Assume the universe consists of only two realms, Asgard and Midgard, and their economies are described by the Solow growth model. They have the same Cobb- Douglas production function, F(K, L) = A Kº L¹-0 but with different quantities of capital and labour. Asgard saves 32 percent of its income, while Midgard saves 10 percent. Asgard has population growth of one percent per year, while Midgard has population growth of three percent. Both realms have technological progress at a rate of 2 percent per year and depreciation at a rate of 5 percent per year.

Assume the universe consists of only two realms, Asgard and Midgard, and their economies are described by the Solow growth model. They have the same Cobb- Douglas production function, F(K, L) = A Kº L¹-0 but with different quantities of capital and labour. Asgard saves 32 percent of its income, while Midgard saves 10 percent. Asgard has population growth of one percent per year, while Midgard has population growth of three percent. Both realms have technological progress at a rate of 2 percent per year and depreciation at a rate of 5 percent per year.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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B. The rate of technological progress rises. 2. Describe how, if at all, each of the following developments affects the break-even and actual investment lines in our basic diagram for the Solow model: a. The rate of population growth falls. B. The rate of technological progress rises. C. The production function is Cobb-Douglas, F(K,AL) = K" (AL)1-" , and capital"s share, ", rises. D. Workers exert more effort, so that output per unit of effective labor for a given value of capital per unit of effective labor is higher than before.
Suppose an economy described by the Solow model is in steady state with population growth n of 1.8 percent per year and technological progress g of 1.8 percent per year. total output and total capital grow at 3.6 percent per year. suppose further that the capital share of output is 1/3. if you used the growth accounting equation to divide output growth into three sources- capital, labor, and total factor productivity- how much would you attribute to each source? compare your results to the figures we found for the united states in tables 9-2.
Suppose that we modify the Solow growth model by allowing long-run technological progress. That is, suppose that z = 1 for convenience and that there is labor-augmenting technological progress, with a production function Y =F(K,bN) where b denotes the number of units of "human capital" per worker, and bN is "efficiency units" of labor. Letting b' denote future human capital per worker, assume that b' = (1 + f ) b, where f is the growth rate in human capital. (c) In the real world, we usually consider education level as a proxy to human capital. To examine the theory, what suggestions can you make to growth economists? What are factors other than education can you think of that contribute to human capital?
The Solow Growth Model is an exogenous model of economic growth that analyzes changes in the level of output in an economy over time as a result of changes in the population growth rate, the savings rate, and the rate of technological progress. Consider the Solow model. a) Explain using a graph why there is a poverty trap in this model b)Describe how an economy such as one characterized by this model may break out of a poverty trap.
Suppose an economy described by the Solow model is in a steady state with population growth n of 1.8 percent per year and technological progress g of 1.8 percent per year. Total output and total capital grow at 3.6 percent per year. Suppose further that the capital share of output is 1/3. If you used the growth-accounting equation to divide output growth into three sources—capital, labor, and total factor productivity—how much would you attribute to each source?
Consider the Solow model. Draw the paths over time for the log of y, c and k for an economy that starts below its balanced-growth path.
Consider the Solow growth model in which we allow for long-run techno- logical progress. Assume N′ = (1 + n)N where N is the population (labor force) in the current period, N′ is the population (labor force) in the future period, and n is the pop- ulation growth rate. Assume that z = 1 for simplicity, and there is labour-augmenting technological progress. The production technology is given by Y = F(k,bN) where Y is the output of the consumption good, K is the current period capital stock, b denotes the number of units of “human capital” per worker, and bN is the “efficiency units” of labour. Assume that b′ = (1 + β)b where β > 0 is the growth rate in human capital. Consumers save a constant fraction, s, of their disposable income, where 0 < s < 1. The production function F exhibits constant returns to scale. (a) Define a variable k as the quantity of capital per efficieny units of labor (as opposed to quantity of capital per labour). Using equilibrium conditions derive the…
Explain the central paradox at the heart of the Solow model, with constant and exogenous technologies. Given this paradox, why is the Solow model still relevant?
Consider the Solow model. Using suitable diagrams, compare the different dynamics for the levels and growth rates of capital per capita and output per capita following: (a) a new wave of immigration, (b) an increase in the saving rate, (c) a one-shot foreign investment which increase the size of the available stock of capital, (d) an important technological advance.
In 1998, Brazil had a per capita GDP of about $4,500, compared to per capita GDP of about $28,000 in the US. (A) If per capita growth were to average 2% per year indefinitely in the US and 5% per year in Brazil, how many years would it take Brazil to catch up with the US? (B) Using the assumptions of the Cobb-Douglas production function, how fast would capital stock have to grow for per capita GDP to rise 5% per year? How does that compare with capital stock growth of 3% per year in the US (assume technology advances 1% per year in both countries)? (C) In mature industrialized societies, the capital/output ratio is approximately 3.0. If the average depreciation rate is 0.04, what would be the current saving and investment ratio in the US? What would it be in Brazil if per capita GDP rose 5% per year?
The Solow model without exogenous productivity growth predicts that rich countries with more capital will grow faster than poor countries with less capital, assuming other economic conditions are equal. Is this statement true or false? Explain.
Some analysts claim that the economy is subject to a “paradox of thrift.” That is, increases in saving will cause consumption and GDP to fall. In support, they point to the fact that consumer spending is more than ⅔ of GDP. (a) Does the Solow model (described in Chapter 28 of Cowen and Tabarrok), show the paradox of thrift? Explain. (b) What about the real world? Do the data in Figure 28.8 below suggest a paradox of thrift? Explain.