find the steady state level of capital per worker (k*). In the Solow model, this is given by the equation:

k* = (s / δ)^(1 / (1 - α))

where s is the saving rate, δ is the depreciation rate, and α is the capital share of income. In this case, α = 1/2 (since capital and labor are equally weighted in the production function), s = 0.12, and δ = 0.06.

Substituting these values in, we get:

k* = (0.12 / 0.06)^(1 / (1 - 0.5)) = 2

Next, we substitute k* into the production function to find y*. The production function is given by:

Y = AK^(1/2)L^(1/2)

In per worker terms, this becomes y = Ak^(1/2). Substituting in A = 1 and k* = 2, we get:

y* = 1 * 2^(1/2) = 1.41

Finally, we find the steady state level of consumption per worker. In the Solow model, this is given by:

c* = y* - δk*

Substituting in y* = 1.41, δ = 0.06, and k* = 2, we get:

c* = 1.41 - 0.06 * 2 = 1.29

So, none of the given answer choices are correct. The correct answer would be "Output per worker is 1.41 and consumption per worker is 1.29".

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