Download The Dynamic Macro Model with Money

 The Dynamic Macro Model with Money F ir s t - C la s s U n iv e r s it y T u t o r s
The “Cash-­‐in-­‐Advance” Model We are now introducing money into our model. Money is very important in an economy because it acts as a medium of exchange, meaning that we don’t have to barter for goods. This is good because otherwise I’d have to do a hell of a lot of tuition to be able to trade education services for a car! Introducing money into our model brings with it the introduction of banks. Banks have two roles in the real world and we want to include both of these in our model. Firstly, banks allow us to have current accounts so that we can buy goods without cash. In economics, we call these transactions deposits because they allow for easy transactions. Secondly, banks allow us to save our money and pay us interest to make it worth while. We call these savings deposits obviously. Consumers can hold their wealth in three ways: Holding Notation Cash (Money) M Credit Balances (Credit Card) X Savings (Bonds) B Pros and Cons useful because it is ready to use (liquid) but has an opportunity cost because it receives no interest are even more liquid than cash, but the banks charge a credit rate, q for using them. However, they can allow payments to be delayed until the end of the period, meaning that interest is received on savings before paying off the credit card receives interest at the nominal interest rate, 1 + R, but cannot be accessed until the next time period and therefore cannot be accepted as payment Introducing the Credit Market Banks offer ATMs and credit cards and these are costly to run. Therefore, the bank charges for these facilities. We denote the price of credit card facilities, q www.theprofs.co.uk 1 F ir s t - C la s s U n iv e r s it y T u t o r s
(because p is used to mean price of goods). Intuitively, q could be understood as the rate charged for using a credit card. This is different from borrowing because the consumer has the money but is choosing to use a credit card for convenience and because money in the bank can still receive interest. The market for Credit Card Balances has a upward sloping supply curve. We assume that the credit market is highly competitive and q is the marginal cost of providing credit services. This MC is upward sloping because, in the short run, increasing the number of ATMs and hiring more labour needed to monitor credit histories is increasingly costly. Therefore, higher q is required for banks to extend their credit facilities. The Supply of Price of Credit Credit Cards Card Balances, q XS(q) XS(q) is upward sloping because the marginal cost of providing more credit services increases (in the short run) Why use a credit card? Quantity of Credit Card Balances, X Paying by credit means that you can hold the money in bonds (savings) to receive the nominal interest rate before paying off the credit card fee. The Benefit of using a credit card is therefore the interest occurred on the money left in bonds. Every purchase, P, using credit earns R interest that it would not receive if money was used instead. So 𝑅×𝑃 is the benefit. The Cost of using a credit card is q per unit, so purchasing P units means having to cough up 𝑃×𝑞 at the end of the period. Net Benefit: 𝑅𝑃 – 𝑞𝑃 = (𝑅 − 𝑞)𝑃 This represents a trade-­‐off between the interest on extra bond holds and the credit card fee.
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The Credit Market at Equilibrium (q=R) Price of Credit Card Balances, q The Supply of Credit Cards, XS(q) Xd is flat at equilibrium so that there is no additional benefit to using credit over money. The maximum amount of Xd possible is Y, all transactions The Demand for Credit, Xd q=R X* Y Quantity of Credit Card Balances, X And why is Xd flat? R > q R < q R = q Net Benefit of using a credit card (𝑹 − 𝒒)𝑷 The bank will lose money on credit services as consumers will receive more from the interest they receive than the bank charges Now credit cards are pointless as they cost more than the interest they receive so consumers will stop using them altogether and only use money This must be the equilibrium and also the only way that the credit market can exist. If the price of credit facilities equals the nominal interest rate then it is horizontal because R is constant. At the equilibrium, consumers are indifferent between purchasing goods with money or credit cards. It just comes down to preferences, convenience and how much you can squeeze into your wallet. The Bottom Line: The cost of a credit card is the nominal interest rate, the rate at which the bank charges for borrowing Economics: Overcomplicated Solutions to Uncomplicated Problems www.theprofs.co.uk 3 F ir s t - C la s s U n iv e r s it y T u t o r s
The Nominal Interest Rate is the Link Between the Credit and Money Markets When the nominal interest rate increases, this shifts the demand for credit card balances up and so banks can afford to increase the supply of credit facilities. At the new equilibrium, X is higher. Note: first the nominal interest rate rises, then consumers put more money into savings deposits to gain from the relatively higher interest rates, and so banks can afford to extend their credit facilities and so we move up the same supply curve. An Increase in the Nominal Interest Rate, R on the credit market Price of Credit Card Balances, XS(q) q Xd2 q2=R2 When the nominal interest rate rises, the demand for Xd1 credit cards increases q1=R1 because there is more incentive to convert money into savings bonds to gain the higher interest X* X** Y Quantity of Credit Card Balances, X We have now seen that the equilibrium quantity of credit cards X*(R) is really a function of the nominal interest rate, R. As R increases, so too does the use of credit cards. There is a positive relationship between the nominal interest rate R and the equilibrium credit card balances, X As money is the alternative way of purchasing goods to credit cards, money demand must be negatively related to the nominal interest rate. We can use this link between credit card balances and the nominal interest rate to better understand our money demand equation. www.theprofs.co.uk 4 F ir s t - C la s s U n iv e r s it y T u t o r s
Deriving the Money Demand Equation Our study of the credit market is important for us to better understand the demand for money because credit is the only substitute for money. Therefore, the demand for money will be the value of all purchases minus the value of all purchases made with credit cards: ∗
𝑀! = 𝑃(𝑌 – 𝑋(!)
) Glossary Md is the demand of money in the economy P the average/general price level of the economy Y is the total output of our economy PY is the total value of the output of our economy X*[R] is the equilibrium quantity of credit card purchases (which is a function of the Nominal Interest Rate) PX*[R] is the value of the credit card purchases Note Md doesn’t need a P in front of it because it is already a monetary unit and Md/P is the Real Money Demand which is the quantity of units of money Economists often leave out the intermediary credit card balances step and rewrite the equation succinctly as: 𝑀! = 𝑃𝐿 𝑌, 𝑅 Glossary L[…] The “liquidity function” is the mathematical function that relates money demand to Y and R. It could be as simple as L[Y,R] = Y + R Money Demand in terms of the Real Interest Rate The demand for money relies on the nominal interest rate. However, given that the rest of our model uses the real interest rate, economists often write the money demand equation in terms of r instead using the Fisher Equation (approximation): 𝑅 = 𝑟 + 𝑖 The real and nominal interest rates move together, and if we assume that there is no expected inflation within our economy so that i=0 then this fudge allows us to rewrite the equation as 𝑀! = 𝑃𝐿 𝑌, 𝑟 www.theprofs.co.uk 5 F ir s t - C la s s U n iv e r s it y T u t o r s
The Money Market in Equilibrium The Price Level, P MS Md=PL(Y,r) P* M* Quantity of Money in the economy, M Factors that Shift the Money Supply Curve The Money Supply is MS is the amount of money that the Government/Bank of England, has allowed to be printed. It is fixed because only the Central Bank/Government can authorise an increase or decrease in the money supply. Method of Explanation increasing MS If the government wants to increase the amount of money circulating around the economy it can simply print money and buy assets such as housing and offices Buying/Selling Assets off of consumers and firms, thus giving them the money, off Households and Firms More commonly though, the government will use this money to buy back its own bonds (loans) with the same (Open Market overall affect of increasing the amount of money in Operations) circulation. To decrease the money supply they issue new bonds, encouraging households/firms to lock money into government saving schemes. If taxes are reduced, households and firms have more Reducing Taxes money to spend because less is leaking out of their pay checks. This is called a “helicopter drop” of money. The Government can of course simply print money and Seigniorage (the splash that money on government spending across the economy. This is called Seigniorage. However, this has inflation tax) huge inflationary implications that will be looked at later. www.theprofs.co.uk 6 F ir s t - C la s s U n iv e r s it y T u t o r s
Factors that Shift the Money Demand Curve Variable Effect Explanation Positive Higher prices mean that more money is needed to Price Level, P carry out transactions Positive Higher Income means money is flowing around the Income, Y economy, implying more transactions and therefore more money is demanded Negative Savings and Credit Cards are now relatively more Nominal attractive, and so less money is demanded Interest Rate, R Negative Same as above because the real interest rate Real Interest moves with the nominal interest rate after Rate, r adjusting for inflation Negative A decrease in the supply of credit will lead to a fall The Supply of S
in equilibrium X* and therefore higher money Credit X [q] demand as money is the only substitute for credit More factors that affect the supply of credit Price of Credit Card Balances, q XS(q)2 XS(q)1 If XS[R] shifts inwards then the equilibrium quantity of Credit Card Usage decreases, q=R d
thus increasing the demand X for money Y Quantity of X* Credit Card X** Balances, X Technological advances such as ATM machines and contactless payment cards affect cost of electronic payments system. Financial innovation such as sweep accounts that automatically move idle balances into interest-­‐earning accounts affects opportunity cost of holding money. Government regulation/deregulation (e.g. the abolition of Regulation Q prohibiting interest being paid on demand deposits in U.S.) In addition to the longer-­‐term trends, there can also be shifts in money demand due to: Changes in perceived riskiness of banks -­‐ will depositors be able to get access to their www.theprofs.co.uk 7 F ir s t - C la s s U n iv e r s it y T u t o r s
money? Regular shifts in spending patterns: weekends vs. weekdays, holidays, etc. Sudden disruption to payment systems such as a technical failure or power cut The Transactions Constraint In the “Cash-­‐in-­‐Advance” Model, consumers and firms face a transactions constraint, which means that consumers have to pay for their consumption before receiving their income. Therefore, all purchases have to be paid for with money from the previous period. note: any variable in our economy that is not already priced in terms of monetary value will now need a P, the price level, in front of it. Consumers and Firms can either spend at the price level, P, or save their money in savings accounts by buying bonds (priced in nominal terms so no P is needed) Bd. Total Spending by Households and Firms is C + I + T because money is needed to buy goods, capital and also to pay taxes. Therefore Total Spending in our economy is 𝑃(𝐶 + 𝐼 + 𝑇), which can be abbreviated to PY, plus Bd. This total spending can be funded by: 1. Money from last period, M0, 2. Credit at the current price level, PXd 3. Savings (bonds) that have matured from last period, B0(1 + R). 𝑃 𝐶 + 𝐼 + 𝑇 + 𝐵! = 𝑀! + 𝑃𝑋 ! + 𝐵! 1 + 𝑅 must be Total Spending Total Wealth from last in the economy purchased with period or credit cards What effect does the transaction constraint have on our economy? The important point about the transactions constraint is that we can only purchase goods with money brought over from last period, or credit. This means that consumers will not be paid until the end of the period, and they cannot spend their wages until the next period. This is how it is in the real world when you have to wait for your next pay day to go out drinking. Effectively, consumers can only spend what their money wage is worth tomorrow and this delay means that the money wage must be discounted by the nominal interest rate. This delay changes the consumer’s optimal work-­‐leisure decision: www.theprofs.co.uk 8 F ir s t - C la s s U n iv e r s it y T u t o r s
𝑀𝑅𝑆!,! = 𝑤
1+𝑅
Therefore, higher R will decrease the labour supply curve because it effectively reduces the consumer’s wage. This will be important when studying inflation. Hang on… I’m confused But wait, the Intertemporal leisure decision tells us that a higher real interest ! (!!!)
rate, r, will increase the labour supply because 𝑀𝑅𝑆!,!! = ! ! and the !
Fisher equation 𝑅 = 𝑟 + 𝑖 tells us that higher R will increase r. We assume that the effect of the real interest rate dominates the effect of the transactions constraint, and so our model is unaffected unless there is inflation. The “Wages-­‐in-­‐Advance” model (an extension) A logical extension of the Cash-­‐in-­‐Advance model in which firms must set aside cash for the wage bill because they must pay wages before they receive their revenue. Therefore, money that is set aside for wages does not earn interest, but is paid at the end of the period at which time it has effectively grown it value. This changes the firm’s demand for labour: 𝑀𝑃! = 1 + 𝑅 𝑤 In the Wages-­‐in-­‐Advance model, a rise in the nominal interest rate decreases the labour supply. The Government The Government’s Budget Constraint is now extended to a far more realistic version. In each period, the government needs money to spend at the current price, PG, and also to pay off the interest on its bonds from last period, (1 + R)B0 There are three ways in which the government can raise finances: 1. Taxes at the current price level, PT 2. Issuing New Bonds, B 3. Printing more money, (M – M0) The Government’s Budget Constraint 𝑃𝐺 + 1 + 𝑅 𝐵! = 𝑃𝑇 + 𝐵 + (𝑀 − 𝑀! ) www.theprofs.co.uk 9 F ir s t - C la s s U n iv e r s it y T u t o r s
The Full Macroeconomic Model with Money The addition of the Money and Credit markets has therefore had little affect on our economy. In the “Cash-­‐in-­‐Advance” model we now have a transactions constraint that affects the labour supply curve, yet this affect is dominated by the pre-­‐existing Intertemporal Substitution of labour effect. However, in the little-­‐
used “Wages-­‐in-­‐Advance” extension, the labour demand curve is affected by the nominal interest rate. Overall, we shall see that the addition of money to our economy has little affect on the whole model because the price level simply adjusts to keep our final market in equilibrium, and no real variables are affected by the price level. We therefore call money neutral because a change in money and prices has no affect on the rest of the economy. Quick Intuition Image you woke up one morning to find that all prices had doubled. Your wage is just the price of labour and this has doubled like all the other prices. So the !
real wage ( ! ) is unaffected. You now have twice as much money and everything costs exactly twice as much. Therefore, your real purchasing power is completely unaffected and no real variables in the economy change The Neutrality of Money To demonstrate this, let’s imagine that the government printed a one-­‐off, permanent and unexpected increase in the money supply. When the money supply increases, the price level of the economy adjusts to devalue the existing money’s purchasing paper so that the real money supply is unaffected. If 10% more money is printed, then a all prices will increase by 10% so that no relative prices or real variables will change. www.theprofs.co.uk 10 F ir s t - C la s s U n iv e r s it y T u t o r s
The Neutrality of Money means that an increase in the money supply has no effects on real variables or relative prices, so our labour and goods markets remain unaffected The Super-­‐Neutrality of Money?? Money is neutral because an increase in the money supply had no real effects on our economy. However, money is not superneutral because an increase in the growth of the money supply does have real affects. A one-­‐off increase in the money supply was met by a one-­‐off increase in the price level. However, a permanent increase in the growth rate of the money supply will lead to an increase in the growth rate of the price level, and this causes inflation. We shall now extend our money model to show the adverse affects of inflation. Suppose the money supply grows at a constant rate, x 𝑀! = (1 + 𝑥)𝑀! Glossary x the growth rate of the money supply and therefore the growth of prices, inflation Now inflation is no longer 0. Therefore, according to the Fischer Equation (approximation) inflation will cause the nominal interest rate to rise. 𝑅 = 𝑟 + 𝑖 The Cash-­‐in-­‐Advance model had one affect on our labour supply curve 𝑤
𝑤
𝑀𝑅𝑆!,! = = 1+𝑅
(1 + 𝑟)(1 + 𝑖)
Therefore, sustained inflation caused by a change in the growth rate of money has a real affect on our labour supply, shifting it inwards leading to a fall in employment as consumers substitute away from work and towards leisure. This fall in employment will also decrease output. www.theprofs.co.uk 11 F ir s t - C la s s U n iv e r s it y T u t o r s
Seigniorage: The Costs of Inflation from Printing Money This long-­‐run growth in the money supply has caused increased inflation, which has led to an increase in the nominal interest rate, decreasing the demand for money and increasing the price level. The Transaction Constraint means that wages can’t be spent until next period, meaning that they depend on the nominal interest rate. 𝑀𝑅𝑆!,! = 𝑤
1+𝑅
The nominal interest rate has risen, decreasing the effective wage, therefore discouraging Labour and lowering employment. Lower employment will mean lower output (the production function has not been shown here) Lower effect wages will mean less Consumption and hence output demand also shifts in. This lower output, Y, further decreases the demand for money as less transactions will cause place. This long-­‐run growth in the money supply has caused increased inflation, which has led to an increase in the nominal interest rate. This led to a decrease in the labour supply and real effects on the wage, interest rate and output. Bottom Line: inflation fucks your economy www.theprofs.co.uk 12 F ir s t - C la s s U n iv e r s it y T u t o r s
The Friedman Rule The Optimal Monetary Policy Key Premise: Inflation creates inefficiency because it distorts the decision to work. The Pareto Optimal Condition for an economy is 𝑀𝑅𝑆!,! = 𝑤 = 𝑀𝑅𝑇!,! (= 𝑀𝑃! ) However, with the Cash-­‐in-­‐Advance Transaction Constraint and inflation this optimality condition is distorted; money is costly to hold because it gains no interest and loses value with inflation. The effect real wage loses value because it is not received until the end of the period, and it loses the interest it could have received if received at the beginning of the period. So the market instead allocates: !
𝑀𝑅𝑆!,! = !!! and so 𝑀𝑅𝑆!,! =
!"#!,!
!!!
Meaning that less labour will be supplied than is Pareto optimal and so the economy will have too much leisure, too little output and consumption and too little money circulating around it. Problem: The Nominal Interest Rate has driven a wedge between the 𝑀𝑅𝑆!,! and the 𝑀𝑅𝑇!,! because it has made money costly to hold. Solution: R = 0 so that the wedge is removed and money is not longer costly to hold. An Intuitive Explanation The bank provision of credit cards imposes a resources cost on the economy, q, which could be used for alternative output (rather than ATMs and credit checks). As the alternative to credit is money, which imposes a negligible cost to the economy, it is efficient to use money instead of credit. If R = 0 then there would be no benefit to using credit cards and all purchases would be made using money, thus removing the resource cost of credit cards. www.theprofs.co.uk 13 F ir s t - C la s s U n iv e r s it y T u t o r s
When R=0, the cost of paying off a credit card is always above the benefit of saving the money. Thus the credit market collapses and all transactions are made using money. Friedman Advocates Deflationary Monetary Policy To achieve R = 0 the government/Central Bank can decrease in the money supply, causing deflation. Fisher Approximation: 𝑅 = 𝑟 + 𝑖 Setting 𝑅 = 0 𝑖 = −𝑟 The rate of inflation, i, is the amount that will exactly counter the real interest rate, -­‐r. Inflation is caused by a growth in the money supply 𝑖 = 𝑥 The Friedman Rule: 𝑥 = −𝑟 Therefore, negative growth of the money supply is needed to deflate the economy so that there is no benefit to holding credit cards and the consumers work-­‐leisure decision is undistorted. www.theprofs.co.uk 14