1. Consider a Cobb-Douglas production function that features capital-augmenting technology: Y(t) = [A(t) K(t)]aL(t)¹-a. Assume thattechnology A(t) grows at rate u: A(t) = μA(t). Show that the economy converges to a balanced growth path, and find the growth rates of Y andK on the balanced growth path.2. Let the production function be Y(t) = J(t)aL(t)1-a, where J(t) is the effective capital stock. The dynamics of J(t) are given byj (t) = sA(t)Y (t) — 8(t). The presence of the A(t) term in this expression means that the productivity of investment at t depends on thetechnology at t. Show that the economy converges to a balanced growth path. What are the growth rates of Y and J on the balanced growth path?dy* Sas y*3. Find the elasticity of output on the balanced growth path with respect to s:Consider a Solow economy that is on its balanced growth path. Assume for simplicity that there is no technological progress. Now suppose that the rate ofpopulation growth falls.1. What happens to the balanced growth path values of capital per worker, output per worker, and consumption per worker? Sketch the paths of thesevariables as the economy moves to its new balanced growth path.2. Describe the effect of the fall in population growth on the path of output (that is, total output, not output per worker).250227POLA2250150

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Consider a Solow economy that is on its balanced growth path. Assume for simplicity that there is no technological progress. Now suppose that the rate of population growth falls. 1. What happens to the balanced growth path values of capital per worker, output per worker, and consumption per worker? Sketch the paths of these variables as the economy moves to its new balanced growth path. 2. Describe the effect of the fall in population growth on the path of output (that is, total output, not output per worker).

Consider a Solow economy that is on its balanced growth path. Assume for simplicity that there is no technological progress. Now suppose that the rate of population growth falls. 1. What happens to the balanced growth path values of capital per worker, output per worker, and consumption per worker? Sketch the paths of these variables as the economy moves to its new balanced growth path. 2. Describe the effect of the fall in population growth on the path of output (that is, total output, not output per worker).

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Question

1. Consider a Cobb-Douglas production function that features capital-augmenting technology: Y(t) = [A(t) K(t)]aL(t)¹-a. Assume that
technology A(t) grows at rate u: A(t) = μA(t). Show that the economy converges to a balanced growth path, and find the growth rates of Y and
K on the balanced growth path.
2. Let the production function be Y(t) = J(t)aL(t)1-a, where J(t) is the effective capital stock. The dynamics of J(t) are given by
j (t) = sA(t)Y (t) — 8(t). The presence of the A(t) term in this expression means that the productivity of investment at t depends on the
technology at t. Show that the economy converges to a balanced growth path. What are the growth rates of Y and J on the balanced growth path?
dy* S
as y*
3. Find the elasticity of output on the balanced growth path with respect to s:
Consider a Solow economy that is on its balanced growth path. Assume for simplicity that there is no technological progress. Now suppose that the rate of
population growth falls.
1. What happens to the balanced growth path values of capital per worker, output per worker, and consumption per worker? Sketch the paths of these
variables as the economy moves to its new balanced growth path.
2. Describe the effect of the fall in population growth on the path of output (that is, total output, not output per worker).
250227
POLA
2250150

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Explain how and why we need to extend the standard Solow model of long-run economic growth without technological progress to account for the increase of global GDP over the last 200 years. Critically discuss the standard Solow model with technological progress.
9. Consider our graph of the basic Solow growth model. steady state dk y=F(() F() (-7' in LF equilibrium) On the graph above: y represents real output (or income) per worker; y-F(k) is the production function; is the capital stock per worker; s is the savings rate; 8 is the rate of depreciation of capital; 'i' represents business investment (purchases of capital) per worker); 'LF' stands for Loanable Funds. (For purposed of intuition, think of capital as 'machines.) If we started out with a capital (per worker) stock higher than the steady-state stock (above), we would expect to see which of the following happen over time? Positive growth rates while the capital stock increases. Positive growth rates while the capital stock stays less than the steady-state level. Negative growth rates while the capital stock increases. Positive growth rates while the capital stock decreases. Negative growth rates while the capital stock decreases.
9. Consider a numerical example using the Solow growth model. Suppose that F(K, N) KO.5N0.5, with d = z = 1, and take a period to be a year. (a) Determine capital per worker, income per capita, and consumption per capita in the steady state. 0.1, s = 0.2, n = 0.01, and
The validity and ability of the Solow Growth Model in explaining the long-term growth of a country has been tested empirically.(a) In the Solow Growth Model we are introduced to the concept of the Golden Rule; optimum level of saving and capital formation to support growth. Is this Golden Rule concept proven empirically?(b) From what we have learned from the Solow Growth Model, describe some policies that can improve a country's economic growth rate.
a. Show graphically what happens in the Solow Model when population growth increases. Label your graph clearly. b. Explain clearly the impact of this increase in population growth on i. income per capita ii. the growth rate of income per capita (in transition and at the new steady state) iii. the growth rate of total GNP.
12. According to Solow's model of economic growth, what determines the growth rate of income per person for a nation that is not in its steady state? What determines the growth rate of income per person for a nation that is in its steady state? In what sense is technological progress necessary for sustained growth of income per person in Solow's model?
Consider our graph of the basic Solow growth model. On the graph above: y represents real output (or income) per worker; y=F(k) is the production function; k is the capital stock per worker; s is the savings rate; δ is the rate of depreciation of capital; ‘i’ represents business investment (purchases of capital) per worker); ‘LF’ stands for Loanable Funds. (For purposed of intuition, think of capital as ‘machines.’) If we started out with a capital (per worker) stock lower than the steady-state stock ( , above), we would expect to see which of the following happen over time? Group of answer choices A) Positive growth rates while the capital stock increases. B) Negative growth rates while the capital stock increases. C) Negative growth rates while the capital stock decreases. D) Positive growth rates while the capital stock stays less than the steady-state level. E) Positive growth rates while the capital stock decreases.