Module 03 · Chapters 4

Financial Markets I

Money, bonds, and the central bank's interest-rate target.

“How the central bank picks i — and why the LM curve became flat.”

~30 min· 4 sub-skills·6 exercisesExam frequency · high0% mastered

The goods market told us output adjusts to demand. The next question is: what determines the interest rate that drives investment? In modern central-bank practice, the interest rate is set as a policy choice. But to understand what that choice means, we need the underlying money-market plumbing.
Money demand
$M^d \;=\; \$Y \cdot L(i)$
$M^d$
nominal money demand (cash + checking)
$\$Y$
nominal GDP — transactions volume
$L(i)$
decreasing in i — the opportunity cost of holding money
More transactions → more money demanded. Higher interest rate → less, because cash earns nothing while bonds earn i.
Definition·Money supply M^s
Money supply M^s is set by the central bank. In the textbook, M^s is exogenous. In modern central banking it's whatever quantity is consistent with the interest-rate target — see the modern LM below.
Figure · Money-market equilibrium
Modern (rate-targeting): CB picks i, M^s adjusts to clear.
Vertical M^s, downward-sloping M^d. Equilibrium i where they cross.
Money-market equilibrium condition
$M^s \;=\; \$Y \cdot L(i)$
If M^s rises (CB expansion), i falls. If $Y rises (boom), i rises. This is the LM logic.
Insight·Modern LM is **horizontal**
In the textbook (and in this course), the central bank chooses the interest rate i directly. M^s adjusts endogenously to whatever level is needed. Geometrically: the LM curve is a horizontal line at the chosen i.

This matters because it changes the comparative statics. With a flat LM, fiscal policy has its full multiplier — there's no crowding-out from a rising i.
Common misconception
When the central bank raises rates, bond prices rise.
ActuallyBond prices and yields move in **opposite** directions. Higher rates ⇒ existing fixed-coupon bonds are less attractive ⇒ their price falls.
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A 1-year zero with face value €100 priced at €95.24 yields 5%. If yields rise to 7%, the price drops to €93.46.
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Price of a one-period zero
$P_B \;=\; \frac{F}{1 + i}$
$P_B$
current bond price
$F$
face value (paid back at maturity)
$i$
one-period yield
Solve for i: $i = F/P_B - 1$. Yield and price are inverses around 1.
Exercise · predict shift · +10 XP
Money demand response to income
Real income rises 10%. Holding i fixed, what happens to nominal money demand?
Scenario: ΔY > 0, i unchanged.
Exercise · predict shift · +10 XP
Money demand response to i
The interest rate rises. What happens to real money demand?
Scenario: Δi > 0, $Y unchanged.
Exercise · numerical · +14 XP
Equilibrium i from M^s and M^d
$Y = 1000, M^s = 200. The function L(i) = 0.25 − 1.25·i. Find i*.
Your answer (decimal (e.g., 0.04 = 4%))
Exercise · numerical · +14 XP
Modern LM — what M^s does the CB choose?
$Y = 1200. The CB targets i = 3% with the L function from above. What M^s must it provide?
Your answer
Exercise · numerical · +12 XP
Bond price from yield
A 1-year zero has face value €100. The 1-year yield is 5%. What is its price today?
Your answer (EUR)
Exercise · numerical · +12 XP
Yield from price
A 1-year zero with face €100 trades at €92.59. What is its yield?
Your answer (decimal (0.08 = 8%))

Mastery check

5 questions · pass with 80%

Answer all five to confirm you've internalised the module. A passing run unlocks the next module.

Q1
"Bond prices and yields move in the same direction."
Q2
Which raises real money demand?
Q3
"In the modern LM model, M^s is endogenous to the interest-rate target."
Q4
$Y rises and the CB holds M^s fixed. What happens to i?
Q5
A 1-year zero face €100 trades at €98.04 (i = 2%). The CB raises i to 4%. New price?

0 / 5 answered

Exam pitfalls

Treating money demand as a function of *real* income only. It scales with **nominal** $Y, which captures both Y and P.
Drawing the LM curve as upward-sloping in the 'modern' framework. The exam in this course uses the flat-LM convention.
Confusing M^s changes (which used to set i) with i changes (modern: i is set; M^s adjusts).
Saying 'higher rates make bonds more valuable'. They make bonds *more attractive* on a yield basis, but make existing low-coupon bonds *less* valuable.