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Graph and its inverse function in the same rectangular

Precalculus | 4th Edition | ISBN: 9780321559845 | Authors: Robert F. Blitzer ISBN: 9780321559845 209

Solution for problem 3.1.94 Chapter 3.1

Precalculus | 4th Edition

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Precalculus | 4th Edition | ISBN: 9780321559845 | Authors: Robert F. Blitzer

Precalculus | 4th Edition

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Problem 3.1.94

Graph and its inverse function in the same rectangular coordinate system

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Chapter 7 ~ Production and Growth Economic Growth around the World Economic prosperity, as measured by GDP per person (per capita), varies substantially around the world. The average income in the world’s richest countries is more than ten times that in the world’s poorest countries. Because growth rates of real GDP also vary substantially, the relative positions (rankings) of countries can change dramatically over time. (Economic Growth = Economic Prosperity).  The level of real GDP is a good gauge of economic prosperity  The growth of real GDP is a good gauge of economic progress  Productivity ~ is the amount of goods and services produced per unit of labor (Y/L)  Because of differences in growth rates, the ranking of countries by income changes over time  Fact 1 ~ There are vast differences in living standards (GDP per capita) around the world  Fact 2 ~ There is a great variation in growth rates across countries Productivity: Its Role and Determinants The standard of living in an economy depends on the economy’s ability to produce goods and services. Productivity, in turn, depends on the physical capital, human capital, natural resources and technological knowledge available to workers and determines a country’s standard of living. Productivity ~ is the average quantity of goods and services produced from each unit of labor-input and reflects a country’s standard of living. (Y/L) 1. GDP ~ an economy’s income is its output. (output = income = expenditures) 2. When productivity grows rapidly, so do the standards of living Productivity is the result of 4 factors or 4 Determinates: 1. Physical Capital per Worker (capital equipment) ~ physical capital is the stock of equipment and structures that are used to produce goods and services  These are the factors of production  When there are more tools, equipment and machines, workers are more productive 2. Human Capital per Worker (knowledge, training, experience) ~ the knowledge and skills that workers acquire through education, training and experience  It is also, like physical capital, a produced factor of production  It involves the transmission of understanding to the labor force (through books, teachers and time)  Productivity is higher when the average worker has more human capital (education and skills) 3. Natural Resources per Worker (supplies) ~ are the inputs into the production of goods and services that are provided by nature; such as, land, rivers and mineral deposits  Renewable (trees can be replanted)  Non-renewable (oil, ores)  Countries can import the natural resources they don’t have for their production needs 4. Technological Knowledge ~ is society’s understanding of the best ways to produce goods and services and how the world works: Technological knowledge means that any advance in knowledge that boosts technology will allow society to get increased output (efficiency) from its scarce resources.  Common knowledge ~ what most everyone already knows  Proprietary knowledge ~ knowledge protected by patents or by producers  Involves the quality of training received “Technological knowledge is the quality of society’s text books, whereas, human capital is the amount of time that the population has devoted to reading them.”  Technological knowledge refers to society’s understanding of how to produce goods and services which can be easily and effortlessly shared.  Human capital results from the effort people expend to acquire this knowledge, and it is generally “tied” to the individuals that expend the time and effort to acquire it (knowledge, skills). The Production Function: Y = AF(L, K, H, N) This is a graph or equation showing the relation between outputs and inputs. F( ) is an equational function that shows how inputs are combined to produce outputs. Its graph is curved. The graph is drawn at a given value of other determinates Constant Returns to Scale (CRS, Alpha > 0) ~ If a production function has constant returns to scale with a given technology constant, then doubling all inputs causes the amount of output to double as well: xY = AF(xL, xK, xH, xN) also Y/L = AF(1, K/L, H/L, N/L) Y = output, A = technology, L = laborers, K = physical capital, H = human capital, N = resources  Y/L = amount of output per laborer (productivity)  Since technological knowledge can be easily shared, that’s why “A” is not divided by “L” (above).  Doubling all inputs causes the amount of output to double too.  Changing all inputs by the same percentage causes output to change by that percentage too.  When alpha = 1/L then: Y/L = AF(1, K/L, H/L, N/L) Economic Growth and Public Policy ~ the roles of Government Government policies can try to influence the economy’s growth rate in many ways: By encouraging saving and investment, encouraging investment from abroad, fostering education, promoting good health, maintaining property rights and political stability, allowing free trade and promoting the research and development of new technologies. The accumulation of capital is subject to diminishing returns. The more capital an economy has, the less additional output the economy gets from an extra unit of capital. As a result, although higher saving leads to higher growth for a period of time, growth eventually slows down as capital, productivity and income rise. Also, because of diminishing returns, the return to capital is especially high in poor countries. Other things being equal, these countries can grow faster because of the catch-up effect. 1. Saving and Investing: Because resources are scarce, devoting more resources to producing capital requires devoting fewer resources to producing goods and services for current consumption: It requires that society sacrifice consumption of goods and services in the present to enjoy higher consumption in the future. Extra saving funds the production of investment goods: The trade-off. 2. Diminishing Returns and the Catch-up Effect ~ is the property (attribute, characteristic) whereby the benefit from an extra unit of an input declines as the quantity of the input increases.  In the long-run, the higher saving rate leads to a higher level of productivity and income but NOT to higher growth in these variables (productivity, income).  It is easier for a country to grow fast if it starts out relatively poor which is referred to as the catch-up effect.  The production graph shows this diminishing returns which are similar to decreasing marginal utility. The catch-up effect ~ is the property (attribute, characteristic) whereby countries that start off poor tend to grow more rapidly (based on starting points) than countries that start off rich.  The crucial assumption of the catch-up effect is that both countries are assumed to have the same production function.  Because of “diminishing returns,” the “gap” between them shrinks over time. 3. Investment from Abroad Foreign Direct Investment ~ is a capital investment that is owned and operated by a foreign entity. Foreign Portfolio Investment ~ is an investment that is financed with foreign money but operated by domestic residents. GDP is the income earned within a country by both residents and non-residents. GNP is the income earned by residents of a country both at home and abroad. Some of the returns from these investments flow back from these countries to the country that did the initial investing in the foreign country. It is especially beneficial in poor countries that cannot generate enough saving to fund investment projects on their own to seek foreign investments and investors. Investment from abroad also helps poor countries learn state-of-the-art technologies developed elsewhere. 4. Education is an investment in human capital.  Education has an opportunity cost ~ time in school versus time spent working and earning money  Education is regarded as a positive “externality”  “Brain-drain” occurs when educated individuals immigrate to (live) and work where they can make more money and enjoy a better standard of living. 5. Health and Nutrition is an investment in human capital ~ leads to increased income per capita  Production is increased when people are healthy  Production is increased when people are well-fed  One’s height has been shown to be an indicator of productivity and income  Caloric increases leads to higher production 6. Property Rights and Political Stability Market prices are the instrument with which the invisible hand of the marketplace brings supply and demand into balance in each of the many thousands of markets that make up the economy. And markets are usually a good way to organize economic activity. An important prerequisite for the price system to work is an economy-wide respect for property rights.  Property rights refer to the ability of people to exercise authority over resource they own  Through the civil justice system, the courts ensure that buyers and sellers live up to their contracts  Through the criminal justice system, the courts discourage theft  Political instability creates uncertainty over whether property rights will be protected in the future  Lower living standards occur when there is fear over property rights  Economic stability, efficiency and healthy growth require law enforcement, effective courts, a stable constitution and honest government officials 7. Free Trade ~ a country that eliminates trade restrictions will experience the same kind of economic growth that would occur after a major technological advance: Trade has similar effects as discovering new technologies because it improves productivity and living standards.  “inward-oriented policies” occur with a closed economy per a country via tariffs and limits on investments from abroad  “outward-oriented policies” occur with countries integrated with the rest of the world because of the elimination of restrictions on trade and investments  Geography plays a role in a country’s ability to trade ~ seaports make international trade easier 8. Research and Development Knowledge is a public good ~ the primary reason that living standards are higher today than they were a century ago is that technological knowledge has advanced over the long-run. One reason is that knowledge is a public good and ideas can be shared freely and therefore it increases the productivity of many. Policies which promote technological progress are:  Patent laws  Tax incentives for research and development  Grants for basic research at universities 9. Population Growth Population growth has a variety of effects on economic growth. On the one hand, more rapid population growth may lower productivity by stretching the supply of natural resources and by reducing the amount of capital available for each worker. On the other hand, a larger population may enhance the rate of technological progress because there are more inventors, scientists and engineers.  A large population means more workers to produce goods and services  A large population means more people to consume those goods and services  Growth in human ingenuity has offset the effects of a larger population by increased productivity  If there are more people, there should be more “smart” people to invent better ways of production  Rapid economic growth may leave workers equipped with less capital to work with (inefficiency) Population growth has some effects on the changes of labor  It stretches various resources when growth is rapid (education system can’t keep up with demand)  It dilutes capital stock when growth is rapid (more workers per capital, inefficiency, unemployment)  More inventors, scientists and engineers

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Chapter 3.1, Problem 3.1.94 is Solved
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Textbook: Precalculus
Edition: 4
Author: Robert F. Blitzer
ISBN: 9780321559845

This full solution covers the following key subjects: . This expansive textbook survival guide covers 92 chapters, and 9372 solutions. Since the solution to 3.1.94 from 3.1 chapter was answered, more than 238 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Precalculus, edition: 4. Precalculus was written by and is associated to the ISBN: 9780321559845. The full step-by-step solution to problem: 3.1.94 from chapter: 3.1 was answered by , our top Calculus solution expert on 01/04/18, 08:34PM. The answer to “Graph and its inverse function in the same rectangular coordinate system” is broken down into a number of easy to follow steps, and 11 words.

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Graph and its inverse function in the same rectangular