Presentation is loading. Please wait.

Presentation is loading. Please wait.

ECO102 Principles of Macroeconomics Problem Session-2 by Research Assistant Serkan Değirmenci 15.03.2012.

Similar presentations


Presentation on theme: "ECO102 Principles of Macroeconomics Problem Session-2 by Research Assistant Serkan Değirmenci 15.03.2012."— Presentation transcript:

1 ECO102 Principles of Macroeconomics Problem Session-2 by Research Assistant Serkan Değirmenci 15.03.2012

2 Today Mankiw (2008), Principles of Economics: - Chapter 27: The Basic Tools of Finance: (pages: 597-612) Questions for Review (QfR): 1-7 (page: 611) Problem and Applications (P&A): 1-11 (page: 611-612) - Chapter 29: The Monetary System: Questions for Review: 1-2-3-4-5-6-7-8-9 (page: 660) Problems and Applications: 2-3-4-5-6-7-8-9-10-11-12-13 (page: 660-661)

3 Chapter 27: QfR-1 (page: 611) The interest rate is 7 percent. Use the concept of present value to compare $200 to be received in 10 years and $300 to be received in 20 years. ANSWER: If the interest rate is 7%, the present value of $200 to be received in 10 years is $200/(1.07) 10 = $101.67. If the interest rate is 7%, the present value of $300 to be received 20 years from now is $300/(1.07) 20 = $77.53.

4 Chapter 27: QfR-2 (page: 611) What benefit do people get from the market for insurance? What two problems impede the insurance company from working perfectly? ANSWER: Purchasing insurance allows an individual to reduce the level of risk he faces. Two problems that impede the insurance industry from working correctly are adverse selection and moral hazard. Adverse selection occurs because a high-risk person is more likely to apply for insurance than a low-risk person is. Moral hazard occurs because people have less incentive to be careful about their risky behavior after they purchase insurance.

5 Chapter 27: QfR-3 (page: 611) What is diversification? Does a stockholder get more diversification going from 1 to 10 stocks or going from 100 to 120 stocks? ANSWER: Diversification is the reduction of risk achieved by replacing a single risk with a large number of smaller unrelated risks. A stockholder will get more diversification going from 1 to 10 stocks than from 100 to 120 stocks. (see Figure 2 on page 604) Dont put all your eggs in one basket.

6 Chapter 27: QfR-4 (page: 611) Comparing stocks and government bonds, which has more risk? Which pays a higher average return? ANSWER: Stocks have more risk because their value depends on the future value of the firm. Because of its higher risk, shareholders will demand a higher return. There is a positive relationship between risk and return.

7 Chapter 27: QfR-5 (page: 611) What factors should a stock analyst think about in determining the value of a share of stock? ANSWER: A stock analyst will consider the future profitability of a firm when determining the value of the stock.

8 Chapter 27: QfR-6 (page: 611) Describe the efficient markets hypothesis and give a piece of evidence consistent with this hypothesis. ANSWER: The efficient markets hypothesis suggests that stock prices reflect all available information. This means that we cannot use current information to predict future changes in stock prices. One piece of evidence that supports this theory is the fact that many index funds outperform mutual funds that are actively managed by a professional portfolio manager.

9 Chapter 27: QfR-7 (page: 611) Explain the view of those economists who are skeptical of the efficient market hypothesis. ANSWER: Economists who are skeptical of the efficient markets hypothesis believe that fluctuations in stock prices are partly psychological. People may in fact be willing to purchase a stock that is overvalued if they believe that someone will be willing to pay even more in the future. This means that the stock price may not be a rational valuation of the firm.

10 Chapter 27: P&A-1 (page: 611) Your bank account pays an interest rate of 8 percent. You are considering buying a share of stock in XYZ Corporation for $110. After 1,2, and 3 years, it will pay a dividend of $5. You expect to sell the stock after 3 years for $120. Is XYZ a good investment? Support your answer with calculations. ANSWER: The value of the stock is equal to the present value of its dividends and its final sale price. This is equal to $5/1.08 + $5/(1.08) 2 + ($5 + $120)/(1.08) 3 = $4.63 + $4.29 + $99.23 = $108.15. Since this is lower than the initial selling price of $110, XYZ stock is not a good investment.

11 Chapter 27: P&A-2 (page: 611) According to an old myth, Native Americans sold the island of Manhattan about 400 years ago for $24. If they had invested this amount at an interest rate of 7 percent per year, how much would they have today? ANSWER: The future value of $24 invested for 400 years at an interest rate of 7% is (1.07) 400 $24 = $13,600,000,000,000 = $13.6 trillion.

12 Chapter 27: P&A-3 (page: 612) A company has an investment project that would cost $10 million today and yield a payoff of $15 million in 4 years. a. Should the firm undertake the project if the interest rate is 11 percent? 10 percent? 9 percent? 8 percent? b. Can you figure out the exact cutoff for the interest rate between the profitability and nonprofitability? ANSWER: a. The present value of $15 million to be received in four years at an interest rate of 11% is $15 million/(1.11) 4 = $9.88 million. Because the present value of the payoff is less than the cost, the project should not be undertaken. The present value of $15 million to be received in four years at an interest rate of 10% is $15 million/(1.10) 4 = $10.25 million. Because the present value of the payoff is greater than the cost, the project should be undertaken. The present value of $15 million to be received in four years at an interest rate of 9% is $15 million/(1.09) 4 = $10.63 million. Because the present value of the payoff is greater than the cost, the project should be undertaken. The present value of $15 million to be received in four years at an interest rate of 8% is $15 million/(1.08) 4 = $11.03 million. Because the present value of the payoff is greater than the cost, the project should be undertaken. b. The exact cutoff for the interest rate between profitability and nonprofitability is the interest rate that will equate the present value of receiving $15 million in four years with the current cost of the project ($10 million): Therefore, an interest rate of 10.67% would be the cutoff between profitability and nonprofitability.

13 Chapter 27: P&A-4 (page: 612) For each of the following kinds of insurance, give an example of behavior that can be called moral hazard and another example of behavior that can be called adverse selection. a. health insurance b. car insurance ANSWER: a. A sick person is more likely to apply for health insurance than a well person is. This is adverse selection. Once a person has health insurance, he may be less likely to take good care of himself. This is moral hazard. b. A risky driver is more likely than a safe driver to apply for car insurance. This is adverse selection. Once a driver has insurance, he may drive more recklessly. This is moral hazard.

14 Chapter 27: P&A-5 (page: 612) Imagine that the U.S. Congress, recognizing the importance of being well dressed, started giveing preferential tax treatment to clothing insurance. Under this new type of insurance, you would pay the insurance company an annual premium, the insurance company would than pay for 80 percent of your clothing expenses (you pay the remaining 20 percent), and the tax laws would partly subsidize your insurance premiums. a. How would the existence of such insurance affect the amount of clothing that people buy? How would you evaluate this change in behavior from the standpoint of economic efficiency? b. Who would choose to buy clothing insurance? c. Suppose that the average person now spends $2000 a year on clothes. Would clothing insurance cost more or less than $2000? Explain. d. In your view, is this congressional action a good idea? How would you compare this idea with the current tax treatment of health insurance? ANSWER: a. The insurance would increase the amount that individuals spend on clothing. The amount of clothing purchased would likely be greater than the efficient level, because those making the purchase decisions are not paying the entire cost. b. Individuals who desire or need to spend a lot on clothing will be those most likely to buy clothing insurance. c. Clothing insurance will cost more than $2,000. Only those who spend more than average will want to purchase the insurance. The insurance company will have to set the premium such that it covers expected losses and administrative costs. Due to the adverse selection problem, the insurance company will end up providing insurance for those who will spend more than $2,000 per year on clothing. Thus, the premium will have to be greater than $2,000. d. No, this is not a good idea. It leads to overspending on clothing. This issue is very different from health insurance, because purchases of medical care can often be life-or-death decisions. In addition, increases in health lead to higher productivity so total output in the economy can be affected by improvements in health. Last, there may be positive externalities associated with some health expenditures (such as vaccinations).

15 Chapter 27: P&A-6 (page: 612) Imagine that you intend to buy a portfolio of ten stocks with some of your savings. Should the stocks be of companies in the same industry? Should the stocks be of companies located in the same country? Explain. ANSWER: To reduce the risk associated with the portfolio, it is better to diversify. This means that the stocks should be of companies from different industries as well as located in different countries.

16 Chapter 27: P&A-7 (page: 612) Which kind of stock would you expect to pay the higher average return: stock in an industry that is very sensitive to economic conditions (such as an automaker) or stock in an industry that is relatively insensitive to economic conditions (such as a water company)? Why? ANSWER: A stock that is very sensitive to economic conditions will have more risk associated with it. Thus, we would expect for that stock to pay a higher return. To get stockholders to be willing to accept the risk, the expected return must be larger than average.

17 Chapter 27: P&A-8 (page: 612) A company faces two kinds of risk. A firm-specific risk is that a competitor might enter its market and take some of its customers. A market risk is that the economy might enter a recession, reducing sales. Which of these two risks would more likely cause the companys shareholders to demand a higher return? Why? ANSWER: Shareholders will likely demand a higher return due to the stocks firm-specific risk. Firm-specific risk is risk that affects only that particular stock. All stocks in the economy are subject to market risk.

18 Chapter 27: P&A-9 (page: 612) You have two roommates who invest in the stock market. a. One roommate says that he buys stock only in companies that everyone believes will experience big increases in profits in the future. How do you suppose the price-earnings ratio of these companies compares to the price-earnings ratio of other companies? What might be the disadvantage of buying stock in these companies? b. Another roommate says he only buys stock in companies that are cheap, which he measures by a low price-earnings ratio. How do you suppose the earnings prospects of these companies compare to those of other companies? What might be the disadvantage of buying stock in these companies? ANSWER: a. If a roommate is buying stocks in companies that everyone believes will experience big profits in the future, the price-earnings ratio is likely to be high. The price is high because it reflects everyones expectations about the firms future earnings. The largest disadvantage in buying these stocks is that they are currently overvalued and may not pay off in the future. b. Firms with low price-earnings ratios will likely have lower future earnings. The reason why these stocks are cheap is that everyone has lower expectations about the future profitability of these firms. The largest disadvantage to buying this stock is that the market may be correct and the firm's stock may provide a low return.

19 Chapter 27: P&A-10 (page: 612) When company executives buy and sell stock based on private information they obtain as part of their jobs, they are engaged in insider trading. a. Give an example of inside information that might be useful for buying and or selling stock. b. Those who trade stocks based on inside information usually earn very high rates of return. Does this fact violate the efficient markets hypothesis? c. Insider trading is illegal. Why do you suppose that is? ANSWER: a. Answers will vary, but may include things like information on new products under development or information concerning future government regulations that will affect the profitability of the firm. b. The fact that those who trade stocks based on inside information earn very high rates of return does not violate the efficient markets hypothesis. The efficient market hypothesis suggests that the price of a stock reflects all available information concerning the future profitability of the firm. Inside information is not readily available to the public and thus is not reflected in the stocks price. c. Insider trading is illegal because it gives some buyers or sellers an unfair advantage in the stock market.

20 Chapter 27: P&A-11 (page: 612) Find some information on an index fund (such as the Vanguard Total Stock Market Index, ticker symbol VTSMX). How has this fund performed compared with other stock mutual funds over the past 5 or 10 years? (Hint: One place to look for data on mutual funds is http://www.morningstar.com.) What do you learn from this comparison?http://www.morningstar.com ANSWER: Answers will vary.

21 Chapter 29: QfR-1 (page: 660) What distinguishes money from other assets in the economy? ANSWER: (PAGE: 643) Money is different from other assets in the economy because it is the most liquid asset available. Other assets vary widely in their liquidity.

22 Chapter 29: QfR-2 (page: 660) What is commodity money? What is fiat money? Which kind do we use? ANSWER: (PAGE: 643-645) Commodity money is money with intrinsic value, like gold, which can be used for purposes other than as a medium of exchange. Fiat money is money without intrinsic value; it has no value other than its use as a medium of exchange. Our economy today uses fiat money. *the term instrictic value means that the item would have value even if it were not used as money.

23 Chapter 29: QfR-3 (page: 660) What are demand deposits, and why should they be included in the stock of money? ANSWER: (PAGE: 646) Demand deposits are balances in bank accounts that depositors can access on demand simply by writing a check. They should be included in the supply of money because they can be used as a medium of exchange.

24 Chapter 29: QfR-4 (page: 660) Who is responsible for setting monetary policy in the United States? How is this group chosen? ANSWER: (PAGE: 648-649) The Federal Open Market Committee (FOMC) is responsible for setting monetary policy in the United States. The FOMC consists of the 7 members of the Federal Reserve Board of Governors and 5 of the 12 presidents of Federal Reserve Banks. Members of the Board of Governors are appointed by the president of the United States and confirmed by the U.S. Senate. The presidents of the Federal Reserve Banks are chosen by each banks board of directors.

25 Chapter 29: QfR-5 (page: 660) If the Fed wants to increase the money supply with open- market operations, what does it do? ANSWER: (PAGE: 653) If the Fed wants to increase the supply of money with open- market operations, it purchases U.S. government bonds from the public on the open market. The purchase increases the number of dollars in the hands of the public, thus raising the money supply.

26 Chapter 29: QfR-6 (page: 660) Why dont banks hold 100 percent reserves? How is the amount of reserves banks hold related to the amount of money the banking system creates? ANSWER: (PAGE: 650-651-653-653) Banks do not hold 100% reserves because it is more profitable to use the reserves to make loans, which earn interest, instead of leaving the money as reserves, which earn no interest. The amount of reserves banks hold is related to the amount of money the banking system creates through the money multiplier. The smaller the fraction of reserves banks hold, the larger the money multiplier, because each dollar of reserves is used to create more money.

27 Chapter 29: QfR-7 (page: 660) What is the discount rate? What happens to the money supply when the Fed raises the discount rate? ANSWER: (PAGE: 655-656) The discount rate is the interest rate on loans that the Federal Reserve makes to banks. If the Fed raises the discount rate, fewer banks will borrow from the Fed, so both banks' reserves and the money supply will be lower.

28 Chapter 29: QfR-8 (page: 660) What are reserve requirements? What happens to the money supply when the Fed raises reserve requirements? ANSWER: (PAGE: 654) Reserve requirements are regulations on the minimum amount of reserves that banks must hold against deposits. An increase in reserve requirements raises the reserve ratio, lowers the money multiplier, and decreases the money supply.

29 Chapter 29: QfR-9 (page: 660) Why cant the Fed control the money supply perfectly? ANSWER: (PAGE: 656) The Fed cannot control the money supply perfectly because: (1) the Fed does not control the amount of money that households choose to hold as deposits in banks; and (2) the Fed does not control the amount that bankers choose to lend. The actions of households and banks affect the money supply in ways the Fed cannot perfectly control or predict.

30 Chapter 29: P&A-2 (page: 660) Which of the following are money in the U.S. economy? Which are not? Explain your answers by discussing each of the three functions of money. a. a U.S. penny b. a Mexican peso c. a Picasso painting d. a plastic credit card ANSWER: a.A U.S. penny is money in the U.S. economy because it is used as a medium of exchange to buy goods or services, it serves as a unit of account because prices in stores are listed in terms of dollars and cents, and it serves as a store of value for anyone who holds it over time. b.A Mexican peso is not money in the U.S. economy, because it is not used as a medium of exchange, and prices are not given in terms of pesos, so it is not a unit of account. It could serve as a store of value, though. c.A Picasso painting is not money, because you cannot exchange it for goods or services, and prices are not given in terms of Picasso paintings. It does, however, serve as a store of value. d.A plastic credit card is similar to money, but represents deferred payment rather than immediate payment. So credit cards do not fully represent the medium of exchange function of money, nor are they really stores of value, because they represent short-term loans rather than being an asset like currency.

31 Chapter 29: P&A-3 (page: 660) What characteristics of an asset make it useful as a medium of exchange? As a store of value? ANSWER: For an asset to be useful as a medium of exchange, it must be widely accepted (so all transactions can be made in terms of it), recognized easily as money (so people can perform transactions easily and quickly), divisible (so people can provide change), and difficult to counterfeit (so people will not print their own money). That is why nearly all countries use paper money with fancy designs for larger denominations and coins for smaller denominations. For an asset to be useful as a store of value, it must be something that maintains its value over time and something that can be used directly to buy goods and services or sold when money is needed. In addition to currency, financial assets (like stocks and bonds) and physical assets (like real estate and art) make good stores of value.

32 Chapter 29: P&A-4 (page: 660) Your uncle repays a $100 loan from Tenth National Bank by writing a $100 check from his TNB checking account. Use T-accounts to show the effect of this transaction on your uncle and on TNB. Has your uncles wealth changed? Explain. ANSWER: When your uncle repays a $100 loan from Tenth National Bank (TNB) by writing a check from his TNB checking account, the result is a change in the assets and liabilities of both your uncle and TNB, as shown in these T-accounts: Your Uncle AssetsLiabilities Before: Checking Account$100Loans$100 After: Checking Account$0Loans$0 Tenth National Bank AssetsLiabilities Before: Loans$100Deposits$100 After: Loans$0Deposits$0 By paying off the loan, your uncle simply eliminated the outstanding loan using the assets in his checking account. Your uncle's wealth has not changed; he simply has fewer assets and fewer liabilities.

33 Chapter 29: P&A-5 (page: 660) Beleaguered State Bank (BSB) holds $250 million in deposits and maintains a reserve ratio of 10 percent. a. Show a T-account for BSB. b. Now suppose that BSBs largest depositor withdraws $10 million in cash from her account. If BSB decides to restore its reserve ratio by reducing the amount of loans outstanding, show its new T-account. c. Explain what effect BSBs action will have on other banks. d. Why might it be difficult for BSB to take the action described in part (b)? Discuss another way for BSB to return to its original reserve ratio.

34 Chapter 29: P&A-5 (page: 660)-cont. ANSWER: a. Here is BSB's T-account: Beleaguered State Bank AssetsLiabilities Reserves$25 millionDeposits$250 million Loans$225 million b. When BSB's largest depositor withdraws $10 million in cash and BSB reduces its loans outstanding to maintain the same reserve ratio, its T-account is now: Beleaguered State Bank AssetsLiabilities Reserves$24 millionDeposits$240 million Loans$216 million c. Because BSB is cutting back on its loans, other banks will find themselves short of reserves and they may also cut back on their loans as well. d. BSB may find it difficult to cut back on its loans immediately, because it cannot force people to pay off loans. Instead, it can stop making new loans. But for a time it might find itself with more loans than it wants. It could try to attract additional deposits to get additional reserves, or borrow from another bank or from the Fed.

35 Chapter 29: P&A-6 (page: 660) You take $100 you had kept under your mattress and deposit it in your bank account. If this $100 stays in the banking system as reserves and if banks hold reserves equal to 10 percent of deposits, by how much does the total amount of deposits in the banking system increase? By how much does the money supply increase? ANSWER: If you take $100 that you held as currency and put it into the banking system, then the total amount of deposits in the banking system increases by $1,000, because a reserve ratio of 10% means the money multiplier is 1/.10 = 10. Thus, the money supply increases by $900, because deposits increase by $1,000 but currency declines by $100.

36 Chapter 29: P&A-7 (page: 660) The Federal Reserve conducts a $10 million open-market purchase of government bonds. If the required reserve ratio is 10 percent, what is the largest possible increase in the money supply that could result? Explain. What is the smallest possible increase? Explain. ANSWER: With a required reserve ratio of 10%, the money multiplier could be as high as 1/.10 = 10, if banks hold no excess reserves and people do not keep some additional currency. So the maximum increase in the money supply from a $10 million open-market purchase is $100 million. The smallest possible increase is $10 million if all of the money is held by banks as excess reserves.

37 Chapter 29: P&A-8 (page: 660) Assume that the reserve requirement is 5 percent. All other thing equal, will the money supply expand more if the Federal Reserve buys $2000 worth of bonds or if someone deposits in a bank $2000 that he had been hiding in his cookie jar? If one creates more, how much more does it create? Support your thinking. ANSWER: The money supply will expand more if the Fed buys $2,000 worth of bonds. Both deposits will lead to monetary expansion. But the Feds deposit is new money. The $2,000 from the cookie jar is already part of the money supply.

38 Chapter 29: P&A-9 (page: 660) Suppose that the T-account for First National Bank is as follows: a. If the Fed requires banks to hold 5 percent of deposits as reserves, how much in excess reserves does First National now hold? b. Assume that all other banks hold only the required amount of reserves. If First National decides to reduce its reserves to only the required amount, by how much would the economys money supply increase? ANSWER: a. If the required reserve ratio is 5%, then ABC Bank's required reserves are $500,000 x.05 = $25,000. Because the banks total reserves are $100,000, it has excess reserves of $75,000. b. With a required reserve ratio of 5%, the money multiplier is 1/.05 = 20. If ABC Bank lends out its excess reserves of $75,000, the money supply will eventually increase by $75,000 x 20 = $1,500,000.

39 Chapter 29: P&A-10 (page: 661) Suppose that the reserve requirement for checking deposits is 10 percent and that banks do not hold any excess reserves. a. If the Fed sells $1 million of government bonds, what is the effect on the economys reserves and money supply? b. Now suppose the Fed lowers the reserve requirement to 5 percent, but banks choose to hold another 5 percent of deposits as excess reserves. Why might banks do so? What is the overall change in the money multiplier and the money supply as a result of these actions? ANSWER: a. With a required reserve ratio of 10% and no excess reserves, the money multiplier is 1/.10 = 10. If the Fed sells $1 million of bonds, reserves will decline by $1 million and the money supply will contract by 10 x $1 million = $10 million. b. Banks might wish to hold excess reserves if they need to hold the reserves for their day-to-day operations, such as paying other banks for customers' transactions, making change, cashing paychecks, and so on. If banks increase excess reserves such that there is no overall change in the total reserve ratio, then the money multiplier does not change and there is no effect on the money supply.

40 Chapter 29: P&A-11 (page: 661) Assume that the banking system has total reserves of $100 billion. Assume also that required reserves are 10 percent of checking deposits, and that banks hold no excess reserves and households hold no currency. a. What is the money multiplier? What is the money supply? b. If the Fed now raises required reserves to 20 percent of deposits, what is the change in reserves and the change in the money supply? ANSWER: a. With banks holding only required reserves of 10%, the money multiplier is 1/.10 = 10. Because reserves are $100 billion, the money supply is 10 x $100 billion = $1,000 billion. b. If the required reserve ratio is raised to 20%, the money multiplier declines to 1/.20 = 5. With reserves of $100 billion, the money supply would decline to $500 billion, a decline of $500 billion. Reserves would be unchanged.

41 Chapter 29: P&A-12 (page: 661) Assume that the reserve requirement is 20%. Also assume that banks do not hold excess reserves and there is no cash held by public. The Federal Reserve decides that it wants to expand the money supply by $40 million dollars. a. If the Fed is using open-market operations, will it buy or sell bonds? b. What quantity of bonds does the Fed need to buy or sell to accomplish the goal? Explain your reasoning. ANSWER: a. To expand the money supply, the Fed should buy bonds. b. With a reserve requirement of 20%, the money multiplier is 1/0.20 = 5. Therefore to expand the money supply by $40 million, the Fed should buy $40 million/5 = $8 million worth of bonds.

42 Chapter 29: P&A-13 (page: 661) The economy of Elmendyn contains 2,000 $1 bills. a. If people hold all money as currency, what is the quantity of money? b. If people hold all money as demand deposits and banks maintain 100 percent reserves, what is the quantity of money? c. If people hold equal amounts of currency and demand deposits and banks maintain 100 percent reserves, what is the quantity of money? d. If people hold all money as demand deposits and banks maintain a reserve ratio of 10 percent, what is the quantity of money? e. If people hold equal amounts of currency and demand deposits and banks maintain a reserve ratio of 10 percent, what is the quantity of money?

43 Chapter 29: P&A-13 (page: 661)-cont. ANSWER: a. If people hold all money as currency, the quantity of money is $2,000. b.If people hold all money as demand deposits at banks with 100% reserves, the quantity of money is $2,000. c.If people have $1,000 in currency and $1,000 in demand deposits, the quantity of money is $2,000. d.If banks have a reserve ratio of 10%, the money multiplier is 1/.10 = 10. So if people hold all money as demand deposits, the quantity of money is 10 x $2,000 = $20,000. e.If people hold equal amounts of currency (C) and demand deposits (D) and the money multiplier for reserves is 10, then two equations must be satisfied: (1) C = D, so that people have equal amounts of currency and demand deposits; and (2) 10 x ($2,000 – C) = D, so that the money multiplier (10) times the number of dollar bills that are not being held by people ($2,000 – C) equals the amount of demand deposits (D). Using the first equation in the second gives 10 x ($2,000 – D) = D, or $20,000 – 10D = D, or $20,000 = 11 D, so D = $1,818.18. Then C = $1,818.18. The quantity of money is C + D = $3,636.36.

44 to be continued…


Download ppt "ECO102 Principles of Macroeconomics Problem Session-2 by Research Assistant Serkan Değirmenci 15.03.2012."

Similar presentations


Ads by Google