1 Econ 202 Problem Set 6 S olutions R eading: The Economy 1.0 Unit 10.1, 10.7 - 10 .14 Banks, Money and the Credit Market Key Terms to Know Money Wealth Income Flow variable Stock variable Consumption Saving Investment Interest rate Problems : From the reading and lectures 1) Credit Markets consist of lenders and borrowers a) Who are lenders in credit markets? Lenders are: • people who have a large amount of wealth and are living off interest income from lending. These are retired people who accumulated assets while working or people who became wealthy as entrepreneurs, entertainers or via inherited wealth. • People who anticipate lower wage income in the future and so are saving (lending) today to accumulate, wealth. For example, people saving for retirement. • Lenders tend to be older and richer people. • Lenders can also be companies with large surpluses of accumulated undistributed profits which are lent to earn interest income. b) Who are borrowers in credit markets? Borrowers are: • People who anticipate higher wage income in the future and so are borrowing today to smooth their consumption spending. This type of borrower tends to be younger and poorer. • People also borrow to finance the purchase of housing and cars. • Companies borrow to financial investment spending, i.e. the purchase of equipment and structures • Governments which borrow to finance Government budget deficits = G - tY Liabilities Assets Net Worth Leverage ratio Bank run Policy interest rate (federal funds rate) Bank lending rate Credit rationing Collateral 2 2) Banks verses the bond market a) How is lending to a bank different from lending in the bond market? Lending to a bank occurs when people deposit funds in bank accounts such as checking and savings accounts. Funds in bank accounts, such as demand deposits (checking accounts) are immediately accessible to make payments. Funds in savings accounts can also b e accessed but sometimes with a penalty. Lending in the bond market occurs when people buy the bonds issued by a corporation or by a government. Purchases of bonds only get paid when the bonds mature or if there's a coupon payment on the bond. b) How is borrowing from a bank different from borrowing in the bond market? Most individuals and small businesses can only borrow from banks These loans take the form of auto loans mortgages lines of consumer credit and small business loans Corporations with good credit ratings and governments can borrow in the bond market by selling bonds to people willing to purchase bonds. Selling bonds is a way of borrowing. 3) B ond prices and interest rates : Consider a bond which matures in one year with a value at maturity of $1000. Denote the current price of the bond as $ 𝑃 𝐵 a) Calculate the interest rate on the bond (i) for following bond prices : $ 𝑃 𝐵 = $909 , $ 𝑃 𝐵 = $952 , $ 𝑃 𝐵 = $926 . Hint: use the growth rate formula! 𝒊 = 𝟏 , 𝟎𝟎𝟎 − $ 𝑷 𝑩 $ 𝑷 𝑩 If $ 𝑷 𝑩 = $ 𝟗𝟎𝟗 then 𝒊 = 𝟏 , 𝟎𝟎𝟎 − $ 𝟗𝟎𝟗 $ 𝟗𝟎𝟗 = $ 𝟗𝟏 $ 𝟗𝟎𝟗 = 𝟎 𝟏𝟎 𝒐𝒓 𝟏𝟎 % If $ 𝑷 𝑩 = $ 𝟗𝟓𝟐 then 𝒊 = 𝟏 , 𝟎𝟎𝟎 − $ 𝟗𝟓𝟐 $ 𝟗𝟓𝟐 = $ 𝟒𝟖 $ 𝟗𝟓𝟐 = 𝟎 𝟎𝟓 𝒐𝒓 𝟓 % If $ 𝑷 𝑩 = $ 𝟗𝟐𝟔 then 𝒊 = 𝟏 , 𝟎𝟎𝟎 − $ 𝟗𝟐𝟔 $ 𝟗𝟐𝟔 = $ 𝟕𝟒 $ 𝟗𝟐𝟔 = 𝟎 𝟎𝟖 𝒐𝒓 𝟖 % b) What happens to the interest rate when bond prices increase? What happens to the interest rate when bond prices decrease? Bond prices and interest rates move in opposite directions. If ↑ $ 𝑷 𝑩 then ↓i If ↓ $ 𝑷 𝑩 𝒕𝒉𝒆𝒏 ↑i 3 4) I mpact of interest rates on borrowing and lending a) How do higher or lower interest rates affect borrowing hence spending? Higher interest rates (↑ r) imply a higher cost of borrowing so borrowers borrow less which implies a decrease in spending, e.g. a decrease in investment spending. Lower interest rates (↓r) imply a lower cost of borrowing so borrowers borrow more which implies an increase in spending, e.g. an increase in investment spending. b) How do higher or lower interest rates affect lending? What is a major concern of lenders if loans are risky and how does this concern impact interest rates and the conditions of the loan ? Lenders might be willing to lend more if interest rates increase and lend less if interest rates decrease. A major concern for of lenders in making risky loans is getting paid back. L enders who are willing to make risky loans will : • Require an interest rate higher than the “safe interest rate” (r) so will be willing to lend at r + “risk premium” • Limit the amount they are willing to lend • Require the borrower to make a “down payment” • And may also require the borrower put up collateral (something the lender gets if the borrower defaults) for the loan. 5 ) Stock Variables and Flow variables: Which of the following which are stocks , flows or neither? Explain WHY! Which flows add to stocks? Income : flow since income is measured as $/time period, e.g. $/year Debt : stock since debt is measured as $ at a point in time, e.g. $ at the end of 2019 Rent: flow since rent is measured $/time period, e.g. $/month Liabilities : stock since liabilities are measured as $ at a point in time, e.g. $ at the end of 2019. Price of coffee: either since price is measured as $/cup Value of your house : stock since asset values are measured as $ at a point in time, Assets : stock since asset values are measured as $ at a point in time, Net worth or wealth : stock net worth is measured as $ at a point in time. Net worth = assets - liabilities Consumption spending : flow since consumption is measured $/time period, e.g. $/month Saving : flow since saving is measured $/time period. Saving =income – consumption and adds to wealth a stock. Lending : flow since lending is measured $/time period. Lending adds to assets, a stock 4 Borrowing : flow since borrowing is measured $/time. Borrowing adds to debt a stock Money: = currency + funds in demand deposits is a stock since money is measured $/time period. 6) Balance Sheets Suppose Amira owns a condo valued at $300k, had student load debt of $30K, has a mortgage of $250K and has bank deposits of $10k. Draw Amira’s balance sheet putting each of these items in their appropriate place on the balance sheet. Also show Amira’s net worth on the balance sheet. Amira’s B/S Assets Liabilities Condo $300K Bank Deposits $10K Mortgage $250K Student loan debt $40K Net Worth $20K 7 ) Money a) In macroeconomics money is the stuff we use to make payments. What is the “stuff” we use to make payments? We make payments using currency (government money) or using funds in our checking accounts (bank money) which we access by writing paper checks, using debit cards or various forms on online banking. b) In everyday language we say, “let me borrow money”, “she makes a lot of money”, “she has a lot of money”. How would you translate these statements into how economists use the terms money, income and wealth? If I say “let me borrow money” for example, lend me a $5 bill, an economist would say I am asking to borrow MONEY. Unless this person is counterfeiting $100 bills with a printing press in her basement, the phase, “she makes a lot of money”, an economist would say she has a high INCOME. If we say “she has a lot of money” an economist would say she is a high WEALTH individual. 5 8 ) The Payment system: Suppose Ana bank s at Bank A and Bala bank s at Bank B. Bank A Central Bank (Clearing house) Bank B Assets Liabilities Assets Liabilities Assets Liabilities Reserves $100 a) +$50 b) - $175 c) +$25 Loans $1,000 Deposits Ana u $500 a) +$50 b) - $175 Deposits others $500 Other borrowings $0 c) +$25 loan of reserves from Bank B Net Worth $100 Reserves Bank A $100 a) +$50 b) - $175 c) +$25 Bank B $100 a) - $50 b) +$175 c) - $25 Reserves $100 a) - $50 b)+$175 c) - $25 Loans $1,000 c) +$25 loan to bank A Deposits others $500 Deposits Bala $500 a) - $50 b) +$175 Other borrowings $0 Net Worth $100 a) Bala write s Ana a check for $50. Ana deposit s the check in Bank A. The check clears. Indicate how this changes the balance sheets above by labeling balance sheet changes with letter “a)” b) Given event a), now suppose Ana write s Bala a check for $175. Bala deposit s the check in Bank B. Indicate how this changes the balance sheets above by labeling the changes with letter “b)”. Will Ana’s check clear? Why or why not? Check doesn’t clear because Bank A doesn’t have enough reserves to clear the check c) How much does bank A have to borrow in order for Ana’s check to clear? Who can Bank A borrow from? What is this market called? Indicate how this changes the balance sheets above by labeling the changes with letter “c)”. Bank A has to borrow $25 in reserves in order for Ana’s check to clear. Bank A might borrow $25 in reserves from bank B in the “interbank market” or as it is called in the US, the Federal funds market. In the US the interest rate that banks charge each other in the Federal funds market is called the “Federal f unds rate”. Another possibility would be that Bank A borrows from the central bank (The FED). Loans from central banks directly to banks are called “discount loans”. In the case sheets would be: Bank A Central Bank (Clearing house) Bank B Assets Liabilities Assets Liabilities Assets Liabilities Reserves $100 a) +$50 b) - $175 c) +$25 Loans $1,000 Deposits Ana $500 a) +$50 b) - $175 Deposits others $500 Other borrowings $0 c) +$25 discount loan from CB Net Worth $100 c) +$25 discount loan to bank A Reserves Bank A $100 a) +$50 b) - $175 c) +$25 Bank B $100 a) - $50 b) +$175 Reserves $100 a) - $50 b)+$175 Loans $1,000 Deposits others $500 Deposits Bala $ 500 a) - $50 b) +$175 Other borrowings $0 Net Worth $100 6 The interest rate that central bank charge on “discount loans” is sometimes called the “discount rate”. Notice that in case the total amount of reserves has increased by $25. Trick question: Where did the central bank get the additional $25 in reserves to lend to Bank A? Answer: the central bank created them by the action of making the loan to Bank A! 9 ) Explain how the central bank lower ing the policy interest rate will influence the lending interest rate and amount of borrowing. If the central bank lower s the policy interest rate this enabl es banks to borrow from other banks at a lower interest rate. This causes banks to decrease the bank lending interest rate = policy interest rate + risk - term premium ( The risk - term premium is a markup to cover risk and the fact that bank s lend for a lon ger period than they borrow for). At a lower lending interest rate, borrowers demand more loans, which if granted increases the amount of borrowing by households to purchase cars, houses, condos and also increases borrowing by firms to purchase equipment and structures In short lower interest rates increase spending as we ’ ve been assuming in the multiplie r w here investmen t is given by t he equation : 𝑰 = 𝒂 𝟎 − 𝒂 𝟏 𝒓 1 0 ) How Central banks create and destroy reserves Bank A Central Bank Assets Liabilities Assets Liabilities Reserves $100 Interbank Lending Loans and other assets $1,000 DD you $500 DD of others $485 Interbank borrowing Discount loan $15 Net Worth $100 Govt bonds $220 Discount Loans $30 Reserves Bank A $100 Bank B $100 Net worth $50 a) The Central Bank does an “open market purchase” (Quantitative Easing) of $ 50 in government bonds from Bank A. How does the central bank pay for the purchases of bonds? What happens to the b/s of Bank A and the b/s of the central bank? What happens to bond prices and interest rate s ? The central bank pays for the purchase of government bonds by creating new reserves by the merge action of writing $50 into the reserve account of bank A. The increase in the demand for bonds by the central bank → ↑ bond prices →↓ interest rate b) The Central Bank does an “open market sale” (quantitative tightening)_ of $ 50 in government bonds from Bank A. What happens to the b/s of Bank A and the b/s of the central bank? What happens to bond prices and interest rate s ? 7 The increase in the supply of bonds by the central bank → ↓ bond prices →↑ policy interest rate b/s for a) and b): Bank A Central Bank Assets Liabilities Assets Liabilities Reserves $100 a) +$50 b) - $50 Loans and other assets $1,000 a) - $50 b) +$50 DD you $500 DD of others $485 Discount loan $15 Net Worth $100 Govt bonds $220 a) +$50 b) - $50 Discount Loans $30 Reserves Bank A $100 a) +$50 b) - $50 Bank B $100 Net worth $50 1 1 ) How banks can create bank money (deposits) Bank A Central Bank Assets Liabilities Assets Liabilities Reserves $100 Interbank Lending Loans and other assets $1,000 DD Abby $500 D eposits of others (some of whi ch are uninsured) $485 Interbank borrowing Discount loan $15 Net Worth $100 Govt bonds $220 Discount Loans $30 Reserves Bank A $100 Bank B $100 Net worth $50 a) Bank A makes $ 200 loan to Abby by increasing Abby ’ s de mand d eposits (DD) by $ 200 What happens to the balance sheet of Bank A? What happens to the supply of reserves in th e banking syst em? Bank A Central Bank Assets Liabilities Assets Liabilities Reserves $100 Interbank Lending Loans and other assets $1,000 a) + 20 0 loan to Abby DD Abby $500 a) +$ 20 0 loan to Abby D eposits of others (some of which are uninsured) $ 485 Interbank borrowing Discount loan $15 Net Worth $100 Govt bonds $220 Discount Loans $30 Reserves Bank A $100 Bank B $100 Net worth $50 The supply of reserves doesn’t change 8 b) What will cause in a de cline in Bank A ’ s net worth? Calculate what happens to B ank A ’s leverage ratio How does the change in the leverage ratio influence the chan ce of Ban k A becom ing in sol vent (net worth < 0) so uninsured deposits take losses ? How will uninsured deposit ors of Bank A react if they think they might takes losses ? Bank A ’ s net worth = Assets – Liabilities will d ecline if the v alue of Bank A ’ s asset decline in value. For example , is Bank A ha s lent to people so they can buy houses, and then a bunch of people d efault on t he loans (mort gages) the Bank As value of assets will fal l and Bank A ’ s net worth will fall. Bank A ’ s leverage ratio increases f rom $1 ,100/$100 = 11 t o $1, 300 /$1 00 = 1 3 T h e increase in the leverage ratio increases the chan ce of Ban k A becom ing in sol vent (net wor th <0) which s wipes o ut the equity of the owners of Bank A and forc es losses on uninsured deposit ors. The uninsured deposit ors of Bank A will “ run ” on the bank (attempt to pul l out all the ir deposits) if they think Bank A is going in so l vent. c) A more fragile banking sys tem is mor e likely to experience a run by the u ninsur ed depositors. How do es the leverage rat io of bank s in fluence the “ f ragility ” of the bank ing syst em? A higher bank leverage rat io of bank s increa ses the lik elihood of run by the uninsured deposit o rs. Hence gr eater bank leverage ratio s → ↑ “ f ragility ” of the bank ing syst em 12 ) Fractional reserve banking and bank runs Consider the balance b elow. Assume initial ly there is no cur rency in the economy so the mon etary base co nsists solely of reserves. Privates banks can swap their reserves for currency f ro m the central bank ( “ T h e Fed ” ) on demand. Private Bank ing System Central Bank ( “ The Fed ” ) Assets Liabilities Assets Liabilities Reserves $100 Interbank Lending Loans and other assets $1,000 In sured deposits $500 Uni nsured D eposits $ 5 50 Interbank borrowing Discount loan $0 Net Worth $ 50 Govt bonds $ 110 Discount Loans $0 R eserves $100 Currency $0 Net worth $ 10 9 a ) Suppose that the uninsured depos i tors suddenly run on private banks and demand all their uninsured deposits out in the form of currency “Federal Reserve Notes” . In this situation can bankers meet the demands of their depositors? Why or why not? No. Since banks only hold a fraction of deposits as reserves ($100 in reserves comp ared with $ 550 in uninsured depos its ) , they will not be able to meet the demands of all of their uni nsured depositors. b) Given your answer to part a) and assuming no intervention by The Fed , what will banks do to try to obtain reserves? As a group will banks be successful? Given the actions of banks what is likely to happen to loans and the prices of other assets? In an attempt to obtain more reserves banks will 1 ) call in those loans that are callable and will also stop any new lending and 2 ) attempt to sell their “ l oans other assets” to ob tain reserves As a group banks will not be successful. In this example, without Fed intervention there is only $100 in reserves for the entire banking system. Banks will reduce lending. With many banks attempting to sell loan assets, the value of l oan s on the asset side of the private bank bal ance will decrease reducing the net worth of banks and thus incre asing the lik eliho od that banks w ill be come insolvent forcing uninsured depositors to tak e losses. c) How will a bank run influence aggregate demand and hence output and unemployment? Bank runs cause banks to decrease lending to try to hold onto to reserves. A decrease in bank lending will decrease autonomous consumption and autonomous investment thus decreasing aggregate demand resulting in falling real GDP and higher unemployment. d ) What can the central bank, i.e. the Federal Reserve do to stop bank run by the uninsured depositors ? Use the numerical example below and show your solution on the balance sheets of the private banks and the Fed assuming all depositors attempt to withdraw their funds from banks in the form of currency. ( Private banks can s wap reserves for currency on demand T he Fed c an len d $ 4 50 in discount loans to private banks by creating $ 4 50 more in reserves. If this happened the balance of the banks and The Fed would look like: Private Bank ing System Central Bank ( “ The Fed ” ) Assets Liabilities Assets Liabilities Reserves $100 + $ 450 Interbank Lending Loans and other assets $1,000 In sured deposits $500 Uni nsured D eposits $ 550 Interbank borrowing Discount loan + $ 450 Net Worth $ 50 Govt bonds $ 110 Discount Loans + $ 450 R eserves $100 +$ 450 Curr ency $0 Net worth $ 10 10 I f all deposits were withdrawn from private banks as currency the balance sheets would look like: Private Bank ing System Central Bank ( “ The Fed ” ) Assets Liabilities Assets Liabilities Reserves $100 + $ 450 - $ 550 Interbank Lending Loans and other assets $1,000 In sured deposits $500 Uni nsured D eposits $ 550 - $550 Interbank borrowing Discount loan + $ 450 Net Worth $ 50 Govt bonds $ 110 Discount Loans + $ 450 R eserves $100 +$ 450 - $ 550 Curr ency + $ 550 Net worth $ 10 Bal ance S heet of uninsured depositors Assets Liabilities Uni nsured D eposits $ 550 - $550 C urrency + $ 550 d) If the central bank (T h e Fed) ac t s as “ lender of last res ort ” as in your answer to part c) what would happ en to loans and prices of other assets? Banks would no longer have a need to call in loans or stop additional lending or to sell assets. By acting as “lender of last resort” the Fed in part c) reduces the impact the run on banks has on the rest of the economy