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Solution: In 1117, determine the inverse Laplace transform

Fundamentals of Differential Equations and Boundary Value Problems | 6th Edition | ISBN: 9780321747747 | Authors: Kent Nagle ISBN: 9780321747747 138

Solution for problem 14 Chapter 7

Fundamentals of Differential Equations and Boundary Value Problems | 6th Edition

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Fundamentals of Differential Equations and Boundary Value Problems | 6th Edition | ISBN: 9780321747747 | Authors: Kent Nagle

Fundamentals of Differential Equations and Boundary Value Problems | 6th Edition

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Problem 14

In 1117, determine the inverse Laplace transform of the given function.

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Exam 2 Review 1. Jen values her time at $ 60 an hour. She spends 2 hours giving Colleen a massage. Colleen was willing to pay as much at $ 300 for the massage, but they negotiate a price of $ 200 . In this transaction, a) consumer surplus is $ 20 larger than producer surplus. b) consumer surplus is $ 40 larger than producer surplus. c) producer surplus is $ 20 larger than consumer surplus. d) producer surplus is $ 40 larger than consumer surplus. 2. The demand curve for cookies is downward sloping. When the price of cookies is $ 2 , the quantity demanded is 100 . If the price rises to $ 3 , what happens to consumer surplus a) It falls by less than $ 100 . b) It falls by more than $ 100 . c) It rises by less than $ 100 . d) It rises by more than $ 100 . 3. John has been working as a tutor for $ 300 a semester. When the university raises the price it pays tutors to $ 400 , Emily enters the market and begins tutoring as well. How much does producer surplus rise as a result of this price increase a) by less than $ 100 b) between $ 100 and $ 200 c) between $ 200 and $ 300 d) by more than $ 300 4. When a market is in equilibrium, the buyers are those with the _____ and the sellers are those with the _______ willingness to pay costs. a) highest, highest b) highest, lowest c) lowest, highest d) lowest, lowest 5. An efficient allocation of resources maximizes a) consumer surplus. b) producer surplus. c) consumer surplus plus producer surplus. d) consumer surplus minus producer surplus. 6. Producing a quantity larger than the equilibrium of supply and demand is inefficient because the marginal buyer’s willingness to pay is a) negative. b) Zero. c) positive but less than the marginal seller’s cost. d) positive and greater than the marginal seller’s cost. 7. A tax on a good has a deadweight loss if a) the reduction in consumer and producer surplus is greater than the tax revenue. b) the tax revenue is greater than the reduction in consumer and producer surplus. c) the reduction in consumer surplus is greater than the reduction in producer surplus. d) the reduction in producer surplus is greater than the reduction in consumer surplus. 8. Jane pays Chuck $ 50 to mow her lawn every week. When the government levies a mowing tax of $ 10 on Chuck, he raises his price to $ 60 . Jane continues to hire him at the higher price. What is the change in producer surplus, change in consumer surplus, and deadweight loss a) $ 0 , $ 0 , $ 10 b) $ 0 , − $ 10 , $ 0 c) + $ 10 , − $ 10 , $ 10 d) + $ 10 , − $ 10 , $ 0 9. Eggs have a supply curve that is linear and upward sloping and a demand curve that is linear and downward sloping. If a 2 cent per egg tax is increased to 3 cents , the deadweight loss of the tax a) increases by less than 50 percent and may even decline. b) increases by exactly 50 percent . c) increases by more than 50 percent . d) the answer depends on whether supply or demand is more elastic. 10. Peanut butter has an upward sloping supply curve and a downward sloping demand curve. If a 10 cent per pound tax is increased to 15 cents , the government’s tax revenue a) Iincreases by less than 50 percent. b) increases by exactly 50 percent . c) increases by exactly 50 percent . d) The answer depends on whether supply or demand is more elastic. 11. The Laffer curve illustrates that, in some circumstances, the government can reduce a tax on a good and increase the a) deadweight loss. b) government’s tax revenue. c) equilibrium quantity. d) price paid by consumers. 12. If a policymaker wants to raise revenue by taxing goods while minimizing the deadweight losses, he should look for goods with ________ elasticities of demand and ______ elasticities of supply. a) Small, small b) small, large c) large, small d) large, large 13. If a nation that does not allow international trade in steel has a domestic price of steel lower than the world price, then a) the nation has a comparative advantage in producing steel and would become a steel exporter if it opened up trade. b) the nation has a comparative advantage in producing steel and would become a steel importer if it opened up trade. c) the nation does not have a comparative advantage in producing steel and would become a steel exporter if it opened up trade. d) the nation does not have a comparative advantage in producing steel and would become a steel importer if it opened up trade. 14.When the nation of Ectenia opens itself to world trade in coffee beans, the domestic price of coffee beans falls. Which of the following describes the situation a) Domestic production of coffee rises, and Ectenia becomes a coffee importer. b) Domestic production of coffee rises, and Ectenia becomes a coffee exporter. c) Domestic production of coffee falls, and Ectenia becomes a coffee importer. d) Domestic production of coffee falls, and Ectenia becomes a coffee exporter. 15.When a nation opens itself to trade in a good and becomes an importer, a) producer surplus decreases, but consumer surplus and total surplus both increase. b) producer surplus decreases, consumer surplus increases, and so the impact on total surplus is ambiguous. c) producer surplus and total surplus increase, but consumer surplus decreases. d) producer surplus, consumer surplus, and total surplus all increase. 16. If a nation that imports a good imposes a tariff, it will increase a) the domestic quantity demanded. b) the domestic quantity supplied. c) the quantity imported from abroad. d) all of the above. 17. Which of the following trade policies would benefit producers, hurt consumers, and increase the amount of trade a) the increase of a tariff in an importing country b) the reduction of a tariff in an importing country c) starting to allow trade when the world price is greater than the domestic price d) starting to allow trade when the world price is less than the domestic price 18. The main difference between imposing a tariff and handing out licenses under an import quota is that a tariff increases a) consumer surplus. b) producer surplus c) international trade. d) government revenue. 19.If the price of a hot dog is $2 and the price of a hamburger is $4, then 30 hot dogs contribute as much to the GDP as ______ hamburgers. a) 5 b) 15 c) 30 d) 60 20.Anus the sheep farmer sells wool to Barnaby the knitter for $20. Barnaby makes two sweaters, each of which has a market value of $40. Collete buys one of them, while the other remains on the shelf of Barnaby’s store to be sold later. What is the GDP here a) $40 b) $60 c) $80 d) $100 21.Which of the following does NOT add to U.S. GDP a) Air France buys a plane from Boeing, the U.S. aircraft manufacturer. b) General Motors builds a new auto factory in North Carolina. c) The city of New York pays a salary to a policeman. d) The federal government sends a Social Security check to your grandmother. 22.An American buys a pair of shoes manufactured in Italy. How do the U.S. national income accounts treat the transaction a) Net exports and GDP both rise. b) Net exports and GDP both fall. c) Net exports fall, while GDP is unchanged. d) Net exports are unchanged, while GDP rises. 23.If all quantities produced rise by 10 percent and all prices fall by 10 percent, which of the following occurs a) Real GDP rises by 10 percent, while nominal GDP falls by 10 percent. b) Real GDP rises by 10 percent, while nominal GDP is unchanged. c) Real GDP is unchanged, while nominal GDP rises by 10 percent. d) Real GDP is unchanged, while nominal GDP falls by 10 percent. Year Price of Milk Quantity of Milk Price of Honey Quantity of Honey 2013 $1 100 quarts $2 50 quarts 2014 $1 200 $2 100 2015 $2 200 $4 100 24. Using the chart below calculate the GDP deflator for 2015, using 2013 as the base year. a) 100 b) 200 c) 400 d) 800 25. The consumer price index measures approximately the same economic phenomenon as a) Normal GDP b) Real GDP c) The GDP deflator d) The unemployment rate 26. The largest component in the basket of goods and services used to compute the CPI is a) food and beverages b) housing c) medical care d) Apparel 27. If a Pennsylvania gun manufacturer raises the price of rifles it sells to the U.S. Army, its price hikes will increase a) both the CPI and the GDP deflator. b) neither the CPI nor the GDP deflator. c) the CPI but not the GDP deflator. d) the GDP deflator but not the CPI. 28. Because consumers can sometimes substitute cheaper goods for those that have risen in price, a) the CPI overstates inflation. b) the CPI understates inflation. c) the GDP deflator overstates inflation. d) the GDP deflator understates inflation. 29. If the consumer price index is 200 in year 1980 and 300 today, then $ 600 in 1980 has the same purchasing power as ________ today. a) $400 b) $500 c) $700 d) $900 30. You deposit $ 2 , 000 in a savings account, and a year later you have $ 2 , 100 . Meanwhile, the consumer price index rises from 200 to 204 . In this case, the nominal interest rate is _________ percent, and the real interest rate is __________ percent. a) 1, 5 b) 3, 5 c) 5, 1 d) 5, 3 31. For a given year, productivity in a particular country is most closely matched with that country's a) level of real GDP over that year. b) growth rate of real GDP per person over that year. c) level of real GDP divided by hours worked over that year. d) growth rate of real GDP divided by hours worked over that year. 32. “When workers already have a large quantity of capital to use in producing goods and services, giving them an additional unit of capital increases their productivity only slightly.” This statement a) represents the traditional view of the production process. b) is made under assumption that the quantities of human capital, natural resources, and technology are being held constant. c) is an assertion that capital is subject to diminishing returns. d) all of the above. 33. The key determinant of the standard of living in a country is a) the amount of goods and services produced from each hour of a worker's time. b) its growth rate of real GDP c) the total amount of goods and services produced within that country d) the total amount of its physical capital 34. Which of the following is not correct a) Countries that have had higher output growth per person have typically done so without higher productivity growth. b) Increases in productivity can be used to increase output or leisure. c) A country's standard of living and its productivuty are closely related. d) Productivity refers to output produced per hour worked. 35. Other things the same, when an economy increases its saving rate a) consumption and production rise now. b) consumption falls now and production falls later. c) consumption rises now and production rises later. d) consumption falls now and production rises later. 36. In an economy where net exports are zero, if saving rises in some period, then in that period a) consumption and investment fall. b) consumption rises and investment falls. c) consumption falls and investment rises. d) consumption rises and investment falls. Key 1.A 2.D 3.B 4.B 5.D 6.B 7.A 8.B 9.A 10A 11B 12A 13A 14C 15A 16B 17A 18D 19B 20C 21D 22C 23B 24A 25C 26B 27D 28.A 29.A 30.A 31.C 32.D 33.A 34.A 35.D 36.C

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Chapter 7, Problem 14 is Solved
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Textbook: Fundamentals of Differential Equations and Boundary Value Problems
Edition: 6
Author: Kent Nagle
ISBN: 9780321747747

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Solution: In 1117, determine the inverse Laplace transform