Monetary Economics & Financial Markets
Monetary economics analyzes how central banks control the money supply, how money affects output and prices, and how financial markets allocate capital across time and risk. The Quantity Theory of Money ($MV = PY$) links the money supply to the price level. The Fisher equation separates nominal and real interest rates. The IS-LM model synthesizes the goods market (IS curve) with the money market (LM curve) to determine equilibrium output and interest rates. The Taylor rule provides a practical guide for central bank interest-rate setting. Asset pricing — from bond valuation to the Capital Asset Pricing Model — shows how financial markets determine prices under uncertainty.
Money, Interest Rates & Monetary Policy
$$MV = PY$$
$M$ = money supply, $V$ = velocity of money, $P$ = price level, $Y$ = real output. If $V$ and $Y$ are stable, $\uparrow M \Rightarrow \uparrow P$ (inflation). Growth rate form: $\hat{M}+\hat{V}=\hat{P}+\hat{Y}$, so $\pi \approx \hat{M} - \hat{Y}$ when $\hat{V} \approx 0$.
$$1 + i = (1 + r)(1 + \pi) \approx r + \pi$$
$i$ = nominal interest rate, $r$ = real rate, $\pi$ = expected inflation. Irving Fisher's insight: expected inflation is built into nominal rates, so monetary expansion raises $i$ in the long run (Fisher effect).
$$M = \frac{1}{rr} \times \text{Monetary Base}$$
$rr$ = reserve requirement ratio. A $\$1$ injection of base money creates $1/rr$ dollars of broad money (M2) through the banking system's lending cycle.
IS curve (goods market equilibrium): Output $Y$ falls as interest rate $r$ rises (higher $r$ crowds out investment):
$$Y = C(Y-T) + I(r) + G$$
LM curve (money market equilibrium): $Y$ rises as $r$ rises (higher income raises money demand, requiring higher $r$ to restore equilibrium):
$$\frac{M}{P} = L(r, Y)$$
IS-LM equilibrium determines $(Y^*, r^*)$ jointly. Fiscal policy shifts IS; monetary policy shifts LM.
A central bank guideline for setting the nominal interest rate:
$$i = r^* + \pi + 0.5(\pi - \pi^*) + 0.5\left(\frac{Y - Y^*}{Y^*}\right)$$
$r^*$ = neutral real rate, $\pi^*$ = inflation target, $Y^*$ = potential output. The rule raises rates when inflation exceeds target or output exceeds potential, and vice versa.
Price of a bond paying coupon $C$ annually with face value $F$ maturing in $n$ years, at yield (discount rate) $y$:
$$P = \sum_{t=1}^{n} \frac{C}{(1+y)^t} + \frac{F}{(1+y)^n} = C \cdot \frac{1-(1+y)^{-n}}{y} + \frac{F}{(1+y)^n}$$
Bond prices and yields move inversely.
$$E[R_i] = R_f + \beta_i(E[R_m] - R_f)$$
$R_f$ = risk-free rate, $\beta_i$ = systematic risk of asset $i$, $(E[R_m]-R_f)$ = market risk premium. Assets with $\beta > 1$ move more than the market; $\beta < 1$ less. CAPM implies that only systematic (non-diversifiable) risk earns a premium.
Money supply grows $7\%$, velocity is stable, real GDP grows $2\%$. What is expected inflation?
- $\pi \approx \hat{M} - \hat{Y} = 7\% - 2\% = 5\%$.
5-year bond, face $\$1{,}000$, annual coupon $\$60$, yield $y = 5\%$. Find its price.
- $P = 60\cdot\frac{1-1.05^{-5}}{0.05} + \frac{1000}{1.05^5} = 60(4.329) + 783.53 = 259.75 + 783.53 \approx \$1{,}043.28$. Since coupon rate $> $ yield, bond trades at a premium.
$R_f = 2\%$, market premium $= 6\%$, $\beta = 1.4$. Find required return.
- $E[R] = 2 + 1.4(6) = 2 + 8.4 = 10.4\%$.
Practice Problems
Show Answer Key
1. $P = MV/Y = (3\times 5)/10 = 1.5$ (price level index $= 1.5$).
2. Multiplier $= 1/0.10 = 10$. M2 could expand by $\$1\text{T}$.
3. Approx: $r \approx 4\%$. Exact: $r = 1.07/1.03 - 1 \approx 3.88\%$.
4. $i = 2+4+0.5(4-2)+0.5(-1) = 2+4+1-0.5 = 6.5\%$.
5. $P = 1000/1.04^3 \approx \$889.00$.
6. Yield rises (inverse relationship: lower price means higher yield to maturity).
7. $E[R] = 3+0.7(5) = 6.5\%$.
8. Open-market purchase increases bank reserves → expands money supply → LM curve shifts right → interest rates fall → investment rises → IS-LM equilibrium moves to higher $Y$ and lower $r$.
9. QE is large-scale asset purchases by the central bank (typically longer-term securities) used when the policy rate is near zero (zero lower bound). It injects base money and compresses long-term yields.
10. Coupon rate $5\% < $ yield $7\%$ → bond trades at a discount (below $\$1{,}000$).
11. Lenders demand a higher nominal rate to compensate for the loss of purchasing power due to inflation; $i = r + \pi$ rises one-for-one with $\pi$ in the long run.
12. $\beta < 0$ means the asset moves counter-cyclically (zigs when the market zags). It provides insurance against market downturns, so investors accept a return below $R_f$. Gold and some defensive assets have mildly negative betas.