Macro Formulas

GDP Gap

Y - Y* , actual GDP minus potential GDP

Simple GDP formula

GDP = C + I +G + (X-M)

Net Exports NX

X-M, exports - imports

GDP in terms of income

GDP = GNI – Net income from abroad

The Implicit GDP Deflator

Implicit deflator = (𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝐺𝐷𝑃 / 𝑅𝑒𝑎𝑙 𝐺𝐷𝑃) x 100

PPP exchange rate

PPP rate = Price in local currency/ Price in USD

Inflation rate

Inflation rate = (CPI𝑡 − CPI𝑡−1) / CPI𝑡−1 × 100 → (percentage change in CPI)

Deflating a nominal value (Real quantity)

Real quantity = Nominal quantity/CPI for that period × 100

CPI

CPI = nominal income/ real income

Real interest rate

Real interest rate   =  Nominal interest rate − Inflation rate

Labour Force

Labour Force = Employed + Unemployed

Labour Force Participation Rate (LFPR)

𝐿𝐹𝑃𝑅 = 𝐿𝐹 / 𝑊𝐴𝑃 × 100%, where LF = labour force, WAP = working age population

Employment rate (E)

𝐸 = 𝑁𝑜 𝑜𝑓 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑑 / 𝑊𝐴𝑃 × 100%, where WAP = working age population

Unemployment rate

𝑈 = 𝑁𝑜 𝑜𝑓 𝑢𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑑 / 𝐿𝐹 × 100%

Exchange Rate

𝐸 = FC / DC, where FC = foreign currency, and DC = domestic currency (DC)

Price elasticity

𝑃𝐸𝐷 = %∆𝑄 / %∆P

Real Exchange Rate

Real exchange rate (q) = 𝐸 × 𝑃domestic/ 𝑃foreign, where E = nominal exchange rate

Implied PPP exchange rate

𝐸^𝑃𝑃𝑃 = 𝑃𝑓𝑜𝑟𝑒𝑖𝑔𝑛 / 𝑃𝑑𝑜𝑚𝑒𝑠𝑡𝑖c

Misvaluation of domestic currency exchange rate

% Misvaluation = E − 𝐸^𝑃𝑃𝑃 / 𝐸^𝑃𝑃𝑃 × 100

Relative PPP: exchange rate changes?

%ΔE ≈ π domestic​ − π foreign​

Aggerate spending/expenditure (AE)

𝐴𝐸 = 𝐶 + 𝐼 + 𝐺 + (𝑋 − 𝑀)

Consumption Function (no taxes)

𝐶 = 𝑎 + 𝑏𝑌, where 𝐶 = Desired consumption spending, 𝑎 = autonomous consumption, 𝑌= Disposable income

Average propensity to consume (APC)

𝐴𝑃𝐶 = 𝐶 /𝑌d

Marginal propensity to consume (MPC)

𝑀𝑃𝐶 = ∆𝐶 /∆Yd

Average propensity to save (APS)

𝐴𝑃𝑆 = 𝑆 /𝑌d, where s = savings, yd = disposable income

Marginal propensity to save (MPS)

𝑀𝑃𝑆 = ∆𝑆 /∆𝑌𝑑

Relationships between APS and APC

𝐴𝑃𝐶 + 𝐴𝑃𝑆 = 1

Relationship between MPC and MPS

𝑀𝑃𝐶 + 𝑀𝑃𝑆 = 1

The aggregate spending/expenditure function (expanded)

AE=(a+I)+bY, where (a+I) = autonomous spending, b = slope = ∆𝐴𝐸 /∆Y

Slope of AE function

ΔAE/ΔY

Savings Function

S=−a+(1−b)Y

The multiplier (closed economy)

𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 = ∆𝑌 /∆𝐴 = 1/ (1 − b), where b = marginal propensity to consume

Disposable income, Yd

𝑌𝑑 = 𝑌 + 𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠 − 𝑇𝑎𝑥 payments, where Y = total income

Net Taxes

𝑁𝑒𝑡 𝑡𝑎𝑥𝑒𝑠 = 𝑇 = 𝑇𝑎𝑥 𝑟𝑒𝑣𝑒𝑛𝑢𝑒𝑠 − 𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑝𝑎𝑦𝑚𝑒𝑛𝑡s

Government budget balance (fiscal balance)

𝐵𝑢𝑑𝑔𝑒𝑡 𝑏𝑎𝑙𝑎𝑛𝑐𝑒 = 𝑇 – G, where T = tax revenue, and G = government spending

Net Exports Function

NX = 𝑋 − 𝑚𝑌, where X = exports, m = marginal propensity to import, Y = income

Consumption function with net taxes

C = 𝑎 + 𝑏 (𝑌 − 𝑇)

Expanded aggregate expenditure formula (open economy)

𝐴𝐸 = 𝐴 + (𝑏 − 𝑚)Y, where A = 𝑎 + 𝐼 + 𝐺 + 𝑋 − 𝑏T

AE function closed economy (basic):

AE = C+I+G

The multiplier (open economy)

𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 = ∆𝑌 /∆𝐴 = 1 /(1 − 𝑏 + 𝑚), where m is the marginal propensity to import

Government spending multiplier (open economy)

change in y/change in G = 1 / (1 - b + m)

Tax multiplier

-b / (1 - b + m)

injection-leakage equilibrium

I + G + X = S + T + M

Balanced Budget Multiplier (Open Economy)

Δ𝑌/ Δ𝐺 < 1

Balanced Budget Multiplier (Closed Economy)

Δ𝑌 /Δ𝐺 = 1

Investment function

𝐼 = 𝐼0 − 𝑑r, where I = total investment, I0​ = autonomous investment, r = real interest rate, d = sensitivity of investment to the interest rate

IS Curve Equation

𝑟 = (𝐴/ 𝑑) − (1 − 𝑏 + 𝑚) /𝑑 x Y

Slope of the IS Curve

𝑆𝑙𝑜𝑝𝑒 = ∆𝑟 / ∆𝑌 = − (1 − 𝑏 + 𝑚)/ 𝑑

High-powered money

H=C+R, where H = high-powered money / monetary base, C = cash (currency) held by public, R = bank reserves

Reserve ratio equation

R=xD, where x= reserve ratio , D= deposits

Cash–deposit ratio

C=bD, where b = cash-deposit ratio

Deposit multiplier

∆𝐷 /∆𝐻 = 1 (𝑏+𝑥), b = cash-deposit ratio

Money supply identity (2 ways)

M=C+D

M= m x R, where m = money multiplier

Money multiplier

∆𝑀/ ∆𝐻 = 𝑏+1 / (𝑏+𝑥), where x = the desired reserve ratio of banks

Simplified money multiplier

𝑀/ ∆𝐻 = 1 / x (when b = 0)

Present value formula

𝑃𝑉 = FV / (1 + 𝑖) 𝑡

Interest rate from bond prices

𝑖 = FV−𝑃V /𝑃V

Real money demand function

𝐿 = 𝐿_ + 𝑘𝑌 − ℎi, where 𝐿_ = autonomous (exogenous) money demand, k = sensitivity of money demand to real GDP (Y), h = sensitivity of money demand to nominal interest rate (i)

Money market equilibrium

𝑀𝑆/ 𝑃 = L, real money supply = real money demand

LM Curve Equation

𝑖 = − 1 /ℎ x 𝑀𝑆 /𝑃 + 𝑘/ ℎ x 𝑌

LM slope

Δi/ΔY​=k/h

Aggregate demand equation

AD = C + I + G + (X − M)