Module 4 · Economics

Monetary Policy

EN: Money creation, the Fisher equation, the Taylor rule, and central-bank tools.
VN: Tạo tiền, phương trình Fisher, quy tắc Taylor, công cụ ngân hàng trung ương.

1. Money Multiplier Core

About: 1 / reserve requirement. Maximum amount of money the banking system can create from $1 of base money. Lower reserve req → larger multiplier.Tóm tắt: 1 / dự trữ bắt buộc. Lượng tiền tối đa hệ thống ngân hàng tạo ra từ 1 đồng tiền cơ sở.

\[ \text{Money multiplier} = \frac{1}{\text{Reserve requirement}} \]

Practice problem

Reserve requirement = 10%. Maximum money multiplier?

Show solution

1 / 0.10

= 10

2. Quantity Theory of Money (Fisher) Core

About: MV = PY. With V (velocity) stable, money growth maps directly to inflation if real output is given. Foundation of Monetarist view.Tóm tắt: MV = PY. Khi V ổn định, tăng cung tiền → inflation nếu Y cho trước. Nền tảng Monetarist.

\[ M \cdot V = P \cdot Y \]

Components

M Money supply.
V Velocity (turnover) — assumed stable.
P Price level.
Y Real output.

In growth rates: %ΔM + %ΔV ≈ %ΔP + %ΔY → if V and Y stable, money growth maps to inflation.

Practice problem

Money supply M grows 6%, velocity stable, real GDP grows 2%. Predicted inflation?

Show solution

%ΔM + %ΔV ≈ %ΔP + %ΔY

6 + 0 = π + 2 → π = 4

≈ 4% inflation

3. Fisher Equation (Real vs Nominal) Core

About: Nominal rate ≈ real rate + expected inflation. Tells you the inflation-expectation embedded in any nominal rate. Nominal − real = inflation expectation.Tóm tắt: Lãi suất danh nghĩa ≈ lãi suất thực + kỳ vọng lạm phát. Cho biết kỳ vọng lạm phát ẩn trong nominal.

\[ R_{nom} \approx R_{real} + \pi^{e} \]

π^e = expected inflation. See Quant M1 for the exact compounded form.

Practice problem

Real rate 1%, expected inflation 3%. Approx nominal rate?

Show solution

≈ 1% + 3%

≈ 4%

4. Taylor Rule Core

About: Prescriptive rule for central-bank policy rate based on inflation gap and output gap. Each gap weighted 0.5. Useful benchmark — actual Fed rates often differ but track it loosely.Tóm tắt: Quy tắc đề xuất lãi suất chính sách dựa trên gap lạm phát và gap output. Mỗi gap trọng số 0.5.

\[ R_{target} = R_{neutral} + 0.5\,(\pi - \pi^{*}) + 0.5\,(Y - Y^{*}) \]

Components

R_neutral Long-run equilibrium policy rate.
π − π* Inflation gap (actual minus target).
Y − Y* Output gap (% deviation from potential).

Practice problem

Neutral rate 2%, inflation 4%, target 2%, GDP 1% above potential. Taylor-rule target rate?

Show solution

R = 2 + 0.5(4 − 2) + 0.5(1) = 2 + 1 + 0.5

= 3.5%

5. Central-Bank Tools Concept

About: Open market ops (most-used) buy/sell securities to set rates. Discount rate = lending to banks. Reserve req. = money multiplier. QE = large-scale purchases when at zero lower bound.Tóm tắt: Open market (chính), discount rate, reserve req., QE (khi rate ≈ 0).

Open market Buy/sell government securities — most-used.
Discount rate Rate at which CB lends to commercial banks.
Reserve req. Reserve requirement ratio.
QE Large-scale asset purchases when policy rate near zero.