Macroeconomics
Complete Formula Sheet & Theory Guide
1. GDP & National Accounts
Core Concepts
GDP (Gross Domestic Product) measures the value of all final goods and services produced
within a country's borders, regardless of who produced them. GNP (Gross National Product)
measures production by a country's nationals, regardless of where they are located.
Key Formulas
Formula Explanation
GDP = C + I + G + X - Expenditure approach: Consumption + Investment + Government +
IM Exports - Imports
GNP = GDP + NI NI = Net Income from abroad (payments received from rest of world
minus payments made to rest of world)
GDP per capita = GDP / Used to compare living standards across countries. ~$54,000 =
Population developed; ~$13,000 = middle-income; ~$2,700 = low-income
Real GDP growth = (Q2 Keep PRICES fixed at base year, change only QUANTITIES
- Q1) / Q1 between years
Inflation = (P2 - P1) Keep QUANTITIES fixed at base year, change only PRICES
/ P1 between years
GDP Deflator vs CPI
Formula Explanation
P_t = Nominal GDP_t / GDP Deflator: covers all domestically produced goods. Does NOT
Real GDP_t include imports.
Inflation = (P_t - Rate of change of the price level (applies to both GDP deflator and
P_{t-1}) / P_{t-1} CPI)
CPI = Cost of basket CPI: fixed basket of goods bought by households. DOES include
(current year) / Cost imports.
of basket (base year)
x 100
, Nominal GDP = GDP The key relationship between nominal and real quantities
Deflator x Real GDP
Nominal GDP growth = Approximate decomposition of nominal growth
Inflation + Real GDP
growth
📌 Exam trick: If imported smartphone prices rise → CPI rises, GDP deflator unchanged. If
exported French goods prices rise → GDP deflator rises, CPI unchanged.
2. The Goods Market
Equilibrium Output (IS)
The goods market is in equilibrium when output (Y) equals total demand (Z). Consumption
depends on disposable income. The multiplier effect means a change in autonomous spending
leads to a larger change in output.
Exogenous Taxes (T = T̅ fixed)
Formula Explanation
Z = C + I + G Total demand (closed economy)
C = c0 + c1 * YD Consumption function: c0 = autonomous consumption, c1 = marginal
propensity to consume (0 < c1 < 1)
YD = Y - T Disposable income = output minus taxes
Y* = 1/(1-c1) * (c0 - Equilibrium output with exogenous taxes
c1*T + I + G)
Multiplier = 1/(1 - Each €1 of autonomous spending increases output by 1/(1-c1)
c1)
Endogenous Taxes (T = t0 + t1*Y)
Formula Explanation
T = t0 + t1*Y Taxes depend on income (t1 = marginal tax rate). Acts as automatic
stabilizer.
YD = Y - t0 - t1*Y = Disposable income with endogenous taxes
Y(1-t1) - t0
, Multiplier = 1 / (1 - Smaller multiplier than exogenous case: automatic stabilizers
c1(1-t1) - b1) dampen shocks
ΔY = Multiplier * ΔG Change in output from change in government spending
ΔY = Multiplier * (- Change in output from change in autonomous taxes
c1) * Δt0
📌 Endogenous taxes = smaller multiplier = less volatility. If income falls, taxes fall too,
cushioning the blow. This is why output falls LESS with endogenous taxes when autonomous
savings rises.
Paradox of Thrift
If all individuals decide to save more (c0 falls), total output falls. But since I = S + (T - G) and I,
T, G don't change, total savings in the economy CANNOT change - it stays the same. The
individual goal of saving more is collectively self-defeating.
3. Financial Markets & Money
Money Supply & High-Powered Money
Formula Explanation
H = CU + R High-powered money (monetary base) = Currency in circulation +
Bank Reserves at central bank
M = (1 / (c + θ(1-c))) Money supply: money multiplier x high-powered money
* H
Money multiplier = 1 / c = cash preference ratio, θ = reserve ratio. Higher c or θ = lower
(c + θ(1-c)) money supply
M^d = $Y * L(i) Nominal money demand: proportional to nominal income, decreasing
in interest rate i
(M^d / P) = Y * L(i) Real money demand: proportional to real output, decreasing in
interest rate i
📌 Central bank BUYS bonds → reserves increase → money supply rises. Central bank SELLS
bonds → reserves decrease → money supply falls.
Central Bank Balance Sheet
, Formula Explanation
Assets (closed): Bonds In a closed economy, the only asset on the central bank's balance
only sheet is bonds
Assets (open): Bonds + In an open economy, foreign currency/gold are also assets
Gold + Foreign
Reserves
Liabilities: Reserves Central bank money (H) = liabilities of the central bank
+ Currency
4. IS-LM Model
The IS Curve (Goods Market)
The IS curve shows all combinations of interest rate (r) and output (Y) where the goods market
is in equilibrium. It is downward sloping because higher interest rates reduce investment,
reducing demand and output.
Formula Explanation
I = b0 + b1*Y - b2*(r Investment function: b1 = sensitivity to output, b2 = sensitivity to
+ x) interest rate, x = default premium
r = real policy rate The real interest rate firms face when deciding to invest
Flatter IS = more Economy A (more sensitive) has a flatter IS curve than economy B
interest-sensitive (less sensitive)
IS shifts RIGHT if: G rises, T falls, c0 rises, I rises, or expected future r falls
IS shifts LEFT if: G falls, T rises, c0 falls (paradox of thrift), or expected future r rises
The LM Curve (Money Market)
The LM curve shows all combinations of interest rate and output where money supply equals
money demand. Its slope depends on the central bank's operating target.
Formula Explanation
M/P = Y * L(i) Money market equilibrium: real money supply = real money demand
LM is horizontal If central bank TARGETS interest rate (adjusts money supply as
needed) - most common today
LM is upward sloping If central bank TARGETS money supply (fixed M)
r = i - π^e Fisher equation: real rate = nominal rate - expected inflation
Complete Formula Sheet & Theory Guide
1. GDP & National Accounts
Core Concepts
GDP (Gross Domestic Product) measures the value of all final goods and services produced
within a country's borders, regardless of who produced them. GNP (Gross National Product)
measures production by a country's nationals, regardless of where they are located.
Key Formulas
Formula Explanation
GDP = C + I + G + X - Expenditure approach: Consumption + Investment + Government +
IM Exports - Imports
GNP = GDP + NI NI = Net Income from abroad (payments received from rest of world
minus payments made to rest of world)
GDP per capita = GDP / Used to compare living standards across countries. ~$54,000 =
Population developed; ~$13,000 = middle-income; ~$2,700 = low-income
Real GDP growth = (Q2 Keep PRICES fixed at base year, change only QUANTITIES
- Q1) / Q1 between years
Inflation = (P2 - P1) Keep QUANTITIES fixed at base year, change only PRICES
/ P1 between years
GDP Deflator vs CPI
Formula Explanation
P_t = Nominal GDP_t / GDP Deflator: covers all domestically produced goods. Does NOT
Real GDP_t include imports.
Inflation = (P_t - Rate of change of the price level (applies to both GDP deflator and
P_{t-1}) / P_{t-1} CPI)
CPI = Cost of basket CPI: fixed basket of goods bought by households. DOES include
(current year) / Cost imports.
of basket (base year)
x 100
, Nominal GDP = GDP The key relationship between nominal and real quantities
Deflator x Real GDP
Nominal GDP growth = Approximate decomposition of nominal growth
Inflation + Real GDP
growth
📌 Exam trick: If imported smartphone prices rise → CPI rises, GDP deflator unchanged. If
exported French goods prices rise → GDP deflator rises, CPI unchanged.
2. The Goods Market
Equilibrium Output (IS)
The goods market is in equilibrium when output (Y) equals total demand (Z). Consumption
depends on disposable income. The multiplier effect means a change in autonomous spending
leads to a larger change in output.
Exogenous Taxes (T = T̅ fixed)
Formula Explanation
Z = C + I + G Total demand (closed economy)
C = c0 + c1 * YD Consumption function: c0 = autonomous consumption, c1 = marginal
propensity to consume (0 < c1 < 1)
YD = Y - T Disposable income = output minus taxes
Y* = 1/(1-c1) * (c0 - Equilibrium output with exogenous taxes
c1*T + I + G)
Multiplier = 1/(1 - Each €1 of autonomous spending increases output by 1/(1-c1)
c1)
Endogenous Taxes (T = t0 + t1*Y)
Formula Explanation
T = t0 + t1*Y Taxes depend on income (t1 = marginal tax rate). Acts as automatic
stabilizer.
YD = Y - t0 - t1*Y = Disposable income with endogenous taxes
Y(1-t1) - t0
, Multiplier = 1 / (1 - Smaller multiplier than exogenous case: automatic stabilizers
c1(1-t1) - b1) dampen shocks
ΔY = Multiplier * ΔG Change in output from change in government spending
ΔY = Multiplier * (- Change in output from change in autonomous taxes
c1) * Δt0
📌 Endogenous taxes = smaller multiplier = less volatility. If income falls, taxes fall too,
cushioning the blow. This is why output falls LESS with endogenous taxes when autonomous
savings rises.
Paradox of Thrift
If all individuals decide to save more (c0 falls), total output falls. But since I = S + (T - G) and I,
T, G don't change, total savings in the economy CANNOT change - it stays the same. The
individual goal of saving more is collectively self-defeating.
3. Financial Markets & Money
Money Supply & High-Powered Money
Formula Explanation
H = CU + R High-powered money (monetary base) = Currency in circulation +
Bank Reserves at central bank
M = (1 / (c + θ(1-c))) Money supply: money multiplier x high-powered money
* H
Money multiplier = 1 / c = cash preference ratio, θ = reserve ratio. Higher c or θ = lower
(c + θ(1-c)) money supply
M^d = $Y * L(i) Nominal money demand: proportional to nominal income, decreasing
in interest rate i
(M^d / P) = Y * L(i) Real money demand: proportional to real output, decreasing in
interest rate i
📌 Central bank BUYS bonds → reserves increase → money supply rises. Central bank SELLS
bonds → reserves decrease → money supply falls.
Central Bank Balance Sheet
, Formula Explanation
Assets (closed): Bonds In a closed economy, the only asset on the central bank's balance
only sheet is bonds
Assets (open): Bonds + In an open economy, foreign currency/gold are also assets
Gold + Foreign
Reserves
Liabilities: Reserves Central bank money (H) = liabilities of the central bank
+ Currency
4. IS-LM Model
The IS Curve (Goods Market)
The IS curve shows all combinations of interest rate (r) and output (Y) where the goods market
is in equilibrium. It is downward sloping because higher interest rates reduce investment,
reducing demand and output.
Formula Explanation
I = b0 + b1*Y - b2*(r Investment function: b1 = sensitivity to output, b2 = sensitivity to
+ x) interest rate, x = default premium
r = real policy rate The real interest rate firms face when deciding to invest
Flatter IS = more Economy A (more sensitive) has a flatter IS curve than economy B
interest-sensitive (less sensitive)
IS shifts RIGHT if: G rises, T falls, c0 rises, I rises, or expected future r falls
IS shifts LEFT if: G falls, T rises, c0 falls (paradox of thrift), or expected future r rises
The LM Curve (Money Market)
The LM curve shows all combinations of interest rate and output where money supply equals
money demand. Its slope depends on the central bank's operating target.
Formula Explanation
M/P = Y * L(i) Money market equilibrium: real money supply = real money demand
LM is horizontal If central bank TARGETS interest rate (adjusts money supply as
needed) - most common today
LM is upward sloping If central bank TARGETS money supply (fixed M)
r = i - π^e Fisher equation: real rate = nominal rate - expected inflation
