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A plane is capable of flying at a speed of 180 kmyh in

Calculus | 8th Edition | ISBN: 9781285740621 | Authors: James Stewart ISBN: 9781285740621 127

Solution for problem 4 Chapter 12

Calculus | 8th Edition

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Calculus | 8th Edition | ISBN: 9781285740621 | Authors: James Stewart

Calculus | 8th Edition

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Problem 4

A plane is capable of flying at a speed of 180 kmyh in still air. The pilot takes off from an airfield and heads due north according to the planes compass. After 30 minutes of flight time, the pilot notices that, due to the wind, the plane has actually traveled 80 km at an angle 5 east of north. (a) What is the wind velocity? (b) In what direction should the pilot have headed to reach the intended destination?

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Econ 202 ~ Chapter 5 ~ Measuring A Nation’s Income The Economy’s Income and Expenditure Microeconomics is the study of how households and firms make decisions and how they interact in markets. Macroeconomics is the study of economy-wide phenomena, including inflation, unemployment and economic growth. The goal of macroeconomics is to explain the economic changes that affect many households, firms and markets simultaneously. Because every transaction has a buyer and a seller, the total expenditure in the economy must equal the total income in the economy. GDP ~ measures the total income of everyone in an economy via incomes and expenditures. It is based on accounting identities (GDP = y = c+i+g+nx ~ National Income Identity) of goods and services. GDP is the best single indicator of the economy. GDP = Total Income ~ GDP measures the flow of money by two ways: 1. GDP = Total Expenditures on goods and services spent by households in the market 2. GDP = Total Factor Payments which are the wages, rent and profit paid by firms in the markets There are two agents or two actors (buyers/sellers) which are households and firms. There are two markets: 1. Markets for Goods and Services 2. Markets for Factors of Production (land, labor, capital, natural resources) GDP ~ is the market value of all final goods and services produced within a country in a given period of time. 1. Goods are valued at their market price and measured in the same units; such as, dollars 2. Final goods and services refer to items intended to be readily bought and used by a customer: They embody the value of the intermediate goods used in the production of a final good. 3. Goods are tangible and services intangible 4. Produced goods and services are recently (currently) produced. They are NOT from the past (inventories). 5. It measures only the value of the production which occurs within the domestic boarder of a country. 6. It is usually measured by a year or quarters like 3 months. Exclusions from GDP:  Things that don’t have a market value; such as, housework, cleaning, cooking, mowing the lawn  Underground transactions which can be legal or illegal; such as, baby sitting, yard sales, bartering The Measurement of GDP Gross domestic product (GDP) measures an economy’s total expenditure on newly produced goods and services and the total income earned from the production of these goods and services. More precisely, GDP is the market value of all final goods and services produced within a country in a given period of time: It is the total overall spending of a nation:  Market prices reflect the value of those goods and services by their purchasers  It includes all items produced and sold legally in the markets (houses are regarded as imputed rents)  It only includes the value of final goods and NOT intermediate goods  It includes both tangible and intangible goods  It only includes recent (current) items and NOT past purchases (used cars)  The products only produced domestically belong to that particular country’s GDP  Finally, these items have a given time period to them (1 year or 1 quarter) Quarterly data is adjusted to take out or take in account the seasonal effects and discrepancies. On the other hand, Gross National Product (GNP) is the total income earned by a nation’s permanent residents (called nationals) and measures the levels of production of any person or corporation of its country. It differs from GDP in that it includes income that our citizens and corporations earn abroad, and the GNP excludes the income that foreigners earn here.  GNP ~ is the total income of all residents of a nation; including the income from factors of production produced abroad. GNP is about citizenship and who (what country) owns the factors of production. GNP = GDP + Income from abroad – income paid to foreign citizens and foreign entities. Net national product (NNP) is the total income of a nation’s residents (GNP) minus losses from depreciation. National income is the total income earned by a nation’s residents in the production of goods and services. Personal income is the income that households and non-corporate businesses receive. Disposable income is the income that households and non-corporate businesses have left over after satisfying all their obligations to the government. The Components of GDP GDP is divided among four components of expenditure: consumption, investment, government purchases and net exports. Consumption includes spending on goods and services by households, with the exception of purchases of new housing. Investment includes spending on new equipment and structures, including households’ purchases of new housing. Government purchases include spending on goods and services by local, state and federal governments. Net exports equal the value of goods and services produced domestically and sold abroad (exports) minus the value of goods and services produced abroad and sold domestically (imports). Y = C + I + G + NX (accounting identities ~ GDP) Consumption ~ is the total spending by households on goods and services with the exception of new housing.  Excludes purchases of new homes; however, homes are treated via imputed rental values.  Includes rent payments and the purchases of tangible and intangible goods and services. Investments ~ include (1) capital equipment, (2) structures and buildings, (3) inventories & (4) new housing.  Goods that will be used in the future to produce more goods. Personal houses fall in this category. Government purchases ~ is the spending on the goods and services purchased by local, state and federal governments.  Transfer payments; such as, social security and unemployment insurance are excluded, because the government is not purchasing any goods or services from this clientele. Net Exports ~ is the monetary difference between exports and imports.  Exports ~ are to be consumed outside of a country.  Imports ~ are to be consumed within a country. Real GDP versus Nominal GDP Nominal GDP uses current (recent) prices to value the economy’s production of goods and services. Real GDP uses constant (fixed) base-year prices to value the economy’s production of goods and services. The GDP deflator, calculated from the ratio of nominal to real GDP, measures the level of prices in the economy. Inflation ~ is a general increase in prices Nominal GDP  Output (production) is valued by using the current (recent) price of the item  It is not corrected for inflation  Changes reflect changes in both the prices and quantities of an item or items Real GDP  Is based upon or valued by using a fixed (constant) base price from a prior (past) year  It is corrected for inflation  It measures only the changes in the number (quantity) of produced items  It reflects the change the GDP would change if prices remained the same  It incorporates a “base year” in which to use its “base year” prices for future calculations The totals of the base (initial) year of the nGDP and the rGDP are equal. The GDP deflator (dGDP) ~ is a measure of the overall level of changes in prices: It takes the “inflation” out of the nGDP (nominal GDP).  The dGDP ~ is a measure of the price level calculated as the ratio of nGDP/rGDP X 100.  It reflects what is happening to item prices and NOT to quantities of items  Its components are used in the calculation of time-over-time inflation (deflation) rates  It measures what is currently produced, and NOT goods and services consumed  It changes the group of goods (basket) over time as the GDP changes  It is not affected by imports and excludes imported consumer goods  It includes capital goods (re-investments back into one’s business) One way to measure the economy’s inflation rate is to compute the percentage increase in the dGDP (GDP deflator) from one year to the next: dGDP = 100 for the base year. 1. Calculate the nGDP and rGDP for the given years of study 2. Calculate the dGDP for each year: dGDP = nGDP/rGDP X 100 3. Calculate the inflation rate by calculating yearly (deflators) dGDP’s: dGDP(t) – dGDP(t-1) / dGDP(t-1) X 100 Is GDP a Good Measure of Economic Well-Being GDP is a good measure of economic well-being because people prefer higher to lower incomes. But it is not a perfect measure of well-being. For example, GDP excludes the value of leisure and the value of a clean environment.  Real GDP per capita is the main indicator of the average person’s standard of living  It is not a perfect indicator of individual satisfaction  GDP is used as a proxy of the quality of living  GDP increases over time (in the long-run)  Growth rate is not steady because of recession periods  Growth = the percentage change in real GDP Gross Domestic Product does not value (measure):  The quality of the environment  Leisure time  Non-market (household) activity; such as, child care a parent provides for his or her child at home  An equitable distribution of income and monies

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Chapter 12, Problem 4 is Solved
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Textbook: Calculus
Edition: 8
Author: James Stewart
ISBN: 9781285740621

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A plane is capable of flying at a speed of 180 kmyh in