Macroeconomics: Key Formulas and Symbols

Essential Formulas in Macroeconomics

Symbols Used in Formulas

• A represents technological advances or progress when used in the production function.
• A signifies capital consumption allowances, depreciation of fixed capital, or replacement investment in the national accounts system.
• A denotes autonomous spending.
• AD stands for aggregate demand.
• AE represents aggregate expenditures.
• AEP signifies aggregate planned expenditures.
• AS stands for aggregate supply.
• apc is the average propensity to consume.
• aps is the average propensity to save.
• b represents the interest sensitivity of investment demand.
• B denotes bonds.
• BD signifies the demand for bonds.
• BS signifies the supply of bonds.
• BB indicates a balanced budget.
• BD represents a budget deficit.
• BS signifies a budget surplus.
• C represents consumption spending or consumption demand.
• C represents autonomous consumption spending.
• CPI stands for the consumer price index.
• currency ratio (currency-to-deposit ratio) = cr
• CU denotes currency.
• D represents deposits.
• DI stands for disposable income.
• def signifies the GDP deflator.
• Δ represents the change of a variable.
• e signifies the nominal exchange rate.
• Ex denotes exports.
• F signifies loanable funds.
• FD signifies the demand for loanable funds.
• FS signifies the supply of loanable funds.
• G represents government purchases of goods and services.
• GDP stands for gross domestic product.
• GNP stands for gross national product.
• H signifies human capital in the production function.
• H denotes the monetary base or high-powered money in the money market.
• h represents the interest sensitivity of money demand.
• i represents the nominal interest rate.
• I signifies investment spending or investment demand.
• I represents autonomous investment spending.
• Igross signifies gross investment.
• Iinv represents inventory investment.
• Inet signify net investment.
• Ip represents planned investment spending.
• Iun represents unintended inventory investment.
• Im represents imports.
• Im signifies autonomous imports.
• K represents physical capital.
• k represents the income sensitivity of money demand.
• L represents labour.
• M represents money or money stock.
• MD represents nominal demand for money.
• M/P represents real money balances or the purchasing power of money.
• (M/P)d represents real demand for money.
• MS represents nominal money supply, equivalent to money supply aggregate M1.
• MS/P represents real money supply.
• mpc represents the marginal propensity to consume.
• mpi represents the marginal propensity to invest.
• mpm represents the marginal propensity to import.
• mps represents the marginal propensity to save.
• mult represents the multiplier.
• multA represents the autonomous spending multiplier.
• multTx represents the lump-sum taxes multiplier.
• multTr represents the transfer payments multiplier.
• multBB represents the balanced budget multiplier.
• multD represents the deposit multiplier.
• multL represents the loan multiplier.
• mm represents the money multiplier.
• N represents the total population.
• N represents natural resources in the production function.
• NI represents national income.
• NDP represents net domestic product.
• NNP represents net national product.
• NX represents net exports.
• P represents the general price level or the domestic price level in an open economy.
• PI represents personal income.
• PE represents the equilibrium price level.
• PF represents the foreign price level.
• Pt represents the price level in the current year.
• Pt-1 represents the price level in the previous year.
• π is the rate of inflation.
• Q represents quantity.
• r represents the real interest rate.
• rr represents the reserve ratio.
• R represents reserves, or actual reserves.
• Rreq represents required reserves.
• Rexcess represents excess reserves.
• S represents private sector saving.
• SG represents government sector saving.
• SF represents foreign sector saving.
• SNAT represents national saving.
• SAGG represents aggregate saving.
• T represents net taxes.
• t represents the tax rate.
• Tr represents transfer payments.
• Tx represents taxes.
• T represents lump-sum taxes.
• U represents the number of unemployed.
• u represents the rate of unemployment.
• u* represents the natural rate of unemployment.
• V represents the velocity of money.
• V represents constant velocity of money.
• W represents the nominal wage.
• W/P represents the real wage.
• Y represents aggregate output, aggregate income, or actual real GDP.
• YD represents disposable income.
• YE represents equilibrium output or equilibrium real GDP.
• Y* represents the full-employment level of output, potential output, or the natural level of output, equivalent to real GDP.
• YF represents foreign output or foreign income.
• Yt represents real GDP of the current year.
• Yt-1 represents real GDP of the previous year.
• YN represents nominal GDP.
• YR represents real GDP.

Important Formulas

• Actual Budget Deficit (BDactual) calculation includes actual government purchases (G), transfer payments (Tr), actual tax revenues (Tx), and tax rate (t) times income (Y): BDactual = (G + Tr) - (Tx + t × Y).
• Actual Bank's Reserves consist of required reserves and excess reserves, calculated as deposits minus loans.
• Aggregate Demand (AD) is shown as consumption (C) + investment (I) + government spending (G) + net exports (NX): AD = C + I + G + NX.
• Aggregate Expenditure formula in a simple private model shows Consumption + Investment: AE = C + I
• Aggregate Expenditure Formula in mixed closed economy: AE = C + I + G
• Aggregate Expenditure accounts for all spending in an open economy: AE = C + I + G + NX.
• Autonomous Spending Multiplier (multĀ) calculates the change in output (ΔY) divided by the change in autonomous spending (ΔĀ).
• Autonomous Spending Multiplier in a closed economy with lump-sum tax system: multA = 1 / (1 - mpc)
• The lump-sum tax system and induced investment spending Autonomous spending multiplier calculates: multA = 1 / (1 - mpc + mpi)
• The proportional income tax system and autonomous investment spending Autonomous spending multiplier calculates: multA = 1 / (1-mpc(1-t))
• The proportional income tax system and induced investment spending Autonomous spending multiplier calculates: multA = 1 / (1 - mpc(1 - t) - mpi)
• The lump-sum tax system and autonomous investment spending in the open economy Autonomous spending multiplier calculates: multA = 1 / (1 - mpc + mpm)
• The proportional income tax system and autonomous investment spending Autonomous spending multiplier calculates: multA = 1 / (1 - mpc(1 - t) + mpm)
• in the open economy with the proportional income tax system and induced investment spending Autonomous spending multiplier calculates: multA = 1 / (1 - mpc(1 - t) - mpi + mpm)
• Average Propensity to Consume definition and calculation formula: apc = C / YD
• Average Propensity to Save definition and calculation formula: aps = Save / YD
• Average Propensity to Consume and Average Propensity to Save Sum Formula: apc + aps = 1
• Balanced Budget Multiplier in the closed economy with the lump-sum tax system and autonomous investment spending: multBB = 1
• Balanced Budget Multiplier in the closed economy with the lump-sum tax system and induced investment spending: multBB ≠ 1
• Balanced Budget Multiplier in the closed economy with the mixed (lump-sum + proportional) tax system and autonomous investment spending: multBB ≠1
• Balanced Budget Multiplier in the open economy with the lump-sum tax system and autonomous investment spending: multBB ≠1
• Balanced Budget Multiplier in the open economy with the mixed (lump-sum + proportional) tax system and autonomous investment spending: multBB ≠ 1
• Balanced Budget Multiplier in the open economy with the mixed (lump-sum + proportional) tax system and induced investment spending: multBB ≠1
• Bank's Balance Sheet Identity Formula is: Assets = Liabilities
• Bank's Reserve Ratio Formula is: rr = R / D with (Bank reserves / Total deposits)
• Government budget deficit (BD) calculation with excess expenditures over collections: BD = G - T > 0 or BD = (G + Tr) – (Tx + t × Y) > 0
• Note: G - government spending,Tr - transfer payments,Tx - Taxes/tax revenues,t - tax rate, and Y - income
• Government budget surplus (BS) is indicated by excess tax collections over government expenditures: BS = T - G > 0
• Note: BS = -BD or BS = (Tx+txY) – (G + Tr) > 0
• Capital Formation Equation where Domestic investment spending = Aggregate saving: I = SAGG
• Domestic investment spending equals private sector + public sector + foreign sector saving. I = S + SG + SF = S + (T-G) + (Im – Ex)
• Consumer Price Index (CPI) calculation using base year quantities and current year prices.
• Consumption spending includes autonomous consumption spending and induced consumption spending: C = C + mpc × YD or C = C + mpc × (Y - T)
• Currency Ratio Calculation involves Currency outside banks divided by Deposits: cr = CU / D
• Cyclical Budget Deficit Formula includes actual budget deficit, structural budget deficit: BDcyclical = t × (Y* – Y)
• Deposit Multiplier is obtained by relation between Deposits, Reserves and Reserve ratio: multD = 1 / rr
• Disposable Income equation from national income minus net taxes: YD = Y - T = Y – (Tx – Tr) or YD = Y - Tx − t ×Y+Tr
• Definition: Disposable income = consumption spending + saving
• Disposable Personal Income (DI) Calculation In National Accounts System can be calculated using Formula: DI = PI – personal income taxes
• Equation of Exchange Definition and Formula: M × V = P × Y.
• Excess Reserves Formula: Rexcess = D × (1 – rr)
• Exchange Rate Formula: e = amount of foreign currency / unit of national currency
• Expenditures-Income Identity = Total expenditures = total income: C + I + G + NX = C + S+T
• Foreign Sector Saving is derived by subtracting exports from imports: SF = Im - Ex
• Government Sector Saving calculation includes Taxes/tax revenues, government spending and transfer payments: SG = (Tx+t×Y)−(G+Tr)
• The formula to calc GDP (expenditure approach): GDP = C + I + G + NX
• GDP (income approach) includes wages, interest, rent, profit etc: GDP = wages + interest + rent + profit
• Gross National Product: GNP = GDP + net factor income from abroad
• Growth Rate of Real Output Formula includes Current year real GDP: g = (Yt - Yt-1)/Yt-1
• Gross investment spending formula: Igross = Inet + A
• The consumption of personal saving and disposable income defines Household (or personal) saving: Spersonal = YD-C=Y-T-C'
• The definition of total Imports including autonomous imports and induced imports is defined as: Im = Im + mpm×Y
• Income Formula in a simple model using Consumption and Saving is: Y=C+S
• Income Formula in model with government and foreign sectors includes Consumption, saving and net taxes Y=C+S+T
• Calculate inflation between two years: (CPIyear Y - CPIyearX)/CPIyearX ×100%
• The simplified calculation for inflation rate is: πt = (Pt - Pt-1)/Pt-1 ×100%
• Inflationary gap : Y > Y*
• injections-leakages identity: investment + government spending + exports = private saving + net taxes + imports I + G + Ex = S + T + Im
• To calculate inventory investment (Inventory investment = value of output – value of sales), I = I(r)
• Loan Multiplier: Loan multiplier = ΔM/AD = 1 / rr -1.
• Marginal Propensity to Consume formula is calculated as: mpc = ΔC/ΔYD
• Marginal Propensity to Imports formula is calculated as: mpm = ΔIm/ΔY
• Marginal Propensity to Invest formula is calculated as: mpi = ΔI/ΔY
• Marginal Propensity to Save formula is calculated as: mps = AS/ΔYD
• The addition of Marginal propensity to consume and the marginal propensity to save is: mpc + mps = 1
• Monetary base formula: H = CU + R
• Money Demand Formula: (M / P)d = k×Y-h×i
• Money multiplier formula: mm = M/Η = (1+ cr)/(cr + rr)
• National Accounts Identity Formula: Y = C + I + G + NX
• To calculate nominal gdp formula: Y* = Σ P* q
• To calculate the nominal intrest rate one can use this formula: i = r + π
• Output Per Capita: Y/N
• Calculating personal Savings with Disposable Income we can define: Spersonal = SH/H = YD - C = Y - T-C
• Production Function: Y = AF (L, K, Η, Ν)
• flexible & rigid version M×V=Px Y*
• Rate of Unemployment = (Number of unemployed/Number of labor force) ×100% = (U/LF) ×100% = (U/E+U) ×100%
• To caluclate structural buldget deficic: BDstructural = G +Tr-Tx-t×Y*

Summary of Key Formulas

• The important macroeconomic formulas have been detailed above. These formulas can be applied in variety of situations to analyze different economies. There are other formulas in the study notes that can further assist in solving for the variables desired.