Study guide 4 econ
5 Pages

Study guide 4 econ

Course Number: ECON 2200, Fall 2011

College/University: Kennesaw

Word Count: 7039

Rating:

Document Preview

A bond is a b. certificate of indebtedness. A cable television broadcast of a movie is b. excludable and not rival in consumption. A country has a comparative advantage in a product if the world price is b. higher than that countrys domestic price without trade. A decrease in demand is represented by d. a leftward shift of a demand curve. A Fed sale of bonds will cause a reduction in the interest rate and an...

Unformatted Document Excerpt
Coursehero >> Georgia >> Kennesaw >> ECON 2200

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

bond A is a b. certificate of indebtedness. A cable television broadcast of a movie is b. excludable and not rival in consumption. A country has a comparative advantage in a product if the world price is b. higher than that countrys domestic price without trade. A decrease in demand is represented by d. a leftward shift of a demand curve. A Fed sale of bonds will cause a reduction in the interest rate and an increase in the equilibrium quantity of money b. False. A firm in China sells toys to a U.S. department store chain. Other things the same, these sales b. decrease U.S. net exports and increase Chinese net exports. A firm in India hires a U.S. firm to provide economic forecasts. By itself this transaction a. increases U.S. exports and so increases the U.S. trade balance. A logical starting point from which the study of international trade begins is d. the principle of comparative advantage. A mortgage interest deduction would be considered d. a tax loophole. A recession today may cause reduced future output capacity because of which of the following: b. a decline in investment spending. A rightward shift in the aggregate demand curve generates a __________ inflation and __________ output. c. demand-pull; higher. A shortage exists in a market if c. the current price is below its equilibrium price. A successful expansionary monetary policy will increase: a. the money supply and the level of investment. A tax increase on households: b. decreases national income by lowering household consumption. A toll collected from each car traveling during rush hour on a congested road is an effective correction to the Tragedy of the Commons for all of the following reasons except c. The toll provides an incentive for commuters to drive more fuel-efficient cars. A U.S. firm buys bonds issued by a technology center in India. This purchase is an example of U.S. a. foreign portfolio investment. By itself it is an increase in U.S. holdings of foreign bonds and increases U.S. net capital outflow. According to liquidity preference theory, a decrease in the price level shifts the c. money demand curve leftward, so the interest rate decreases. According to purchasing-power parity, which of the following necessarily equals the ratio of the foreign price level divided by the domestic price level? b. the nominal exchange rate, but not the real exchange rate. Aggregate demand shifts right when the government b. increases the money supply. An appreciation of the U.S. real exchange rate induces U.S. consumers to buy c. fewer domestic goods and more foreign goods. An important factor in the decline of the U.S. textile industry over the past 100 or so years is a. foreign competitors that can produce quality textile goods at low cost. An income tax in which the average tax rate is the same for all taxpayers would be considered a d. proportional tax. An increase in real interest rates in the United States b. encourages both U.S. and foreign residents to buy U.S. assets. An increase in the budget deficit makes domestic interest rates a. rise because the supply of loanable funds shifts left. An increase in the minimum wage would d. decrease the quantity of labor demanded but increase the quantity of labor supplied. An increase in the MPC a. increases the multiplier, so that changes in government expenditures have a larger effect on aggregate demand. An increase in the U.S. interest rate d. leads to an appreciation of the U.S. dollar. An Italian company builds and operates a pasta factory in the United States. This is.. of Italian a. foreign direct investment that increases Italian net capital outflow. An optimal tax is one that minimizes the b. total deadweight loss from the tax. Assume the money market is initially in equilibrium. If the price level increases, then according to liquidity preference theory there is an excess c. demand for money until the interest rate increases. Assume the MPC is 0.75. Assuming only the multiplier effect matters, a decrease in government purchases of $100 billion will shift the aggregate demand curve to the b. left by $400 billion. Assume, for the U.S., that the domestic price of beef without international trade is lower than the world price of beef. This suggests that, in the production of beef, a. the U.S. has a comparative advantage over other countries and the U.S. will export beef. At a given real exchange rate, which of the following, by itself, would increase the supply of dollars in the market for foreign-currency exchange? b. U.S. citizens want to buy more foreign bonds. At a price of $1.20, a local coffee shop is willing to supply 100 cinnamon rolls per day. At a price of $1.40, the coffee shop would be willing to supply 150 cinnamon rolls per day. Using the midpoint method, the price elasticity of supply is d. 2.60. At the end of World War II many European countries were rebuilding and so were eager to buy capital goods and had rising incomes. We would expect that the rebuilding increased aggregate demand in a. both the United States and Europe. Because there are positive externalities from higher education, a. private markets will under-supply college classes. Consider price level, P, and Real GDP, Y. In the short run, an increase in oil prices will cause a(n) b. increase in P and a reduction in Y. Consternation Corporation has an agreement with its workers to index completely the wage of its employees using the CPI. Consternation Corporation currently pays its production line workers $7.50 an hour and is scheduled to index their wages today. If the CPI is currently 130 and was 125 a year ago, the firm should increase the hourly wages of its workers by c. $0.30. Cost-benefit analysis is important to determine the role of government in our economy because b. cost-benefit analysis identifies the possible gains to society from government provision of a particular good. Currently, U.S. currency is b. fiat money with no intrinsic value. Economists have developed models of risk aversion using the concept of a. utility and the associated assumption of diminishing marginal utility. Economists sometimes give conflicting advice because b. economists have different values and scientific judgment. Economists study poverty and income inequality in order to answer which of the following questions? c. How much inequality is there in society?. Ed is a writer who works from his home. Ed lives nextdoor to Ricky, the drummer for a local band. Ricky needs lots of practice to earn his share of the bands profits, $250. Ed gets distracted by Rickys drumming but needs to get his writing done to earn $500 for his current article. c. less than $500. Equality of opportunities is more important than equality of incomes. This statement would be most likely attributed to which political philosophy? c. Libertarianism. Estimates of the values of which of the following non-market goods or services are included in GDP? c. the estimated rental value of owner-occupied homes Exchange rates are 120 yen per dollar, 0.8 euro per dollar, and 10 pesos per dollar. A bottle of beer in New York costs 6 dollars, 1,200 yen in Tokyo, 7.2 euro in Munich, and 50 pesos in Cancun. Where is the most expensive and the cheapest beer in that order? c. Tokyo, Cancun. Firms that are involved in more than one type of business could be evidence of an attempt to c. reduce the impact of government regulations on their business. Fiscal policy a. uses the federal governments powers of spending and taxation to affect employment, and GDP. For an economy to experience both a recession and inflation at the same time, b. the aggregate supply curve must shift to the left. For private goods allocated in markets, a. prices guide the decisions of buyers and sellers and these decisions lead to an efficient allocation of resources. Fortunade Corporation stock has a price of $100 per share, a dividend of $1.60 per share, and retained earnings of $2.00 per share. The dividend yield on this stock is c. 1.6 percent. From 1950 to today, government spending on Social Security, Medicare, and Medicaid as a percentage of GDP has b. increased from less than one percent to about eight percent. Fundamental analysis shows that Green Leaf Tea Company is fairly valued. Then Green Leaf Tea Company unexpectedly improves its production techniques and unexpectedly hires a new CEO away from another very successful tea producer. Suppose this has no effect on the price of the stock of Green Leaf Tea Company. d. Fundamental analysis would now show the corporation is undervalued. The fact that the price was unchanged is not consistent with the efficient markets hypothesis. Goods that are rival in consumption include both c. common resources and private goods. Highway engineers have proposed improving a dangerous stretch of highway at a cost of $1.5 million. They expect that it will reduce the risk of someone dying in an accident over the life of the highway from 18.3 percent to 7.8 percent. The project would be worth doing as long as a human life is worth at least b. $157,500. Human capital is d. knowledge and skills that workers have acquired. If a bushel of wheat costs $6.40 in the United States and costs 40 pesos in Mexico and the nominal exchange rate is 10 pesos per dollar, then the real exchange rate is a. 1.60. If a country allows trade and, for a certain good, the domestic price without trade is higher than the world price, b. the country will be an importer of the good. If a countrys budget deficit increases, then in the foreign exchange market, c. the supply of its currency shifts left, so the exchange rate rises. If a country's saving rate increases, then in the long run c. productivity and real GDP per person are both higher. If a nation's interest rates are relatively high compared to those of other countries, then the exchange value of its currency will tend to d. appreciate under a system of floating exchange rates. If a paper manufacturer does not bear the entire cost of the dioxin it emits, it will b. emit a higher level of dioxin than is socially efficient. If expected inflation is constant, then when the nominal interest rate increases, the real interest rate b. increases by the change in the nominal interest rate. If GDP is $5 trillion, this implies that d. B and C are correct. If in 2000 the CPI was 103 and your salary was $30,000 and today the CPI is 106 and your salary is $36,000. About how much did your real salary change over the period? d. increased by 16.6%. If net exports is a negative number for a particular year, then d. the value of foreign goods purchased exceeded the value of goods sold to foreigners during the year. If the demand curve and the supply curve for a good are straight lines, then the deadweight loss that results from a tariff is represented on the supply-and-demand graph by c. the combined areas of two different triangles. If the demand for dollars in the market for foreign-currency exchange shifts right, then the exchange rate b. rises and the quantity of dollars exchanged does not change. If the Fed wants to increase the supply of money, it b. buys bonds from banks. If the Federal Reserve is attempting to keep the value of the dollar from falling, the Fed will: b. sell foreign currencies and buy dollars. If the government of Kenya implemented a policy that decreased national saving, its real exchange rate would d. appreciate and Kenyan net exports would fall. If the long-run aggregate supply curve is vertical, the multiplier effect of a change in spending on aggregate output in the long run: c. is zero. If the marginal propensity to consume is 5/6, and there is no investment accelerator or crowding out, a $20 billion increase in government expenditures would shift the aggregate demand curve right by c. $120 billion, but the effect would be larger if there were an investment accelerator. If the MPC is 0.80 and there are no crowding-out or accelerator effects, then an initial increase in aggregate demand of $100 billion will eventually shift the aggregate demand curve to the right by c. $500 billion. If the multiplier is 2.5, then the MPC is b. 0.6. If the nominal exchange rate e is foreign currency per dollar, the domestic price is P, and the foreign price is P*, then the real exchange rate is defined as b. e(P/P*). If the production possibilities frontier is bowed outward, then ? could be d. 250. If the reserve ratio is 4 percent, then $81,250 of new money can be generated by b. $3,250 of new reserves. If the stock market booms, then b. household spending increases. To offset the effects of this on the price level and real GDP, the Fed would decrease the money supply. If the supply of loanable funds shifts left, then d. the real interest rate rises and the equilibrium quantity of loanable funds falls. If the U.S. government imposes a quota on toy imports, then c. the exchange rate rises. If there is a shortage of farm laborers, we would expect a. the wage of farm laborers to increase. If there is shortage of loanable funds, then c. neither curve shifts, but the quantity of loanable funds supplied increases and the quantity demanded decreases as the interest rate rises to equilibrium. If U.S. citizens decide to purchase more foreign assets at each interest rate, the U.S. real interest rate b. increases, the real exchange rate of the dollar depreciates, and U.S. net capital outflow increases. If U.S. citizens decide to save a larger fraction of their incomes, the real interest rate a. decreases, the real exchange rate of the dollar depreciates, and U.S. net capital outflow increases. Imagine a 2,000-acre park with picnic benches, trees, and a pond. Suppose it is publicly owned, and people are invited to enjoy its beauty. When the weather is nice, it is difficult to find parking on summer afternoons. Otherwise, it is a great place. An efficient solution to the parking problem would be to b. charge higher prices for parking at busy times. Imagine that businesses in general believe that the economy is likely to head into recession and so they reduce capital purchases. Their reaction would initially shift b. aggregate demand left. In 2007, approximately how much of federal government spending went to Social Security? b. 20%. In 2008, XYZ Corporation had total earnings of $200 million and 50 million shares of the corporations stock were outstanding. If the price-earnings ratio for In a certain economy, when income is $200, consumer spending is $145. c. $170.20. For this economy, an initial impulse of $10 in consumer spending translates into a $62.50 increase in aggregate demand. In a fractional-reserve banking system, a decrease in reserve requirements a. increases both the money multiplier and the money supply. In analyzing international trade, we often focus on a country whose economy is small relative to the rest of the world. We do so b. because then we can assume that world prices of goods are unaffected by that countrys participation in international trade. In many cases selling pollution permits is a better method for reducing pollution than imposing a corrective tax because a. it is hard to estimate the market demand curve and thus charge the "right" corrective tax. In the circular-flow diagram, b. income payments flow from firms to households, and sales revenue flows from households to firms. In the early 1900s, Henry Ford introduced a. a high-wage policy, and this policy produced many of the effects predicted by efficiency-wage theory. In the economy of Wrexington in 2008, nominal GDP was $20 billion and the GDP deflator was 50. What was Wrexingtons real GDP in 2008? c. $40 billion. In the open-economy macroeconomic model, if a country's interest rate rises, its net capital outflow d. falls and the real exchange rate rises. In the open-economy macroeconomic model, if investment demand increases, then a. the supply of dollars in the market for foreign-currency exchange shifts left. In the open-economy macroeconomic model, if there is a surplus in the market for foreign-currency exchange, which of the following will move the market to equilibrium? b. the real exchange rate depreciates and net exports rise. In the open-economy macroeconomic model, the supply of loanable funds equals a. national saving. The demand for loanable funds comes from domestic investment + net capital outflow. In the short run, which of the following rates of growth in the money supply is likely to lead to the lowest level of unemployment in the economy? d. 9 percent per year. In which of the following cases is the Coase theorem most likely to solve the externality? a. Ed is allergic to his roommates cat. Individual Retirement Accounts and 401(k) plans make the current U.S. tax system d. more like a consumption tax than it otherwise would be. Ipo did not work last week because flooding forced an evacuation of her workplace. The Bureau of Labor Statistics counts Ipo as c. employed and in the labor force. Keynes used the term "animal spirits" to refer to b. arbitrary changes in attitudes of household and firms. Last year, Tealandia produced 50,000 bags of green tea, and tea was the only good Tealandia produced. Each bag sold at 4 units each of Tealandia's currency the Leaf. Tealandia's money supply was 40,000. What was the velocity of money in Tealandia? b. 5 Medicaid and food stamps are b. forms of in-kind assistance. Money demand depends on a. the price level and the interest rate. Most economists believe that a cut in tax rates c. has a relatively small effect on the aggregate-supply curve. Most economists believe that money neutrality holds b. in the long run but not the short run. Oceania buys $40 of wine from Escudia and Escudia buys $100 of wool from Oceania. Supposing this is the only trade that these countries do. What are the net exports of Oceania and Escudia in that order? c. $60 and -$60. Of the following groups, who is eligible for unemployment insurance benefits? b. the unemployed who were laid off because their previous employers no longer needed their skills. On average, the distribution of income tends to be d. more equal in richer countries than in poorer countries. One reason that deadweight losses are so difficult to avoid is that a. taxes affect the decisions that people make. Other things the same, a fall in an economy's overall level of prices tends to b. raise the quantity demanded of goods and services, but lower the quantity supplied. Other things the same, a higher real interest rate raises the quantity of d. loanable funds supplied. Other things the same, an increase in the U.S. interest rate causes the quantity of loanable funds supplied to b. rise because national saving rises. Other things the same, as the real interest rate rises b. domestic investment and net capital outflow both fall. Other things the same, if the price level rises, people d. decrease foreign bond purchases, so the supply of dollars in the market for foreign-currency exchange decreases. Other things the same, if the U.S. real exchange rate depreciated, then U.S. net exports would d. rise and the quantity of dollars demanded in the market for foreigncurrency exchange would rise. Other things the same, in the open-economy macroeconomic model, which of the following would make India's net capital outflow increase? b. a decrease in Indian interest rates. Other things the same, the aggregate quantity of goods demanded in the U.S. increases if c. the dollar depreciates. Other things the same, when the price level rises, interest rates b. rise, which means consumers will want to spend less on homebuilding. People might deposit more money into interest-bearing accounts, a. making the interest rate fall, if there is a surplus in the money market. Prices rise when the quantity of money rises rapidly is an example of a b. positive economic statement. Real GDP b. measures economic activity and income. Refer to Figure 2-12. Taking cause and effect into account, which of the following interpretations would be most reasonable regarding the relationship between coffee and hours without sleep? c. The more coffee a person drinks per day, the more time he can go without sleep. Refer to Figure 2-6. This economy has the ability to produce at which point(s)? c. A, B, C, F, G. Refer to Figure 26-2. Which of the following events would shift the demand curve from D1 to D2? b. Firms become optimistic about the future and, as a result, they plan to increase their purchases of new equipment and construction of new factories. Refer to Figure 27-1. Which distance along the vertical axis represents the marginal utility of an increase in wealth from $600 to $800? d. the distance between point B and point C. Refer to Figure 27-2. Point A represents a situation in which d. All of the above are correct. Refer to Figure 2-8, Panel (a). Production point at K is b.possible but inefficient. Refer to Figure 30-3. If the relevant money-supply curve is the one labeled MS2, then a. when the money market is in equilibrium, one dollar purchases about one-third of a basket of goods and services. Refer to Figure 32-1. In the Figure shown, if the real interest rate is 6 percent, the quantity of loanable funds demanded is b. $20 billion, and the quantity supplied is $60 billion. Refer to Figure 32-3. Which curve is determined by net capital outflow only? d. the supply curve in panel c. Refer to Figure 3-3. If the production possibilities frontiers shown are each for one day of production, then which of the following combinations of tacos and burritos could Bob and Enid together produce in a given day? c. 600 tacos and 150 burritos. Refer to Figure 33-1. If the economy is at A and there is a fall in aggregate demand, in the short run the economy d. moves to D. Refer to Figure 34-5. Suppose the multiplier is 3 and the government increases its purchases by $25 billion. Also, suppose the AD curve would shift from AD1 to AD2 if there were no crowding out; the AD curve actually shifts from AD1 to AD3 with crowding out. Finally, assume the horizontal distance between the curves AD1 and AD3 is $30 billion. The extent of crowding out, for any particular level of the price level, is c. $45 billion. Refer to Figure 3-9. Azerbaijan has an absolute advantage in the production of d. nails and a comparative advantage in the production of nails. Refer to Figure 3-9. Azerbaijans opportunity cost of one nail is a. 1/4 bolt and Uzbekistans opportunity cost of one nail is 1/2 bolt. Refer to Figure 4-10. In this market, equilibrium price and quantity, respectively, are b. $20 and 600. Refer to Figure 4-14. Panel (b) shows which of the following? a. a decrease in demand and a decrease in quantity supplied. Refer to Figure 4-14. Which of the four panels illustrates a decrease in quantity demanded? d. Panel (d). Refer to Figure 4-2. The movement from point A to point B on the graph is caused by b. a decrease in price. Refer to Figure 4-7. The movement from S to S could be caused by b. an improvement in technology. Refer to Figure 5-15. If, holding the supply curve fixed, there were an increase in demand that caused the equilibrium price to increase from $6 to $8, then sellers total revenue would a. increase. Refer to Figure 5-3. Between point A and point B on the graph, demand is d. elastic, but not perfectly elastic. Refer to Figure 5-8. For prices below $5, demand is price b. inelastic, and raising price will increase total revenue. Refer to Figure 9-1. In the absence of trade, total surplus in New Zealand is represented by the area b. A + B + C + D + F. Refer to Figure 9-1. In the absence of trade, total surplus in the New Zealand wool market amounts to d. 412.5. Refer to Figure 9-1. Relative to the no-trade situation, trade with the rest of the world results in a. New Zealand consumers paying a higher price for wool. Refer to Figure 9-1. When trade in wool is allowed, consumer surplus in New Zealand c. decreases by the area B + D. Refer to Figure 9-10. When trade takes place, the quantity Q2 - Q1 is d. the number of cameras imported by Australia. Refer to Figure 9-11. Producer surplus in this market after trade is a. C. Refer to Figure 9-11. Producer surplus plus consumer surplus in this market before trade is b. A + B + C. Refer to Figure 9-12. Consumer surplus after trade is a. $1,600. Refer to Figure 9-12. Producer surplus after trade is c. $6,400. Refer to Figure 9-13. Consumer surplus before trade is d. $3,600. Refer to Figure 9-14. When the country for which the figure is drawn allows international trade in computers, a. consumer surplus for domestic computer consumers decreases. Refer to Figure 9-15. Consumer surplus with the tariff is b. A + B. Refer to Figure 9-16. The tariff b. increases producer surplus by the area C, decreases consumer surplus by the area C + D + E + F, and decreases total surplus by the area D + F. Refer to Figure 9-17. Without trade, consumer surplus is b. $100 and producer surplus is $200. Refer to Figure 9-18. Suppose Isoland changes from a no-trade policy to a policy that allows international trade. If the world price of peaches is $3, then the policy change results in a d. $12.50 increase in total surplus. Refer to Figure 9-2. Without trade, producer surplus is a. $210. Refer to Figure 9-3. The increase in total surplus in China when trade is allowed is b. $500. Refer to Figure 9-4. Which of the following statements is accurate? b. Producer surplus with trade is $375. Refer to Figure 9-5. If this country allows free trade in wagons, a. consumers will gain more than producers will lose. Refer to Scenario 12-1. Assume that the government places a $4 tax on each slice of cheesecake and that the new equilibrium price is $7. What is Joan's consumer surplus from cheesecake? a. zero Refer to Scenario 12-3. At what level of income would the taxpayers marginal tax rate be 30 percent and her average tax rate be 25 percent? d. $80,000 Refer to Scenario 12-3. The taxpayer faces b. an average tax rate of 22.0 percent when her income is $50,000. Refer to Scenario 34-1. For this economy, an initial increase of $500 in net exports translates into a d. $2,500 increase in aggregate demand in the absence of the crowdingout effect. Refer to Scenario 34-1. The multiplier for this economy is d. 5.00. Refer to Scenario 9-1. If trade in tomatoes is allowed, the price of tomatoes in the United States a. will increase, and this will cause consumer surplus to decrease. Refer to Scenario 9-1. If trade in tomatoes is allowed, U.S. producers of tomatoes a. will be better off. Refer to Table 10-1. What is the equilibrium quantity of output in the market? b. 3 units. Refer to Table 12-1. If Celeste has $47,000 in taxable income, her marginal tax rate is c. 25%. Refer to Table 12-12. Charles is a single person whose taxable income is $35,000 a year. What is his average tax rate in 2002? a. 18%. Refer to Table 12-12. Charles is a single person whose taxable income is $35,000 a year. What is his marginal tax rate in 2002? b. 28%. Refer to Table 12-17. A progressive tax is illustrated by tax c. C. Refer to Table 12-2. If Max has taxable income of $227,000, his marginal tax rate is c. 34%. Refer to Table 12-5. What is the marginal tax rate for a person who makes $60,000? d. 50%. Refer to Table 12-7. What is the average tax rate for a person who makes $120,000? b. 35%. Refer to Table 20-4. What is the poverty line for a family of six with three children? b. $24,797. Refer to Table 23-5. Batterlands inflation rate from 2005 to 2006 was c. 33.3%. Refer to Table 23-5. In 2005, Batterlands real GDP was c. $400. Refer to Table 28-1. The number of adults not in the labor force of Wrexington a. increased from 2004 to 2005 and increased from 2005 to 2006. Refer to Table 28-3. What is the adult labor force in Meditor? c. 160 million. Refer to Table 28-3. What is the adult male population in Meditor? d. 135 million. Refer to Table 28-3. What is the adult unemployment rate in Meditor? b. 6.25 percent. Refer to Table 29-3. Starting from the situation as depicted by the T-account, if someone deposits $500 into the First Bank of Johnson City, and if the bank makes new loans so as to keep its reserve ratio unchanged, then the amount of new loans that it makes will be b. $400. Refer to Table 31-1. What are Argentinas net exports? d. -$25 billion. Refer to Table 3-2. Assume that Aruba and Iceland each has 80 labor hours available. If each country divides its time equally between the production of coolers and radios, then total production is c. 60 coolers and 18 radios. Refer to Table 3-3. Zimbabwes opportunity cost of one hairbrush is d. 10/3 toothbrushes and Portugals opportunity cost of one hairbrush is 6/5 toothbrushes. Refer to Table 3-5. Spain should export b. bread and import cheese. Refer to Table 4-8. Which space represents a decrease in equilibrium quantity and an indeterminate change in equilibrium price? d. D Refer to Table 5-3. Using the midpoint method, when price rises from $6 to $9, the price elasticity of demand is c. 1.00 Risk c. Both A and B are correct. Senator Blowhard represents a state in which many textile firms are located. He wants to impose tariffs on all imported textiles. Which of the following is the least likely consequence of such tariffs? c. Domestic textile sellers will have a higher rate of technological advance. Some time ago, the nation of Republica opened up its paper market to international trade. Which of the following results of this policy change is consistent with the notion that Republica has a comparative advantage over other countries in producing paper? b. Republica began exporting paper as a result of the policy change. Stacy places a $20 value on a bottle of wine, and Andrea places a $17 value on it. The equilibrium price for a bottle of wine is $15. Suppose the government levies a tax of $1 on each bottle of wine, and the equilibrium price of a bottle of wine increases to $16. What is total consumer surplus after the tax is levied? d. $5. Suppose a bank has a 10 percent reserve requirement, $4,000 in deposits, and has loaned out all it can given the reserve requirement. b. It has $400 in reserves and $3,600 in loans. Suppose an economy produces only eggs and ham. In 2005, 100 dozen eggs are sold at $3 per dozen and 50 pounds of ham are sold at $4 per pound. In 2004, the base year, eggs sold at $1.50 per dozen and ham sold at $5 per pound. For 2005, d. nominal GDP is $500, real GDP is $400, and the GDP deflator is 125. Suppose Mexico imposes a tariff on lumber. For the tariff to have any effect, it must be the case that c. the world price without the tariff is less than the price of lumber without trade. Suppose that because of the popularity of the low-carb diet, bakeries need fewer workers and steak houses need more workers. This is an example of b. frictional unemployment created by sectoral shifts. Suppose that large-scale pork production has the potential to create ground water pollution. Why might this type of pollution be considered an externality? c. The pollution has the potential for creating a health risk for water users in the region surrounding the pork production facility. Suppose that the inflation rate is higher in Turkey than in the U.S. for the next six months. Then according to purchasing power parity, if exchange rates are given in terms of how many Turkish lira or how many Turkish goods a U.S. dollar buys, a. the nominal exchange rate rises but the real exchange rate does not. Suppose that the real return from operating factories in Ghana rises relative to the real rate of return in the United States. Other things the same, a. this will increases U.S. net capital outflow and decrease Ghanan net capital outflow. Suppose that the U.S. imposes an import quota on lumber. The quota makes the real exchange rate of the U.S. dollar a. appreciate but does not change the real interest rate in the United States. Suppose the real exchange rate is 1/2 gallon of Canadian gasoline per gallon of U.S. gasoline, a gallon of U.S. gasoline costs $5.00 U.S., and a gallon of Canadian gas costs 8 Canadian dollars. What is the nominal exchange rate? a. .80 Canadian dollars per U.S. dollar Suppose there are only two firms in an economy: Cowhide, Inc. produces leather and sells it to Couches, Inc., which produces and sells leather furniture. The average price level is measured by d. the CPI or the GDP deflator. The before-trade price of fish in Denmark is $10.00 per pound. The world price of fish is $6.00 per pound. Denmark is a price-taker in the fish market. If Denmark begins to allow trade in fish, its consumers of fish will become d. better off, its producers of fish will become worse off, and on balance the citizens of Denmark will become better off. The catch-up effect refers to the idea that b. it is easier for a country to grow fast and so catch-up if it starts out relatively poor. The current price of neckties is $30, but the equilibrium price of neckties is $25. As a result, d. All of the above are correct. The fact that borrowers sometimes default on their loans by declaring bankruptcy is directly related to the characteristic of a bond called a. credit risk. The Federal Reserves open market operations involve the c. purchase and sale of government securities. The inflation tax refers to a. the revenue a government creates by printing money. The initial impact of the repeal of an investment tax credit is to shift b. aggregate demand left. The life cycle effect characterizes a lifetime income profile in which income b. rises as a worker gains maturity and experience. The long-run aggregate supply curve shifts right if c. the capital stock increases. The long-run aggregate supply curve shows that by itself a permanent change in aggregate demand would lead to a long-run change b. in the price level, but not output. The marginal benefit John gets from eating a fourth cheeseburger at a picnic is a. the total benefit John gets from eating four cheeseburgers minus the total benefit John gets from eating three cheeseburgers. The money multiplier equals b. 1/R, where R represents the reserve ratio for all banks in the economy. The Ogallala aquifer is a large underground pool of fresh water under several western states in the United States. Any farmer with land above the aquifer can at present pump water out of it. Which of the following statements about the aquifer is correct? c. The aquifer is a common property resource which will be overused if no one owns it. The poverty rate is b. the percentage of the population whose family income falls below a specified level. The president of Improvia, a developing country, proposes that his country needs to help domestic firms by imposing trade restrictions. d. These are inward-oriented policies and most economists believe they would have adverse effects on growth in Improvia. The primary determinant of a country's standard of living is b. the countrys ability to produce goods and services. The quantity of U.S. bonds foreigners want to buy is taken into account c. in the U.S. demand for loanable funds and the supply of dollars in the market for foreigncurrency exchange. The real exchange rate measures the b. price of domestic goods relative to the price of foreign goods. The sticky-wage theory of the short-run aggregate supply curve says that when the price level is lower than expected, d. production is less profitable and employment falls. The tax on gasoline is an example of b. a corrective tax. The theory of liquidity preference is most helpful in understanding c. the interest-rate effect. The type of unemployment that arises during recessions is known as b. cyclical unemployment. The typical goal of countercyclical fiscal policy is to counter the , by managing b. business cycle -- aggregate demand. The U.S. federal government collects approximately what percentage of the taxes in the economy? d. 67%. The utilitarian case for redistributing income is based on the assumption of c. diminishing marginal utility. The world price of a simple electronic calculator is $5.00. Before Singapore allowed trade in calculators, the price of a calculator there was $4.00. Once Singapore began allowing trade in calculators with other countries,Singapore began c. exporting calculators and the price of a calculator in Singapore increased to $5.00. There is a a. short-run tradeoff between inflation and unemployment. To help stabilize the economy the government should run a budget deficit: b. during a recession. Too few resources are devoted to the creation of knowledge because profit-seeking firms c. tend to free-ride on the knowledge that others have developed. U.S. Department of Labor data show that minimum-wage workers tend to be a. young and less educated. Utilitarianism is d. a political philosophy that believes the government should choose policies to maximize the total utility of society. welfare, receives $100 in food stamps. When a certain nation abandoned a policy of prohibiting international trade in automobiles in favor of a free-tree policy, the result was that the country began to import automobiles. The change in policy improved the well-being of that nation in the sense that c. the gains to automobile consumers in that nation exceeded the losses of the automobile producers in that nation. When a country allows trade and becomes an importer of a good, c. consumer surplus increases and producer surplus decreases. When a country that imports a particular good imposes a tariff on that good, b. producer surplus increases and total surplus decreases in the market for that good. When the dollar appreciates, U.S. a. exports decrease, while imports increase. When the price level changes, which of the following variables will change and thereby cause a change in the aggregate quantity of goods and services demanded? d. All of the above are correct. When the U.S. real interest rate falls, owning U.S. assets becomes d. less attractive to both U.S. residents and foreign residents. Which of the following adjust to bring aggregate supply and demand into balance? a. the price level and real output. Which of the following claims concerning the importance of effects that explain the slope of the U.S. aggregate-demand curve is correct? a. The exchange-rate effect is relatively small because exports and imports are a small part of real GDP. Which of the following could explain a decrease in the U.S. real exchange rate? c. the default risk of U.S. assets rise. Which of the following does the Federal Reserve not do? c. convert Federal Reserve Notes into gold. Which of the following examples of production of goods and services would be included in U.S. GDP? a. Samantha, a Canadian citizen, grows sweet corn in Minnesota and sells it to a grocery store in Canada. Which of the following expressions must be equal to national saving for a closed economy? b. Y - C G Which of the following is a contractionary fiscal policy? c. increasing taxes. Which of the following is a correct way to measure productivity? b. Divide the quantity of output by the number of hours worked. Which of the following is always correct? b. NCO = NX. Which of the following is an example of U.S. foreign direct investment? b. A U.S. citizen builds and operates a coffee shop in the Netherlands. Which of the following is included in the supply of U.S. dollars in the market for foreign-currency exchange in the open-economy macroeconomic model? c. A U.S. based law firm wants to build a new office in Japan. Which of the following is the most accurate statement? d. The effects of trade policy are more microeconomic than macroeconomic. Which of the following statements generates the greatest amount of disagreement among economists? d. Government should use fiscal policy to try to stabilize the economy. Which of the following statements is correct? b. Corrective taxes distort economic incentives. Which of the following statements is not correct? a. All states have state income taxes, but the percentages vary widely. Which of the following statements is not correct? b. The decline in welfare benefits since the 1970s has been associated with a decline in the percentage of children living with a single parent. Which of the following would not be included in the calculation of GDP? c. Sandy, who is on Which parable describes the problem of wild animals that are hunted to the point of extinction? b. Tragedy of the Commons. With each $1,000 of leather that it buys from Cowhide, Inc., Couches, Inc. produces a couch and sells it for $3,000. Neither firm had any inventory at the beginning of 2006. During that year, Cowhide produced enough leather for 20 couches. Couches, Inc. bought 80% of that leather for $16,000 and promised to buy the remaining 20% for $4,000 in 2007. Couches, Inc. produced 16 couches during 2006 and sold each one during that year for $3,000. What was the economy's GDP for the 2006? b. $52,000 With which of the Ten Principles of Economics is the study of international trade most closely connected? b. Trade can make everyone better off. XYZ is 20, then what is the price of a share of its stock? c. $80. You are the CEO of a U.S. firm considering building a factory in Chile. If the dollar appreciates relative to the Chilean peso, then other things the same a. it takes fewer dollars to build the factory. By itself building the factory increases U.S. net capital outflow. You bought some shares of stock and, over the next year, the price per share increased by 5 percent and the price level increased by 8 percent. Before taxes, you experienced c. a nominal gain and a real loss, and you paid taxes on the nominal gain.

Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Kennesaw - ECON - 2200
Study guide 4 ECON 2200-6 ch 32.24.35.10.11.9.12.20Multiple ChoiceIdentify the choice that best completes the statement or answers the question.________1. Other things the same, an increase in the U.S. interest rate causes the quantity of loana
Kennesaw - ECON - 2200
STUDY GUIDE 2 EC 2200-6 TR 3.30pm [Covering chapters 31, 32, 33, and 34]Multiple ChoiceIdentify the choice that best completes the statement or answers the question._1. International tradea. raises the standard of living in all trading countries.b.
Kennesaw - ECON - 2200
A bond is a b. certificate of indebtedness.A closed economy does not a. trade with other economies.A country with a relatively low level of real GDP per person is considering adopting d. neither the first nor the secondA decrease in the price of domest
UNC - DRAM - 115
AbsurdAnti-NaturalismAristotle / AristotelianDramaBox SetCamus1. Camus wrote essay called The Myth of Sisyphus, calling Sisyphusan absurd hero2. Traditional vs. Absurdism3. The word absurd in this context does not mean "logicallyimpossible," but
UNC - DRAM - 115
Drama 115/003Spring 2011Exam OneReview plays and notes for an overview of the following:Plays: Basics of plot, character and themes, especially scenes and speeches discussed in class-BacchaeLysistrataHamletTartuffeTopicsQualities of Drama and The
UNC - DRAM - 115
Notes (Amy you owe me! Luh yuh gurl!)What makes theatre?Theatre is the study of human expression and cultural outlets that give insight to societal viewsand culture. (That was my definition, Yes, yes, Amy I know Im a genius)You MUST have actors and an
UNC - ECON - 101
Pure Monopoly1 SellerNo close substitutesMany buyersBarriers to entryNatural MonopolyCost characteristics:1. Large fixed costs2. Relatively small marginal costsPrice Makers/SettersMonopolyMCATCMCD Dead weight lossDMR- Profit maximizing p
UNC - WMST - 101
WMST 101Midterm ReviewWhat is Womens Studies?Intro to KMSBefore the late 1960s there was soWMST, now over 1,000 programsMen, Latino, Black, JewishWhat is Feminism 1st and 2nd wavesThe Politics of Black Womens Studies,BlackAkasha Hull and Barbara
UNC - ASTR - 101
Summer solstice: sun at northernmost pt above celestial equator, June 21, longest day in N; Winter Solstice:sun at southernmost pt below celestial eq., Dec 21, shortest day in N; Autumnal Equinox: Sept 21, 12 hr day,axis not towards or away from sun; Ve
UNC - ASTR - 101
MOON: orbit: about 384000 km from earth, laser-ranging tech allows us to measure orbit within cm-necessary for unmannedspacecraft landings; angular diameter=0.5, radius= 1738km, mass=7.3x1022, density=3300kg/m3, gravity is 1/6 of earth, escapespeed= 2.4
UNC - ASTR - 101
LESSON 7 EQUATIONS-Shield volcanoheight depends on how much weight it cansupport, which depends on how strength ofplanet's surface gravity. On Earth and Venuswhere the surface gravities are similar, shieldvolcanoes can grow to about 10 km. On Marswh
UNC - ASTR - 101
NOTES REFERRENCED WITH CORRESPONDING HOMEWORKS Objects around earthNOTES REFERRENCED WITH CORRESPONDING HOMEWORKSNOTES REFERRENCED WITH CORRESPONDING HOMEWORKSCircumpolar stars stars that never set PolarisNOTES REFERRENCED WITH CORRESPONDING HOMEWORK
UNC - ENGL - 131
Russian Ark ScriptRussian Ghost. I open my eyes and I see nothing. I only remember there was some accident.Everyone ran for safety as best they could. I just cant remember what happened to me. Howstrange. Where am I?[Soldiers and ladies entering the W
University of Florida - MAP - 3302
11Equations for Linear System 1Equations for Linear System 2241.821.61.40x2x21.2120.840.60.460.2021.81.61.4461.21x10.80.60.40.28503214Residuals for Linear System 1x 10480x112345Residuals for Linear Syst
University of Florida - MAP - 3302
12Chapter 2. Solutions: Sensitivity Analysis: When a Little Means a Lot137.9LP Example 1: perturbed solutionsx 10LP Example 1: perturbed function values10.87.850.60.40.27.750.2x27.800.47.70.60.87.650.9990.99920.99940.99960.9998
University of Florida - MAP - 3302
13Solutions to the differential equation1.71.61.5y1.41.31.21.110510152025t3035404550Figure 2.3. Results of Challenge 2.4. The black curves result from settinga = 0.006 and a = 0.009. The blue curves have random rates chosen for eac
University of Florida - MAP - 3302
14Chapter 2. Solutions: Sensitivity Analysis: When a Little Means a Lot
University of Florida - MAP - 3302
Chapter 3Solutions: ComputerMemory and Arithmetic:A Look Under the HoodCHALLENGE 3.1. See problem1.m on the website.CHALLENGE 3.2. The counts of the number of blocks moved are summarizedin the following table:columnorientedstorageroworientedst
University of Florida - MAP - 3302
16Chapter 3. Solutions: Computer Memory and ArithmeticCHALLENGE 3.5. The data cannot be fully explained by our simple model,since, for example, this machine uses prefetching, two levels of cache, and a morecomplicated block replacement strategy than t
University of Florida - MAP - 3302
Chapter 4Solutions: Design ofComputer Programs:Writing Your LegacyCHALLENGE 4.1. See posteddoc.m on the website.CHALLENGE 4.2. Data that a function needs should be specied in variables, not constants.This is ne; C is a variable. Code should be mod
University of Florida - MAP - 3302
18Chapter 4. Solutions: Design of Computer ProgramsTimes for matrices with 200 rows310Original algorithmModified algorithm2101time (sec)1001011021050100150200number of columnsFigure 4.1. Time taken by the two algorithms for matrices
University of Florida - MAP - 3302
Unit IISOLUTIONS: Dense MatrixComputations19
University of Florida - MAP - 3302
University of Florida - MAP - 3302
Chapter 5Solutions: MatrixFactorizationsCHALLENGE 5.1.s = zeros(m,1);for j=1:n,s = s + abs(A(:,j);endCompare with:for i=1:m,s(i) = norm(A(i,:),1);endCHALLENGE 5.2.3x2 = 6 x2 = 2,12x1 + 5x2 = 8 x1 = (8 10) = 1.2The determinant is 2 3 = 6.
University of Florida - MAP - 3302
22Chapter 5. Solutions: Matrix Factorizationsx = b;detA = 1;for i=1:n,x(i) = x(i) / A(i,i);x(i+1:n) = x(i+1:n) - A(i+1:n,i)*x(i);detA = detA * A(i,i);endCHALLENGE 5.4.(a)a11 a21a31a12a22a32a13a23 = a3311210110 0033022313221
University of Florida - MAP - 3302
23CHALLENGE 5.6.for i=1:3,W = planerot(A(i:i+1,i);% Note that the next instruction just operates on the part% of A that changes. It is wasteful to do multiplications% on the rest.A(i:i+1,i:n) = W * A(i:i+1,i:n);endCHALLENGE 5.7. For G to be unita
University of Florida - MAP - 3302
24Chapter 5. Solutions: Matrix FactorizationsAlternatively, using Gram-Schmidt orthogonalization,r11 = 32 + 32 = 3 2,1q1 = 32Then31r12 = qT1q2 =3133.= 4/ 2, 4/ 2q1 ,and r22 = the norm of this vector = 2, so q2 = q2 / 2. If we complete
University of Florida - MAP - 3302
25andv2= (z eT )(z e1 )1= z z z1 z1 + = z z ei z ei ei z ei + z= 2z z 2 z .2ThenQz = (I 2uu )z2vv )z= (I v22v z=zvv2=zv= e1 .(b) Let the second column of A1 be [a, v1 , . . . , vn1 ]T . Use the vector v to form theHouseholder transf
University of Florida - MAP - 3302
26Chapter 5. Solutions: Matrix FactorizationsWe need to sum this from j = 1 to n, but we can neglect all but the highest orderterms (mn3 and n3 ), so only the cost of steps (5) and (6) are signicant. For (5)we getn12(m j + 1)(n j + 1) mn2 n3 ,3j
University of Florida - MAP - 3302
27CHALLENGE 5.12. Denec = Q b =c1c2R10,R =,where c1 is n 1, c2 is (m n) 1, R1 is n n, and 0 is (m n) n. Thenb Ax2= Q (b Ax)= c Rx 2= c1 R 1 x= c1 R 1 x222+ c2 0x22+ c2 .To minimize this quantity, we make the rst term zero by taking
University of Florida - MAP - 3302
28Chapter 5. Solutions: Matrix Factorizationswhere D is a diagonal matrix containing the1 1 21 1 2 22W= . .... ...12rrvalues 1 , . . . , r , andr. . . 11r. . . 21 . ....r. . . r1Now W is a Vandermonde matrix and has full rank r
University of Florida - MAP - 3302
29CHALLENGE 5.16.Form y = U bForm z = 1 yForm x = VzTotal:n2 multiplicationsn multiplications (zi = yi /i )n2 multiplications2n2 + n multiplicationsCHALLENGE 5.17.(a) The columns of U corresponding to nonzero singular values form such a basis,
University of Florida - MAP - 3302
30Chapter 5. Solutions: Matrix Factorizations(b) Substituting the SVD our equation becomesA x = V10U x = b,where 1 is n n with the singular values on the main diagonal. Letting y = U x,we see that a particular solution isygood =soxgood = U1 1
University of Florida - MAP - 3302
31CHALLENGE 5.20.(a) Since UV x = b, we havex = V1 U b.If we let c = U b, then 1 = c1 /1 , and 2 = c2 /2 .(b) Here is one way to look at it. This system is very ill-conditioned. The conditionnumber is the ratio of the largest singular value to the s
University of Florida - MAP - 3302
32Chapter 5. Solutions: Matrix FactorizationsCHALLENGE 5.22. (Partial Solution)(a) Find the null space of a matrix: QR (fast; relatively stable) or SVD (slower butmore reliable)(b) Solve a least squares problem: QR when the matrix is well conditioned
University of Florida - MAP - 3302
Chapter 6Solutions: Case Study:Image Deblurring: I CanSee Clearly Now(coauthored by James G. Nagy)Observe that if y is a p 1 vector and z is a q 1 vectorCHALLENGE 6.1.then2yzpq2yi +=2i=12zi = y22+ z 2.2i=1Therefore,g0KI2f2
University of Florida - MAP - 3302
34Chapter 6. Solutions: Case Study: Image Deblurring: I Can See Clearly Now2UT g VT fVT f==g ff=g022I22f.2CHALLENGE 6.3. Lets write the answer for a slightly more general case: Kof dimension m n with m n.g0I2f2= g f22+ 2 fn
University of Florida - MAP - 3302
35 One common bug in the TSVD section: zeroing out pieces of SA and SB . Thisdoes not zero the smallest singular values, and although it is very ecient intime, it gives worse results than doing it correctly. The data was generated by taking an origina
University of Florida - MAP - 3302
36Chapter 6. Solutions: Case Study: Image Deblurring: I Can See Clearly NowOriginal ImageBlurred Image50501001001501502002002502505010015020025050Tikhonov with = 0.0015100150200250TSVD with p = 250050501001001501502002002
University of Florida - MAP - 3302
Chapter 7Solutions: Case Study:Updating and DowndatingMatrix Factorizations: AChange in PlansCHALLENGE 7.1.(a) Set the columns of Z to be the dierences between the old columns and the newcolumns, and set the columns of V to be the 6th and 7th colum
University of Florida - MAP - 3302
38Chapter 7. Solutions: Case Study: Updating and DowndatingMaking ShermanMorrisonWoodbury time comparable to Backslash300250Rank of update2001501005000100200300400500600Size of matrix7008009001000Figure 7.1. Results of Challenge 4.
University of Florida - MAP - 3302
39(a) (Review)cz1 + sz2sz1 cz2Gz == xe1Multiplying the rst equation by c, the second by s, and adding yields(c2 + s2 )z1 = cx ,soc = z1 /x .Similarly, we can determine thats = z2 /x .Since c2 + s2 = 1, we conclude that22z1 + z2 = x2 ,so we
University of Florida - MAP - 3302
40Chapter 7. Solutions: Case Study: Updating and Downdating=A001So we can take00...Z = 0100...a1,n+1a2,n+1...+0an,n+11 (an+1,n+1 1)a1,n+1a2,n+1...an,n+1(an+1,n+1 1)an+1,10..an+1,n001T;V =an+1,10..an+1,n00
University of Florida - MAP - 3302
Chapter 8Solutions: Case Study:The Direction-of-ArrivalProblem: Coming at YouCHALLENGE 8.1. Let wk = SCzk , and multiply the equation BASCzk =k BASCzk by (BA)1 to obtainwk = k wk ,k = 1, . . . , d.Then, by the denition of eigenvalue, we see that k
University of Florida - MAP - 3302
42Chapter 8. Solutions: Case Study: The Direction-of-Arrival ProblemResults using rectangular windowing3025201510500100200300400500600700Figure 8.1. Results of Challenge 3: the true DOA (blue) and the DOAestimated by rectangular windowi
University of Florida - MAP - 3302
43Results using exponential windowing3025201510500100200300400500600700Figure 8.2. Results of Problem 5: the true DOA (blue) and the DOAestimated by exponential windowing (red) as a function of time.CHALLENGE 8.6.(a) The sum of the squ
University of Florida - MAP - 3302
44Chapter 8. Solutions: Case Study: The Direction-of-Arrival ProblemWe have seen that matrix-based algorithms are powerful tools for signal processing, but they must be used in the light of statistical theory and the problemsgeometry.CHALLENGE 8.8. No
University of Florida - MAP - 3302
Unit IIISOLUTIONS: Optimizationand Data Fitting45
University of Florida - MAP - 3302
University of Florida - MAP - 3302
Chapter 9Solutions: NumericalMethods forUnconstrainedOptimizationCHALLENGE 9.1.f (x) = x4 + x2 (x2 1),14x312x2 1g(x) =12x210, H(x) =02.Step 1:p=12x210024x312x2 11sox480=0232312/3+3/2=4/31/2ex1 +x2 (1 + x1 )ex1
University of Florida - MAP - 3302
48Chapter 9. Solutions: Numerical Methods for Unconstrained OptimizationCHALLENGE 9.3.x = [1;2];for i=1:5,g = [4*(x(1) - 5)^3 - x(2);4*(x(2) + 1)^3 - x(1)];H = [12*(x(1) - 5)^2, -1;-1, 12*(x(2) + 1)^2];p = -H \ g;x = x + p;endCHALLENGE 9.4. Th
University of Florida - MAP - 3302
49To verify the secant condition, computeB(k+1) s(k) = B(k) s(k) (B(k) s(k) y(k) )s(k) T s(k)s(k) T s(k)= B(k) s(k) (B(k) s(k) y(k) )= y(k) ,as desired. If vT s(k) = 0, thenB(k+1) v = B(k) v (B(k) s(k) y(k) )s(k) T vs(k) T s(k)= B(k) v,as desi
University of Florida - MAP - 3302
50Chapter 9. Solutions: Numerical Methods for Unconstrained OptimizationCHALLENGE 9.9.function Hv = Htimes(x,v,h)%%%%%%%%%%%%%Input:x is the current evaluation point.v is the direction of change in x.h is the stepsize for the change,a
University of Florida - MAP - 3302
51 Quasi-Newton: often converges superlinearly when started close enough to asolution, but requires rst derivatives (or good approximations of them) andstorage of a matrix of size 2000 2000, unless the matrix is accumulatedimplicitly by saving the vec
University of Florida - MAP - 3302
52Chapter 9. Solutions: Numerical Methods for Unconstrained Optimization
University of Florida - MAP - 3302
Chapter 10Solutions: NumericalMethods for ConstrainedOptimizationCHALLENGE 10.1. The graphical solutions are left to the reader.(a) The optimality condition is that the gradient should be zero. We calculateg(x) =2x1 x2 + 58x2 x1 + 3H(x) =2 118
University of Florida - MAP - 3302
54Chapter 10. Solutions: Numerical Methods for Constrained OptimizationThe solution is x = 0, = [5, 3]T .(d) Remembering to convert the rst constraint to form, we get102x1T02x1 x2 + 51 =8x2 x1 + 32x2 0,x 0,,1 x2 x2 0,121 x1 + 2 x2 + 3 (
University of Florida - MAP - 3302
55Therefore, our problem is equivalent tomin 5(6 + 2v )4 + (6 + 2v )(1 + v ) + 6(1 + v )2vsubject to6 + 2v 0,1 + v 0.Using a log barrier function for these constraints, we obtain the unconstrainedproblemmin B (v )vwhereB (v ) = 5(6 + 2v )4 + (
University of Florida - MAP - 3302
56Chapter 10. Solutions: Numerical Methods for Constrained Optimization(a) K is the set of vectors that form nonnegative inner products with every vectorthat has nonnegative entries. Therefore, K = K = cfw_x : x 0, the positiveorthant in Rn .(b) The
University of Florida - MAP - 3302
57CHALLENGE 10.6. (Partial Solution) We minimize by making both factorslarge in absolute value and with the same sign. The largest absolute values occur atthe corners, and the minimizers occur when x1 = x2 = 1 and when x1 = x2 = 0. Inboth cases, f (x)
University of Florida - MAP - 3302
58Chapter 10. Solutions: Numerical Methods for Constrained Optimization