EC 313 Intermediate Macroeconomics

Lecture 3Thursday 10/8/2013

• Go to the board to explain the multiplier intuitively with the circular flow diagram

To the board…

• Process takes time to unfold in the real world, probably in the 6-18 months range, perhaps longer for, say, infrastructure spending by the government

An alternative way to look at equilibrium• Recall that equilibrium is where Y = Z, or

where Y = C + I + G• But note that we can write Y, income, as

Y = C + S +T (income goes to taxes or consumption, whatever is left over is saving).

• Then, at equilibrium C + S + T = C + I + G

• Cancel the C terms to get S + T = I + G

• Rearrange terms to get I = S + (T-G)• This says that investment = saving, i.e. S = private

saving and (T-G) is public saving (which can be negative)

• Now, note that S = Y – C – T. Sub in to get S = Y – (c0 + c1(Y-T)) – T

• Or, combining terms S = -c0 + (1-c1)(Y-T)

• This is the saving function, and (1-c1) is the marginal propensity to save.

• Now use this to find the equilibrium (recalling that I = I0)

I0 = S + (T-G)• Sub for S

I0 = -c0 + (1-c1)(Y-T) + (T-G)• Solve for Y

Y = [1/(1 - c1)][c0 + I0 + G – c1T]• This is the same equilibrium. It has to be, it was

derived from Y=Z.

Show graphically on the board…

How easy is this in the real world?• Changing G or T – getting this through Congress –

is not easy• We held all else equal, e.g. investment and net

exports, but when these change and it’s not fully predictable, hitting a policy target is much harder

• Expectations of the future also matter, we have abstracted from this (for now)

• There may be side effects, e.g. deficits or inflation

Practice Problems• Example 1

C = 200 + .8(Y-T) I = 160 G = 300 T = 200– Find equilibrium income, disposable income, and

consumption. How large is the deficit?– Let autonomous consumption increase to 300. Use the

multiplier to find the new equilibrium for output– If full employment is when output = 4000, how much

should G change to reach full employment?

• Example 2 (Balanced Budget Multiplier) C = 300 + .75(Y-T) I = 200 G = 400 T = 400– Find equilibrium income– Notice that the budget is in balance, i.e. G=T. Let both

G and T increase by 50 so that the budget stays in balance. What happens to output?

– If the government spends a dollar more, and takes a dollar back in taxes at the same time, how can output go up? Why does this increase demand?

• Example 3 (paradox of thrift) C = 800 + .75(Y-T) I = 600 G = 500 T = 400– Find equilibrium income. Find saving.– Let autonomous consumption, c0, decrease from 800 to

700. That is, let people be “virtuous” and try to save more and consume less.

– Find the new values for output and saving.– Why doesn’t saving change (this is the paradox, that people

try to save more, but this reduces output and they end up with the same savings as before)

Chapter 4 Financial Markets

The Demand for Money• What determines the demand for money? (Note

the distinction between income, money, and wealth)

• Will assume financial wealth (the accumulation of past saving and dis-saving) can be held as either:– Money (which pays no interest)– Bonds (pay interest – this is a placeholder for all assets

that offer a return)

• Money = currency plus checkable deposits (i.e. M1, will cover M2, etc. later). It can beused for transactions

• Bonds pay interest I, but cannot be used for transactions (again, this is a placeholder – and aggregate – capturing all interest bearing financial assets, in real world many types of assets each with its own interest rate)

• Question for us: How much wealth should be held as money, and how much as bonds?

• Wealth = Money + Bonds• You could leave as much as possible in bonds, and

when you need money transfer over the exact amount by a phone call to a broker, cell phone standing in checkout line, etc. That would maximize interest income.

• But if there is a cost of doing this – and there is – and if each additional time you do make a transfer it gets more irksome and the benefit falls – there is a limit to how many transfers you will make (could be zero, i.e. hold all wealth as money)

• To the board to illustrate…• Money demand will depend upon two variables

– The volume of transactions, which we will capture as income (not perfectly related, but close enough)

– The interest rate which captures the opportunity cost of holding money

• Do people really behave like this? When interest rates are high, people do tend to put as much money as they can in things like money market accounts (the money is used to buy bonds) – we see money move from checking to these types of accounts (and businesses manage their money carefully as well)

• Presently, the benefit is so low (since interest rates are so low) that most people are simply holding money

• So we can write Md = PYL(i) , where PY is nominal income (book uses $Y) and L(i) is a function that is negative in the interest rate. That is, when i increases, L(i) (and hence Md) fall.

• Graphically (show on board)• Negatively related to the interest rate (when i

goes up, move wealth from money to bonds)• Shifts out when P or Y increases (need more for

transactions). If PY doubles, need twice as much money to buy the same amount of stuff (since y held constant)

Determining the Interest Rate• We have a money demand curve, but to get to

an equilibrium (a particular M and i), need to add the money supply

• For now, assume that all cash is in currency, there are no banks and no checking accounts

• Will add banks and demand deposits soon, simplifies things for now.

• Assume monetary authority sets the money supply at whatever level is desired, i.e. Ms = M

• Show Md = Ms on board …– Equilibrium– A change in Y– A change in P– A change in Ms

Figure 4-2 The Determination of the Interest Rate

Figure 4-3 The Effects of an Increase in Nominal Income on the Interest Rate

Figure 4-4 The Effects of an Increase in the Money Supply on the Interest Rate

Monetary Policy and Open Market Operations• Look at how central banks actually change the

money supply (and reintroduce the banking sector)

• In particular, look at “open market operations” which can be expansionary (money supply rises) or contractionary (money supply falls)

• It does this by buying and selling bonds (buying – trading new money for bonds – increases the money supply, and selling – giving people bonds in return for money – reduces it

Bond Prices and Bond Yields• Won’t go into as much detail as the text, but

the point of this section is that the prices of bonds and the interest rate are inversely related

• Explain with an example• Let the price of a bond today be PB, and value a

year today be $100 (what you get when you cash it in a year from today).

• Then i = ($100-PB)/PB

• With a bit of algebra this becomes: PB = $100/(1+i)• Thus, when i increases, PB declines. They are inversely related.• Now think about open market operations. Let the Fed buy

bonds (increase the Ms). This reduces the supply of bonds on private markets, so it must be that PB incfreased, And since I and PB are inversely related, i must have gone down. Thus, the purchase of bonds increases the money supply and reduces the interest rate.

• When the Fed sells bonds, the opposite happens, the supply goes up, PB goes down, and i goes up.

• Explain by referencing the Md-Ms diagram

• Should the Fed choose money or the interest rate? Presently, the Fed targets an interest rate, and lets the money supply adjust as necessary to hit the interest rate target.

• Show graphically on board with Md-Ms diagram