Exercise 1: Qualitative analysis in Solow's ModelExplain graphically how the following events affect output, capital and consumption perunit of labor in the long run and along the transition according to Solow's Model:a) The destruction of 30% of the capital stock because of a natural disaster.A permanent increase in the immigration rate.c) A permanent increase in the labor market participation rate.d) A permanent increase in the depreciation rate.e) A temporal increase in the savings rate.f) A permanent increase in the savings rate.Exercise 2: Growth and development=Countries 1 and 2 have the production function: Y₁ = A₂KL-ª, where country 1 hasTotal Factor Productivity (TFP) of A₁ 25, country 2 has TFP A₂= 100, and a = 0.35for both. In the two countries population is constant and there is no technological progress.Every year capital depreciates by 6% in both countries. Country 1 saves 40% of output, andcountry 2 saves 20%.a) Write down the function of production per unit of labor. Suppose the two countriesstart with an initial capital stock (per unit of labor) of 500, what are the initial income andconsumption per unit of labor in both countries?b) Determine their steady state levels of capital, income and consumption per unit oflabor.c) Determine the difference in their steady state level of income per unit of labor, andhow much of that difference is due to differences in TFP and how much is due to differencesin capital per unit of labor.d) Suppose now that country 2 suddenly has access to the country 1 level of technology.What would you expect to happen both in the short run and in the long run?Exercise 3: Population growth and technological progressConsider a version of Solow's Model:Y₁ = AK&L₁¹-asYt = Kt+1 − Kt + 8KtLt = Lo(1 + n)t

Solow's model is a neoclassical growth model that explains the determinants of long-run economic…

Explain graphically how the following events affect output, capital and consumption per unit of labor in the long run and along the transition according to Solow's Model: a) The destruction of 30% of the capital stock because of a natural disaster. b) A permanent increase in the immigration rate. c) A permanent increase in the labor market participation rate. d) A permanent increase in the depreciation rate. e) A temporal increase in the savings rate. f) A permanent increase in the savings rate.

Explain graphically how the following events affect output, capital and consumption per unit of labor in the long run and along the transition according to Solow's Model: a) The destruction of 30% of the capital stock because of a natural disaster. b) A permanent increase in the immigration rate. c) A permanent increase in the labor market participation rate. d) A permanent increase in the depreciation rate. e) A temporal increase in the savings rate. f) A permanent increase in the savings rate.

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Exercise 1: Qualitative analysis in Solow's Model
Explain graphically how the following events affect output, capital and consumption per
unit of labor in the long run and along the transition according to Solow's Model:
a) The destruction of 30% of the capital stock because of a natural disaster.
A permanent increase in the immigration rate.
c) A permanent increase in the labor market participation rate.
d) A permanent increase in the depreciation rate.
e) A temporal increase in the savings rate.
f) A permanent increase in the savings rate.
Exercise 2: Growth and development
=
Countries 1 and 2 have the production function: Y₁ = A₂KL-ª, where country 1 has
Total Factor Productivity (TFP) of A₁ 25, country 2 has TFP A₂
= 100, and a = 0.35
for both. In the two countries population is constant and there is no technological progress.
Every year capital depreciates by 6% in both countries. Country 1 saves 40% of output, and
country 2 saves 20%.
a) Write down the function of production per unit of labor. Suppose the two countries
start with an initial capital stock (per unit of labor) of 500, what are the initial income and
consumption per unit of labor in both countries?
b) Determine their steady state levels of capital, income and consumption per unit of
labor.
c) Determine the difference in their steady state level of income per unit of labor, and
how much of that difference is due to differences in TFP and how much is due to differences
in capital per unit of labor.
d) Suppose now that country 2 suddenly has access to the country 1 level of technology.
What would you expect to happen both in the short run and in the long run?
Exercise 3: Population growth and technological progress
Consider a version of Solow's Model:
Y₁ = AK&L₁¹-a
sYt = Kt+1 − Kt + 8Kt
Lt = Lo(1 + n)t

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1.9. Factor payments in the Solow model. Assume that both labor and capital are paid their marginal products. Let wo denote ƏF(K, AL)/ƏL and r denote [OF (K, AL)/ƏK] – 6. 47 (a) Show that the marginal product of labor, w, is A [f(k) - kf (k)]. (b) Show that if both capital and labor are paid their marginal products, constant returns to scale imply that the total amount paid to the factors of production equals total net output. That is, show that under constant returns, wL + rK = F(K, AL) – 6K. (c) The return to capital (r) is roughly constant over time, as are the shares of output going to capital and to labor. Does a Solow economy on a balanced growth path exhibit these properties? What are the growth rates of w and r on a balanced growth path? (d) Suppose the economy begins with a level of k less than k*. As k moves toward k*, is a growing at a rate greater than, less than, or equal to its growth rate on the balanced growth path? What about r?
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