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ECON 100 Tutorial: Week 17 www.lancaster.ac.uk/postgrad/murphys4/ s.murphy5@lancaster.ac.uk office hours: 3:00PM to 4:45PM Tuesdays LUMS C85

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Question 1(a)

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A firm can buy a new machine for £50,000. The firm estimates the revenues that will be obtained from the machine as follows: The interest rate is 5%. Should the firm buy the machine? To answer this question, we want to compare the present cost of the machine to the discounted present value of any revenues that we will get from the machine. Year1234 Revenue10,00015,000 20,000

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Question 1(a) A firm can buy a new machine for £50,000. The firm estimates the revenues that will be obtained from the machine as follows: The interest rate is 5%. Should the firm buy the machine? To answer this question, we want to compare the present cost of the machine to the discounted present value of any revenues that we will get from the machine. The present cost of the machine is £50,000. The present value of £10,000 one year in the future is: £10,000 / (1+r) = £10,000 / (1+0.05) = £10,000 / 1.05 = £9,523.81 The present value of £15,000 two years in the future is: £15,000 / (1+r) = £15,000 / (1+0.05)^2 = £15,000 * 1.05^2 = £13,605.44 The present value of £15,000 two years in the future is: £15,000 / (1+r) = £15,000 / (1+0.05)^3= £12,957.56 The present value of £15,000 two years in the future is: £20,000 / (1+r) = £20,000 / (1+0.05)^4= £16,454.05 Year1234 Revenue10,00015,000 20,000

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Question 1(a) A firm can buy a new machine for £50,000. The firm estimates the revenues that will be obtained from the machine as follows: The interest rate is 5%. Should the firm buy the machine? The present cost of the machine is £50,000. The present value of the four future sums are: 9523.81 + 13605.44 + 12957.56 + 16454.05 = 52,540.86 The sum of the present value of future revenues is greater than the cost of the machine then the firm should invest in buying the machine. Year1234 Revenue10,00015,000 20,000

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Question 1(b) A firm can buy a new machine for £50,000. The firm estimates the revenues that will be obtained from the machine as follows: If the interest rate fell to 4%, how would this affect the firm's decision? Using the exact same method as in part (a), we find that the present value of the four future sums when the interest rate is 4% would be: 9615.38 + 13,868.34 + 13,334.95 + 17,096.08 = 53,914.75 So, the present value of the future sums would in all four years be higher. The firm's decision to invest would, therefore, be unaffected by the lower interest rate, but would be more profitable. In general: The lower the discount (interest) rate, the higher the present value of future sums. Year1234 Revenue10,00015,000 20,000

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Year1234 Revenue10,00015,000 20,000 Question 1(c) A firm can buy a new machine for £50,000. The firm estimates the revenues that will be obtained from the machine as follows: Keynes argued that the investment decisions of firms depended crucially on what he called the animal spirits of entrepreneurs. That is, their expectations about future returns would influence their decisions to invest. Suppose in the case of the firm above managers in the firm now think that revenue will be 10% lower every year because of a likely recession. How does this affect the firm's decision to buy the machine when the interest rate is 4%? Expected revenues are now 9,000; 13,500; 13,500; 18,000 Using the same methods as in part (a), Present values are 8653.85 + 12481.51 + 12001.45 + 15386.48 = 48523.29 Buying the machine is no longer profitable for the firm. The effect of expectations on investment decisions among firms is still considered to be important. Year1234 Revenue9,00013,500 18,000

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Relationship between interest rate and demand for capital We can see that as the interest rate falls, the present value of the future payout of an investment increases. If i, then PV of a future pay-out So, if PV of a future pay-out, then Demand for Investment And Capital Stock This shows a negative relationship between the interest rate and the amount of capital stock that people may wish to buy. This relationship is Marginal Efficiency of Capital (MEC) curve, that we see in Question 1(d) The Marginal Efficiency of Capital (MEC), a Keynesian term, is that rate of discount which would make the present value of future returns from an asset equal to that assets supply price.

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Shifts in the MEC The following things would cause the MEC to shift to the right (or we can say, cause investment to become more attractive): 1. Cost of capital becomes cheaper 2. Improvements in technology 3. Optimistic expectations about the future and business confidence 4. Supply of Finance – if banks are more willing to lend money 5. Higher Demand for goods 6. Lower Rates of Taxes Conversely, the opposite of these things will cause MEC to shift left and cause investment to become less attractive.

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Question 1(d) Illustrate on a suitable diagram the effect that more pessimistic expectations about the future among firms would have on the marginal efficiency of capital schedule. The change in expectations shifts the MEC schedule to the left. For a given interest rate, the optimal capital stock will be lower.

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Practice Short-Answer Question What are the four functions of money? In economics, are cheques considered to be a form of money? Why/why not? Some ways to approach this problem: 1.What exactly is the question asking? We can break this up into three questions: a. What are the four functions of money? – List them and explain them. b. In economics, are cheques considered to be a form of money? c. Why/why not? – Explain what cheques are vs. what money is.

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Practice Short-Answer Question 2.Come up with an outline for your answer. a. What are the four functions of money? Medium of Exchange Unit of Account Store of Value Liquidity b. In economics, are cheques considered to be a form of money? No c. Why/why not? Not a store of value, not a unit of account. 3.Does the outline address what the question is asking? 4.Use definitions and key terms to fill out your outline. 5.Check again – did you directly answer the questions being asked?

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Practice Short-Answer Question 4.Use definitions and key terms to fill out your outline. The four functions of money are to be a medium of exchange, a unit of account, a store of value, and liquidity. The primary function of money is to be a medium of exchange – this means that buyers and sellers all are willing to trade goods and services for money. It allows us to walk into a shop and know that our money will be accepted for the items that the shop is selling. To serve as a unit of account, means that money serving as a unit of measure or value. To serve as a store of value means that people can transfer purchasing power from the present to the future. To be liquid means that an asset (a store of value) can easily be converted into the economys medium of exchange. Because money is the medium of exchange, it is by definition, the most liquid asset. Any asset that can easily and with little cost be sold in exchange for money is considered liquid, i.e. stocks and bonds, whereas things like cars and property take longer to sell they are therefore less liquid. Cheques are not considered to be a form of money, in fact they are a note that says that an individual has a specific amount of money in the bank that the recipient is entitled to receive. Cheques are a claim to money that allows for transfer of funds. We do not consider them to be money because they do not meet the primary function of money – being a medium of exchange. They are not a medium of exchange because when you hand over a cheque, the seller can not take your cheque and pay somebody else with it. Debit and Credit Cards are similar to cheques in this way. Similarly, Checques are not used as a unit of account or a store of value (i.e a check is not an asset). For more on this topic, See pgs. 617 – 622 of Mankiw & Taylor, 2 nd Ed.

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Exam Advice It is a Short Answer exam, not an essay exam. That means be brief and to the point. Be direct and brief, theres nothing wrong with using textbook definitions. Many students thought they needed to explain things in their own words – if you know the book definition, write it down, its easier for the grader to recognize as a correct answer. Other students simply write down a list key words, but dont show that they understand what these words mean or use them in a coherent way. If you just list all of the terms you heard in class, you wont get any marks.

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More Exam Advice Most students did a good job of using diagrams. If the question asks for a diagram, you need to draw one to get full marks. (you also need to label it correctly; an unlabeled diagram could be anything.) If you are working a math problem – write down any equations that youre using. You generally would get a mark for having the equation correct, even if you make a mathematical error later or dont have time to finish the question. Finally, be conscious of time. If you can, have a quick look through the exam at the beginning and pace yourself – wear a watch. On the last exam, a lot of students wrote a long essay for Question 1, then didnt have time for Question 5. If the question just asks for a definition, give the definition and move on. If you dont know it, move on to something you do know and you can come back to it later if theres time.

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Question 2(a) What is the opportunity cost to a consumer or business of holding notes and coins? The opportunity cost of holding cash in your hand is the interest that you could have earned had you kept it in an interest-earning account instead.

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Question 2(b) For each of the following assets, state whether you believe the asset performs money's functions as a store of value and a medium of exchange. Explain your answer: i)Building society savings accounts store of value ii)Ordinary company shares store of value iii)Debenture company shares store of value iv)Government bonds store of value v)Notes and coins store of value, medium of exchange vi)UK Treasury bills store of value vii)Deposits in commercial bank current accounts store of value, medium of exchange viii)Certificates of Deposit store of value

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Question 2(c(i)) A banking system consists of five banks, A, B, C, D and E. Each operates with a prudential ratio of 5%. Suppose Eric deposits £1,000 cash in bank A. What would be the initial increase in lending by Bank A following the deposit? The prudential ratio is the proportion of deposits which are kept at hand. This also might be called the reserve ratio. A prudential ratio of 5% means that 5% of all deposits are kept by the bank. So:5%*£1,000= £50 is kept on hand by the bank. So, the bank is able to lend £950 given their prudential ratio.

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Question 2(c(ii)) Bank A then lends to Marie who in turn pays cash to Phil, a customer of Bank B, for a new laptop. He deposits the cash in his bank account. What would be the increase in bank lending possible at Bank B following this deposit? Were assuming that Bank A lends all £950 to Marie, who pays Phil the entire sum and that Phil deposits the £950 in Bank B. If the £950 is deposited in Bank B, then that bank would keep 5%*£950 = £47.50 and lend the remaining £902.50.

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Question 2(c(iii)) This process continues through Banks C, D and E and then back to Bank A and so on. What would be the final increase in bank lending in the banking system? Assuming a similar pattern in the other banks, £857.38 in Bank C, £814.51 in Bank D, £773.78 in Bank E and so on. This is an infinite geometric progression (mentioned in the lecture). The banking system as a whole will increase lending by: Increase in bank deposits = initial deposits/(1-the percentage loaned) Increase in bank deposits= initial deposits/the prudential ratio Increase in bank deposits = £1,000/0.05 Increase in bank deposits = £20,000 Increase in bank lending = £20,000 - £1,000

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Bond Pricing Bond A is priced at $1000 with a coupon of 4%, and its initial yield to maturity is 4% (a bonds coupon is how much it pays per year, either an amount or a percentage of its value when it was issued). In other words, it pays $40 annually. After 1 year the interest rate has increased to 4.5%. A new bond for sale at that time, Bond B, pays $45 annually. What is the price of Bond B? We can guess that it is $1000, since the coupon rate is often set to the interest rate at the time of sale, and 4.5%*$1000=$45. But we can use our knowledge of geometric series. This year the bond pays $45. Next year it pays $45, which has a present value equal to $45/(1+interest rate) or $45/(1+discount rate) (interest and discount rates are set equal for businesses). So the present value of the bond is: £45 + £45/(1+0.045) + £45/(1+0.045)^2 + … This is a geometric progression and works like the mpc and government expenditure multiplier, so we can work out the equation to be: = £45/(1-(1+0.045)) But this reduces to something quite simple: = £45/.045 That is, the value of a bond which gives an infinite stream of payouts of = £45/.045 = £1000 In general, the value of a bond is equal to its annual payout divided by the discount rate (interest rate) If someone wants to sell Bond A, it will need to offer a yield of 4.5%. The coupon (annual $40 payout)always stays the same, the price must fall to $900 in order for the bonds yield to remain the same as Bond B. This is because $40/$900=4.5% Alternately, Bond A has a coupon of 4% and price of $1000 and its initial yield to maturity is 4%. If the following year, the yield on Bond A moves to 3.5% (to match a 3.5% yield on Bond B now on the market), what happens to the price? Since the coupon stays the same, the price must rise to $1142.75 ($40/.035). Due to this increase in price, the yield declines (because the $40 coupon divided by $1142.75 equals 3.5%).

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Bond Pricing Question 3 deals with bonds and bond pricing. Some key terms that we use are: Face value: Nominal value of the bond Coupon rate: The percentage of the face value that the bond yields (pays to bond holders) each year. Coupon value: The amount the bond yields each year. Note: In some problems youre given the coupon rate and have to find the coupon value. In others youre just given the coupon value. Pay attention! Interest rate: The prevailing interest rate is the expected annual rate of return on bond purchases. It is usually equal to the coupon rate of new bonds on the market. Discount rate: When calculating the present value of future gains, this is the rate you use. For businesses, it is usually set to the interest rate.

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Bond Pricing Example (ctd.) Bond A is priced at $1000 with a coupon of 4%, and the initial prevailing interest rate is 4%. (a bonds coupon is how much it pays per year, either an amount or a percentage of its value when issued). In other words, it pays $40 annually. After 1 year the interest rate has increased to 4.5%. A new bond for sale at that time, Bond B, pays $45 annually. What is the price of Bond B? We could guess that it is $1,000, because the coupon rate is often set to the interest rate at the time of sale, and 4.5%*$1000=$45.

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Bond Pricing Or, we can use our knowledge of geometric series: This year Bond B is purchased. Next year it pays $45, which has a present value equal to $45/(1+interest rate) or $45/(1+discount rate) (interest and discount rates are set equal for businesses). So the present value of the bond is: £45/(1+0.045) + £45/(1+0.045)^2 + … Which can be rewritten as: 1/(1+0.045)*(£45 + £45/(1+0.045) + £45/(1+0.045)^2 + …) This is a geometric progression and works like the mpc and government expenditure multiplier, so we can work out the equation to be: = 1/(1+0.045)*(£45/(1-1/(1+0.045))) But this reduces to something quite simple: = £45/.045 That is, the value of a bond which gives an infinite stream of payouts of £45 = £45/.045 = £1000

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Bond Pricing In general, the value of a bond is equal to its annual payout divided by the discount rate (interest rate) That is, the value of a bond which gives an infinite stream of payouts of £45 = £45/.045 = £1000

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Bond Pricing If someone wants to sell Bond A, it will need to offer a yield of 4.5%. The coupon (annual $40 payout)always stays the same, the price must fall to $889in order for the bonds yield to remain the same as Bond B. This is because $40/$889 = 4.5%

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Bond Pricing Alternately, Bond A has a coupon of 4% and price of $1000 and its initial yield to maturity is 4%. If the following year, the yield on Bond A moves to 3.5% (to match a 3.5% yield on Bond B now on the market), what happens to the price? Since the coupon stays the same, the price must rise to $1142.75 ($40/.035). Due to this increase in price, the yield declines (because the $40 coupon divided by $1142.75 equals 3.5%).

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Question 3(a) Keynes suggested that the speculative demand for money was linked to the demand for government bonds. These bonds are a means for a government to borrow money. In the UK, the government issues a piece of paper that has a face (or nominal) value of £100 and an associated coupon of a given percentage. This coupon is the money return on the bond for the bond holder expressed as a percentage of the bond's face value. For example, if the coupon is 5% the bond holder will receive a fixed £5 a year. These bonds, once issued by the government, are then traded on the Stock Exchange. In the case we are considering here, we will assume the government never repays the £100. A fixed coupon means that if interest rates change, the return on the bond can seem either low or high. Suppose interest rates fell to 2%, for example, the bond would yield a very attractive return. But this would mean that demand for the bonds on the Stock Exchange would rise. And we know that means their price would rise from the initial £100. (It's supply and demand again!) And as the price of the bond rose the return on it would fall. With a market interest rate of 2%, the price of the bond would eventually rise to £250. £5 a year is 2% of the new bond price of £250.

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Question 3(a) If the government will never repay the bond, why do people hold them? They hold them in the hope of a capital gain if interest rates change as well as for the (guaranteed) return they receive in the coupon.

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Question 3(b again)

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Question 3(b)

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Question 3(c) Why would a fall in interest rates make the bonds less attractive to speculators and so increase their demand for money? A fall in interest rates will increase the price of bonds. Investors may then speculate that the price will be likely to fall in the future. Investors therefore shift from holding bonds to holding money. Note that this assumes bonds to be a liquid asset that can easily and at relatively low cost be converted into money. In practice, they actually are.

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Question 3(d) Why would a rise in interest rates make the bonds more attractive to speculators and so decrease their demand for money? A rise in interest rates will cause the price of bonds to fall. By similar reasoning to the answer in d), a fall in the price of bonds means that speculators are more likely to want to buy bonds because they believe their price will increase in the future. Their demand for money therefore falls as their demand for bonds rises.

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Bonds vs Liquidity Preference Money Supply So our intuition is that a rise in interest rates will lower the price and increase the demand for bonds. The demand for money falls. Money is equivalent to savings, which roughly equals investment according to the circular flow of money. So an increase in savings increases I and from our Keyensian models, increases GDP (Y). When we look at IS-LM (Investment Saving–Liquidity Preference Money Supply), this relationship explains why the LM curve has a positive slope. The LM curve has to do with Liquidity Preference and Money Supply, and shows a positive relationship between interest rates, r, and output, Y.

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Question 4 The reason barter is not as efficient as money as a medium of exchange is that it suffers from the problem of: a) The double coincidence of wants b) The need to know the rate at which many goods exchange for each other c) The difficulty of deciding the cost of repaying loans in terms of another good d) All of the above

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Question 5 A bank is required by the government to hold 15% of its assets as cash. If the bank has cash of £150 million and loans to customers valued at £850 million, which of the following statements is correct: a) The banks deposits are £1,000 million and it could increase its lending by £50 million b) The banks deposits are £1,000 million and it cannot increase its lending c) The banks deposits are £1,000 million and it must reduce its lending to meet the governments cash requirement d) The banks deposits are £850 million and it must reduce its lending to meet the governments cash requirement

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Question 6 A bank receives £1500 in cash as a deposit. If the bank operates with a prudential ratio of 2% this implies that the bank could make loans to the value of: a) £1,500 b) £20,000 c) £73,500 d) £75,000

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Question 6 A bank receives £1500 in cash as a deposit. If the bank operates with a prudential ratio of 2% this implies that the bank could make loans to the value of: The amount the bank can loan = (1-prudential rate)*deposit amount the bank can loan = 0.98* £1500 = £1470 Note, to get the correct answer to this question, the question should actually be asking what is the increase in money supply that resulted from the £1500 deposit, but is not inclusive of that initial deposit. a) £1,500 b) £20,000 c) £73,500 d) £75,000 Increase in bank lending = initial deposits/the prudential ratio Increase in bank lending = £1500 / 0.02 Increase in bank lending = £75000 Increas e in bank lending minus initial deposit = £75000 - £1500 = £73500

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Question 7 In a modern economy the best working definition of the money supply is: a) Notes and coins in circulation with the public b) Notes and coins deposited in the banks c) Notes and coins in circulation with the public plus commercial bank deposits d) Notes and coins deposited in the banks plus commercial bank deposits

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