ECO102 Lecture 10

ECO102 - Week 09.pdf

Money

• Three functions of money:
  • Medium of exchange
    • If there's no money in the economy, we just have to barter and trade.
    • But what if someone doesn't want what you offer to trade?
    • It 'lubricates' the economy.
  • Store of value
    • You can put your wealth in cash. It will be worth roughly the same amount.
    • Example:
      • Prison, cigarettes.
      • Not a great store of value, but can be used as a medium of exchange.
  • Unit of account
    • Standardizes 'value' and 'prices' between different products and services.
    • If you have only 3 goods in an economy, you just need 3 prices to compare the value of those goods.
    • If you have 4, then you need 6.
    • $\frac{n(n-1)}{2}$ is the number of relative prices you need to compare $n$ goods.
• Evolution of Money
  • You used to have bulk gold.
    • Needed to be weighed and assessed per transaction.
  • Gold coins
    • Standardized weight and purity.
    • But now you need to assess it (if you don't trust it).
    • Otherwise you can trust the goldsmith.
    • Problem:
      • Clipped coins.
      • Shave or trim the edges of the coin and keep the gold for yourself.
    • Milling.
      • Milling the edges of the coin to prevent clipping.
      • Makes it obvious if it was clipped.
      • Have the edges milled with a pattern.
    • Indivisible.
      • Can't be divided into smaller units.
      • Can't buy something worth less than the coin.
  • Bi metal / Tri metal
    • Gold silver and copper coins.
    • Establish a par between gold and silver, etc.
    • British got newton to see how many pounds of silver for 1 pound of gold.
    • He overvalued silver.
    • So silver was driven out of circulation.
    • Gresham's Law says 'bad money drives out good money'.
    • Example:
      • USD chases out Cuban dollars in Cuba.
  • Paper Money
    • Issued by the goldsmith.
    • Backed by gold reserves.
    • Convertible on demand.
    • Eventually people didn't come back to convert.
    • So issue more money than gold available.
  • Fiat
    • Not backed by anything.
    • Value is based on trust in the government.
    • 'In God we Trust', that's the backing.
    • It's backed by law.
  • Debit.
  • Credit is not money, it's a promise to pay money.
• Properties of Commodity Money
  • Homogeneous
    • Gold is gold. Simple.
    • If you have a bar of gold, it's worth the same as any other bar of gold of the same weight and purity.
  • Durable
    • Gold is durable. It doesn't corrode or degrade over time.
  • Portable
    • Need to be able to take your money anywhere.
  • Divisible
    • Good for day to day transactions.
  • Fixed in supply
    • If the supply of money can be easily increased, then it loses its value.
    • This is the problem with fiat money.
  • Which of these properites were improved when they intoduced coins and paper money?:
    • Portable with coins

Money Supply

• 1
  • 5 responsibilities of central banks.
  • Liabilities and equities
    • First, issue currency.
    • Commercial Bank Deposits
      • Bank for the banks.
      • Overnight Rates
        • Example:
          • TD has an account with BOC
          • BOC $\uparrow$ the interest rate. Now TD must pay more to borrow money from BOC. So TD will increase the interest rates they charge to their customers, which will decrease the demand for loans and decrease the money supply in the economy.
        • Set at predictable intervals, so that banks can plan for it.
      • There's not moving of money between commercial banks.
      • It's just a clearing house, where the BOC keeps track of how much money each bank has.
  • Assets
    • Foreign Currency
      • Exchange rates. By buying and selling foreign.
      • Increasing supply of canadian dollars by buying foreign currency, which decreases the value of the canadian dollar.
      • If Canada sells US dollars, they'll take CAD out of circulation, increasing value.
      • One is sustainable the other isn't.
      • Example:
        • Trump criticizes China. Say they're manipulating exchange rate, keeping it low. So exports are cheap. So they buy US dollars to keep the value of their currency low. But if they stop buying US dollars, then the value of their currency will go up, which will make their exports more expensive and less competitive.
        • Maybe they're keeping it artificially low, so that the US has a deficit with China always.
        • To keep the rate low, People Bank of China buy US dollars with yuan.
          • They print their own money to buy money from the US, which increases the supply of yuan and decreases its value.
          • Accumulating US assets.
      • If they want to keep their value high, they sell US dollars. Eventually, you run out though.
      • So there's an asymmetry in this process.
    • Government Bonds
      • Example:
        • If govt has surplus, they put it into the Bank of Canada.
        • Otherwise, they issue Bonds to raise money.
    • Other assets
      • Central bank needs to maintain stability in the financial system.
      • 'Bank run'
        • If everyone tries to withdraw their money at the same time, the bank will run out of cash and go bankrupt.
        • Because they operate at fractional reserve banking, they only keep a fraction of their deposits in cash, and lend out the rest.
        • In a crisis, they have toxic assets, and potentially a bank run.
        • The BOC buys those toxic assets to stabilize the financial system.
        • It's now $\sim 10\mathrm{\%}$, used to be more.
        • BOC can't go bankrupt, because their only customers are Banks.
• 2
  • Fractional Reserve Banking
    • Banks only keep a fraction of their deposits in cash, and lend out the rest.
    • This creates money in the economy, because when a bank lends out money, it creates a new deposit in the borrower's account, which increases the money supply.
    • Example:
      • If the reserve requirement is 10%, and someone deposits $1000, the bank keeps $100 in reserve and lends out $900. The borrower then deposits that $900 in another bank, which keeps $90 in reserve and lends out $810, and so on. This process continues until the total money created is $10,000.
      • $\begin{array}{ccc}\text{Assets}& & \text{Liabilities and Equities}\\ \text{Cash Reserves}& 5& \text{Deposits}& 100\\ \text{Loans}& 115& \text{Equity}& 20\end{array}$
    • Because of this, we have a money multiplier.
    • Example:
      • Commercial banking has reserve ratio of $20\mathrm{\%}$.
      • If the central bank issues $+100\mathrm{\$}$. They will hold $20\mathrm{\$}$ and create $80\mathrm{\$}$ of loans.
      • The next company will take those $80\mathrm{\$}$ and buy more stuff, etc.
      • Eventually that comes back into the bank.
      • $$\begin{array}{cccc}& \text{New Deposits}& \text{New Reserves}& \text{New Loans}\\ \text{Init Deposit}& 100& 20& 80\\ 2& 80& 16& 64\\ 3& 64& \dots & \dots \\ 4& ⋮& ⋮& ⋮\\ \\ \text{Total}& 500& 100& 400\end{array}$$
      • In this case, the money multiplier is $\frac{1}{0.2}=5$.
    • Cash Drain
      • If people withdraw cash from the bank, it reduces the amount of reserves the bank has, which reduces the amount of money they can lend out, which reduces the money supply in the economy.
      • Example:
        • If someone withdraws $100\mathrm{\$}$ from the bank, the bank's reserves decrease by $100\mathrm{\$}$, and they can only lend out $80\mathrm{\$}$ instead of $100\mathrm{\$}$, which reduces the money supply by $20\mathrm{\$}$.
      • Creates a leak in the system when people just keep the money in their pocket and don't consume.
    • Updated money multiplier.
      • $\frac{1}{0.2+0.05}=4.0$
      • with $0.05=c$ c is cash drain.
      • $$\begin{array}{cccc}& \text{New Deposits}& \text{New Reserves}& \text{New Loans}\\ \text{Init Deposit}& 100& 20& 80\\ 2& 80& 16& 64\\ 3& 64& \dots & \dots \\ 4& ⋮& ⋮& ⋮\\ \\ \text{Total}& 400& 80& 320\end{array}$$
• 3
  • Friedman's Quantity Theory of Money
  • $m=\frac{P\times Y}{MS}$
    • $m$ is the velocity of money.
      • How many times does a dollar change hands in a year?
    • $P$ is the price level.
    • $Y$ is the real output of the economy.
      • $P\cdot Y$ is GDP/GDE
    • $MS$ is the money supply.
      • M1, M2, etc. depending on how you define it.
  • Example:
    • $GDP=200$
    • $MS=10$
    • $\frac{200}{10}=20$
    • So each dollar changes hands 20 times a year.
  • Second most influential equation in economics after Keynes.
  • Inflation is a monetary phenomenon.
  • He then rewrote the expression as:
    • $P=\frac{m\cdot MS}{Y}$
    • $\mathrm{\%}\mathrm{\Delta }P=\mathrm{\%}\mathrm{\Delta }m+\mathrm{\%}\mathrm{\Delta }MS-\mathrm{\%}\mathrm{\Delta }Y$
    • Over last $200$ years, $m$ is roughly constant.
    • So inflation, $\mathrm{\%}\mathrm{\Delta }P$ is $0+0.05-0.02=0.03$ per year.
    • If a central bank wants to reduce inflation, they just reduce growth of money supply.
    • Increase interest rates and reduce money supply, which reduces inflation.
  • Trimmed CPI:
    • Exclude volatile prices: Oil, Gas.

Money Demand

• Money
  • Cash + Debit vs Bonds
  • Wealth is allocated between money and bonds.
• Theories
  • Transaction motive
    • to have money on hand for day to day transactions.
    • Money you hold is $\propto$ what you plan to spend.
  • Theory of Liquidity Preference
    • to have money on hand for day to day transactions, but also to have some money on hand for emergencies.
    • When you hold a bond, you'll get $r\mathrm{\%}$ return per year. Cash + Debit has an opportunity cost of $r\mathrm{\%}$ per year, because you could be earning that return if you held a bond instead.
  • Precautionary motive
    • to have some money on hand for emergencies.
    • People who carry lots of cash on hand. Might come from a place with a lot of political instability, or they might be in a situation where they need to have cash on hand for emergencies.
  • $MD=0.2y-2r$
    • $r$ is interest rate
    • $Y=150$
    • $Y$ shifts the demand curve left and right
    • When interest rates go up, there is a decrease in quantity demanded.
    • When uncertainty increases, there's an increase in the demand curve.
    • Example:
      • $Y=150$
      • $v=0.2$
      • $c=0$
      • ${\text{Cash}}_0=4$
      • ${\text{Cash}}_1=5$
      • $MD=30-2r$
      • $\frac{4}{0.2+0.0}=20=MS$
    • Excess supply of money, means excess demand for bonds.
      • When there's an excess demand for anything prices goes up.
      • So price of bonds goes up.
      • $r$ yield on short term bond.
      • $P_{B_0}=50$, $f_{B_0}=100$
        • Par value and face value of the bond.
      • $R_0=\frac{100-50}{50}=1$
      • $P_{B_1}=80$
      • $r_1=\frac{100-80}{80}=\frac{1}{4}=0.25$
      • This is what takes us from point B to C.
    • What's gonna happen in the market during a war?
      • Uncertainty increases, so demand for money increases, which decreases the price of bonds, which increases the interest rate.
• Exchange Rate IRP
  • Interest Rate Parity
  • $e=\frac{r^F}{r}$
  • Reflect interest rate differentials.
  • $r^F=10$ and $r=10$
  • Then $e=1$ between US and Canada
  • If canada has $r=20$ then $r^F=10$. Then money starts flowing into canada.
  • $e=\frac{10}{20}=\frac{1}{2}=0.5$
  • So $e\downarrow$. It's an appreciation of the canadian dollar, because you can buy more US dollars with 1 canadian dollar.
  • Example:
• Bonds and Stocks
  • How does interest rate effect the stock market?
    • This is next week
    • Predict what happens to interest rates if the govt manipulates govt spending, tax rates, interest rates, etc.
  • $p=\frac{\sum _{i=1}^n{d}_i}{(1+r{)}^i}=\frac{d}{r}$ if the dividends are constant and perpetual.
    • $d$ is the dividend in $\mathrm{\$}$
    • $r$ is the interest rate
    • Example:
      • $d=4$ is the Present Discounted Value
      • $d=5$ as interest
      • $\frac{4}{0.05}=80.0$
      • $4$ dollars a year per life is worth $80\mathrm{\$}$ today.
    • Suppose interest rates go up because the war. Then $r\uparrow$, so $p\downarrow$. So stock prices go down.
    • When there's uncertainty caused by a war, higher interest rates, etc. then stock prices go down.
  • Bonds
    • $p_1=\frac{f}{1+r}+\frac{c}{1+r}$
    • Suppose we have a $1$ year bond with $f_B$ and $c=4$ which is coupon.
    • With $r=0.2$
    • PDV is $\frac{100}{1+0.2}+\frac{4}{1+0.2}=86.6666666666667$
    • If $r\uparrow$, then we expect $p\downarrow$. So bond prices goes down.
    • $p_2$
      • two year bond
      • $p_2=\frac{f}{(1+r{)}^2}+\frac{c}{1+r}+\frac{c}{(1+r{)}^2}$
      • $p_2=\frac{100}{(1+0.2{)}^2}+\frac{4}{1+0.2}+\frac{4}{(1+0.2{)}^2}=75.5555555555555$
    • Prices of bonds go down, depending on interest rate no matter the length of the bond, but longer term bonds are more sensitive to interest rate changes.
• IRP Model
  • $AS=5p$
  • $C=14+0.9(Y-10-0.1Y)$
  • $I=15-r$
  • $G=4$
  • $NX=6-0.02Y-0.5P+e$
  • $MS=5$
  • $MD=0.1Y-r$
  • $e=10-r$
  • This is a linear version of $IRP$.
  • We know from IRP that $e=\frac{r^F}{r}$
  • So increasing $r$ will decrease $e$.
  • $MS=MD$ means
    • $5=0.1Y-r$
    • $r=0.1Y-5$
  • So $e=10-0.1Y+5=15-0.1Y$
  • Put $e$ into $NX$
  • $NX=6-0.02Y-0.5P+e$
  • $NX=6-0.02Y-0.5P+15-0.1Y=-0.5P-0.12Y+21$
  • $AS=5P$
  • $Y=5P$
  • $P=0.2Y$
  • $I=15-r$
    • $=20-0.1Y$
  • Sub this into $AE$.
  • $AE=5+0.81Y+20-0.1Y+4+6-0.01Y-0.5(0.2Y)+15-0.1Y=0.5Y+50$
  • Fake AE
    • $AE=0.5Y+50$
    • $Y=100⟹p=20$
    • $r=0.1Y-5$
    • $r=0.1(100)-5=5.0$
    • $e=10-5=5.0$
    • $I=15-5=10$
  • $AE=5+0.81Y+10+4+6-0.1Y-0.5P+5=-0.5P+0.71Y+30$
  • $Y=AE$
    • $AD=150-2.5P$
    • $AS=5P$
    • $p=20$
    • $⟹A{E}_0=20+0.8Y$
  • We have basically removed influence on $e$ and $r$. So it's just previous week's content now.
  • Since from $A\to C$ we have a smaller multiplier because change in price.
  • If $G\uparrow$ then we have that $G\uparrow$ and $Y\uparrow$, so $MD=0.1Y-r$ which shifts to the right.
  • If that shifts to the right, $r\uparrow$ so $e$ appreciates.
  • If $e\downarrow$ in america, they need to spend more to import from us.
  • So our $NX$ goes down. So our multiplier gets even smaller.