Consider the Solow-Swan model of growth. Imagine that the production function is Y = AK¤L¹-a 1. Use the production function to compute output per capita, y = Y/L, as a function of capital per person, k = K/L, A and a. 2. Derive the fundamental equation of the Solow-Swan model. Please show all the steps. Furthermore, imagine that the savings, depreciation, and population growth rates take the values s = 0.3, 8 = 0.15 and n = 0.04 respectively. You do not know the value of A or a. 3. Use the fundamental equation of the Solow-Swan model to compute the growth rate of capital per person as a function of k, A and a.
Consider the Solow-Swan model of growth. Imagine that the production function is Y = AK¤L¹-a 1. Use the production function to compute output per capita, y = Y/L, as a function of capital per person, k = K/L, A and a. 2. Derive the fundamental equation of the Solow-Swan model. Please show all the steps. Furthermore, imagine that the savings, depreciation, and population growth rates take the values s = 0.3, 8 = 0.15 and n = 0.04 respectively. You do not know the value of A or a. 3. Use the fundamental equation of the Solow-Swan model to compute the growth rate of capital per person as a function of k, A and a.
Chapter1: Making Economics Decisions
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Transcribed Image Text:Consider the Solow-Swan model of growth. Imagine that the production function is
Y
= AKa L¹-a
1. Use the production function to compute output per capita, y = Y/L, as a function of capital
per person, k = K/L, A and a.
2. Derive the fundamental equation of the Solow-Swan model. Please show all the steps.
Furthermore, imagine that the savings, depreciation, and population growth rates take the
values s = 0.3, 8 = 0.15 and n = 0.04 respectively. You do not know the value of A or a.
3. Use the fundamental equation of the Solow-Swan model to compute the growth rate of
capital per person as a function of k, A and a.
4. In the steady state, the growth rate of capital is zero. Using the parameters assumed above,
find the steady-state level of capital per person, k* as a function of A and a.
5. Calculate GDP per capita at the steady state, as a function of A and a.
6. Imagine that this country is in its steady state, so its capital stock is k*. Imagine that the
country gives away one unit of capital to the world bank (i.e., the capital stock is now
suddenly k*-1). What is happening immediately to the growth rate after the donation?
Why? What will the capital stock be in the long run? Explain.
5.2 clarification: Derive the fundamental equation of the Solow-Swan model. Please show all the
steps.
5.3 clarification: imagine that the savings, depreciation, and population growth rates take the
values s = 0.3, 6 = 0.15 and n = 0.04 respectively.
You do not know the value of A or a. Use the fundamental equation of the Solow-Swan model to
compute the growth rate of capital per person as a
function of k, A and a.
In other words, The answer to Problem 5.2 should be in terms of s, d, n, k, A, and a.
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