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Consider how unemployment would affect the Solow growth model. Suppose that output is produced according to the production function , where K is capital, L is the labor force, and u is the natural...

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Consider how unemployment would affect the Solow growth model. Suppose that output is produced according to the production function , where K is capital, L is the labor force, and u is the natural rate of unemployment which in this case is 6%. The national saving rate is 20%, the labor force grows at rate 4%, and capital depreciates at rate 10%. a. Express output per worker (y=Y/L) as a function of capital per worker and the natural rate of unemployment. b. Write an equation that describes the steady state of this economy. c.
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Consider how unemployment would affect the Solow growth model. Suppose that output is produced according to the production function =K.3[1-uL].7 , where K is capital, L is the labor force, and u is the natural rate of unemployment which in this case is 6%. The national saving rate is 20%, the labor force grows at rate 4%, and capital depreciates at rate 10%. a. Express output per worker (y=Y/L) as a function of capital per worker and the natural rate of unemployment. b. Write an equation that describes the steady state of this economy. c. Suppose that some change in government policy reduces the natural rate of unemployment to 5%. Describe how this change affects output both immediately and over time. Is the steady state effect on output larger or smaller than the immediate effect? 3. (6 points each part) Suppose and economy described by the Solow model has the following production function: Y=K3/4(LE)1/4 a. For this economy, what is f(k)? b. Use your answer to part a to solve for the steady state value of y as a function of s, n, g, and d. c. Two neighboring economies have the above production function, but they have different parameter values. Atlantis has a saving rate of 25% and a population growth rate of 2% per year. Xanadu has a saving rate of 10% and a population growth rate of 5% per year. In both countries, g=0.02 and d=0.04. Find the steady state value of y for each country

005_5k-huduochf.docx
Answered Same Day Dec 22, 2021

Solution

Robert answered on Dec 22 2021
124 Votes
3. (6 points each part)
Suppose and economy described by the Solow model has the following production function:
a. For this economy, what is f(k)?
In the above given model we can see output(Y) is a function of labour, rather effective labour
and capital. E denotes the knowledge level of labour and thus determines its affectivity. Let y
(Y/LE) denotes output per effective capita and k (K/LE) denotes capital per effective capita in
the economy. Then,
Or y=k
3/4

f(k) = k
3/4

. Use your answer to part a to solve for the steady state value of y as a function of s, n, g, and δ.
We here assume that the model is set in continuous time. The initial level of capital, labour and
knowledge level is given. Labour and knowledge grows at a constant rate, denoted
mathematically as
dL(t)/d(t) = nL(t)
dE(t)/d(t) = gE(t)
We also know that output in the economy at any point is the sum of the consumption and
investment in the economy at that point of time. Thus capital increases at a constant proportion
of the outputs of the economy(s), but is also affected by the depreciation stock. Let δ denote the
ate at which capital deteriorates, then
dK(t)/d(t) = sY(t) – δK(t)
Differentiating K/L gives;
dk/dt = (dK/dt)/L(t)E(t) - {K(t) [...
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