1. ECON 101 Tutorial: Week 22 Shane Murphy s.murphy5@lancaster.ac.uk Office Hours: Monday 3:00-4:00 – LUMS C85

2. Outline Roll Call Problems

3. Chapter 25: Problem 1 About 400 years ago, Lenape Native Americans sold the island of Manhattan for $24. If they had invested this money at an interest rate of 7% per year, how much would they have today? The future value of $24 invested for 400 years at an interest rate of 7 percent is (1.07)^400 * $24 = $13,600,000,000,000 = $13.6 trillion

4. Why do I hate this question? What was the price in real terms? $1000 to $10000 Did the Lenape occupy Manhattan a that time? No Did Indians have a concept of property rights? Yes Is 7% a reasonable return on investments from before the 1900s? No What is the current GDP of Manhattan? ~$1.3 trillion What would be the annual value of a $13.6 trillion endowment? ~$13.6 trillion * 0.05 = ~$0.68 trillion What was the annual per capita GDP at the time? $700 for UK, $526 for Ireland, probably around $100-$300 for Indians Were non-tangible assets (goodwill, alliances) the prime driver of this deal? Yes, for both sides Are there any other examples of private, 400 year long investments? No Does the font get any smaller? Not really

5. Chapter 25: Problem 2 A company that has an investment project that would cost $10 million today and yield a payoff of $15 million in four years. a)For interest rates of 8%, 9%, 10%, and 11%, evaluate this project. The present value of €15 million to be received in four years discounted at an interest rate of 11 percent is €15 million/(1.11)^4 = €9.88 million. For an interest rate of 10%, €15 million/(1.10)^4 = €10.25 million For an interest rate of 9%, €15 million/(1.09)^4 = €10.63 million For an interest rate of 8%, €15 million/(1.08)^4 = €11.03 million b) What is the cut-off interest rate where the project changes from profitable to non-profitable? The exact cut-off for the interest rate between profitability and non- profitability 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): €10 =15/(1 + x)^4 10(1 + x)^4 = 15 (1 + x)^4 = 1.5 1 + x = (1.5)0.25 1 + x = 1.1067 x = 0.1067

6. Chapter 25: Problem 5 For which kind of stock would you expect a higher average return: stock in an industry that is sensitive to economic conditions (such as a car manufacturer), or in an industry that is insensitive to economic conditions (such as a water company)? 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.

7. Chapter 25: Problem 6 A company faces two kinds of risk. An idiosyncratic risk is that a competitor might enter its market and take customers. An aggregate risk is that the economy might enter a recession and reduce sales. Which would be more likely to cause shareholders to demand a higher return? Shareholders will probably demand a higher return due to the stock’s idiosyncratic risk. Idiosyncratic risk is risk that affects only that particular stock. All stocks in the economy are subject to aggregate risk.

8. Chapter 25: Problem 7a One flatmate buys stock only in in companies that everyone believes will experience big increases in profits in the future. How do you suppose the PE ration of these companies compares to others? What are the disadvantages of buying stock in these companies? If a flatmate 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 everyone’s expectations about the firm’s future earnings. The largest disadvantage in buying these stocks is that they are currently overvalued and may not pay off in the future.

9. Chapter 25: Problem 7b If a flatmate buys stock only in companies which are cheap (low PE ratio), how do earnings prospects of these companies compare to those of other companies? What might be the disadvantages of buying stock in these companies? Firms with low price-earnings ratios will probably 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.

10. Chapter 27: Problem 1 M = 500 billion, GDP = 10 trillion, real GDP = 5 trillion a)What is P, V? Nominal GDP = P x Y = €10,000 and Y = real GDP = €5,000, so P = (P x Y)/Y = €10,000/€5,000 = 2. Since M x V = P x Y, then V = (P x Y)/M = €10,000/€500 = 20. b) If V is constant and output grows by 5%, what will happen to nominal GDP and prices if M is constant? If M and V are unchanged and Y rises by 5 percent, then since M x V = P x Y, P must fall by 5 per cent. As a result, nominal GDP is unchanged. c) What money supply should the bank set next year to keep P stable? To keep the price level stable, the central bank must increase the money supply by 5 per cent, matching the increase in real GDP. Then, since velocity is unchanged, the price level will be stable. d) What money supply should the bank set if it want inflation at 10%? If the central bank wants inflation to be 10 per cent, it will need to increase the money supply 15 per cent. Thus M x V will rise 15 per cent, causing P x Y to rise 15 per cent, with a 10 per cent increase in prices and a 5 per cent rise in real GDP.

11. Chapter 27: Problem 2 Suppose that credit card use increases and people hold less cash. a)How does this effect money demand? If people need to hold less cash, the demand for money shifts to the left, since there will be less money demanded at any price level. b) What will happen to prices? If the central bank does not respond to this event, the shift to the left of the demand for money combined with no change in the supply of money leads to a decline in the value of money (1/P), which means the price level rises c) What can the central bank do to keep prices stable? If the central bank wants to keep the price level stable, it should reduce the money supply

12. Chapter 27: Problem 7 Michael farms beans and Dorothy farms rice. Both consume equal amounts of beans and rice. In 2014, the price o beans was 1 and rice was 3. a)If the prices increase to 2 for beans and 6 for rice, what was inflation? Were either farmers better or worse off? When the price of both goods doubles in a year, inflation is 100 percent. The total cost of purchasing equal amounts of beans and rice equals the quantity of each good times its price, added together for all goods. That is, if x is the quantity of beans, which also equals the quantity of rice, then the cost of beans and rice for the year is x(PB + PR). In the second year, the cost is x(PB' + PR'), where the ' mark refers to the price in the second year. Then we can define a price index with a value of one in the first year. In the second year, the price index has the value of the cost of goods in the second year divided by the cost of goods in the first year. Thus the price index in the second year is x(PB' + PR')/x(PB + PR) = (PB' + PR')/(PB + PR) = (€2 + €6)/(€1 + €3) = €8/€4 = 2. The inflation rate is then (2 - 1)/1 x 100% = 100%. Since the prices of all goods rise by 100 percent, the farmers get a 100 percent increase in their incomes to go along with the 100 percent increase in prices, so neither is affected by the change in prices.

13. Chapter 27: Problem 7 Michael farms beans and Dorothy farms rice. Both consume equal amounts of beans and rice. In 2014, the price o beans was 1 and rice was 3. b) If in 2015 the price of beans was 2 and of rice was 4, what was inflation? Were either farmers better or worse off? If the price of beans rises to €2 and the price of rice rises to €4, then the price index in the second year is (PB' + PR')/(PB + PR) = (€2 + €4)/(€1 + €3) = €6/€4 = 1.5, so the inflation rate is (1.5- 1)/1 x 100% = 50%. Michael is better off because his euro revenues doubled (increased 100 percent) while inflation was only 50 per cent. Dorothy is worse off because inflation was 50 percent, so the prices of the goods she buys rose faster than the price of the goods (rice) she sells, which rose only 33 percent.

14. Chapter 27: Problem 7 Michael farms beans and Dorothy farms rice. Both consume equal amounts of beans and rice. In 2014, the price o beans was 1 and rice was 3. c) If in 2015 the price of beans was 2 and the price of rice was 1.5, what was inflation? Were either farmers better or worse off? If the price of beans rises to €2 and the price of rice falls to €1.50, then the price index in the second year is (PB' + PR')/(PB + PR) = (€2 + €1.50)/(€1 + €3) = €3.50/€4 = 0.875, so the inflation rate is (0.875-1)/1 x 100% = -12.5%. Michael is better off because his euro revenues doubled (increased 100 percent) while prices overall fell 12.5 percent. Dorothy is worse off because inflation was -12.5 percent, so the prices of the goods she buys didn't fall as fast as the price of the goods (rice) she sells, which fell 50 percent.

15. Chapter 27: Problem 7 Michael farms beans and Dorothy farms rice. Both consume equal amounts of beans and rice. In 2014, the price o beans was 1 and rice was 3. d) What matters more, the overall inflation rate or the relative prices? The relative price of rice and beans matters more to Michael and Dorothy than the overall inflation rate. If the price of the good that a person produces rises more than inflation, he or she will be better off. If the price of the good a person produces rises less than inflation, he or she will be worse off.

16. Chapter 27: Problem 9 Suppose that people expect inflation to equal 3% but it goes to 5%. How will this effect the following: a)The government Unexpectedly high inflation helps the government by providing higher inflation tax revenue and reducing the real value of outstanding government debt. b) A homeowner with a fixed-rate mortgage Unexpectedly high inflation helps a homeowner with a fixed-rate mortgage because he pays a fixed nominal interest rate that was based on expected inflation, and thus pays a lower real interest rate than was expected. c) A union worker in the 2 nd year of a labour contract Unexpectedly high inflation hurts a union worker in the second year of a labour contract because the contract probably based the worker's nominal wage on the expected inflation rate. As a result, the worker receives a lower than expected real wage. d) A retired person who has invested in government savings bonds Unexpectedly high inflation hurts a retired person that has invested his savings in government bonds because the higher inflation rate means he is receiving a lower real interest rate than he had planned for.

17. Chapter 35: Problem 10 Explain why the following are true, false, or uncertain: a)The statement that "Inflation hurts borrowers and helps lenders, because borrowers must pay a higher rate of interest," is false. Higher expected inflation means borrowers pay a higher nominal rate of interest, but it is the same real rate of interest, so borrowers are not worse off and lenders are not better off. Higher unexpected inflation, on the other hand, makes borrowers better off and lenders worse off. b)The statement that "If prices change in a way that leaves the overall price level unchanged, then no one is made better or worse off," is false. Changes in relative prices can make some people better off and others worse off, even though the overall price level does not change. See problem 7 for an illustration of this. c)The statement that "Inflation does not reduce the purchasing power of most workers" is true. Most workers' incomes keep up with inflation reasonably well.