Formula sheet

$AE$

aggregate (planned) expenditure

$C$

consumption

$I$

investment

$G$

government purchases

$NX$

net exports

you explain fluctuations. In the short run, spending decides output (Lectures 6, 8 to 13).

$A$

technology (productivity)

$K$

capital

$L$

labour

$a, b$

output elasticities of K and L

you explain growth. In the long run, inputs and technology decide output (Lectures 3 to 5). Taking logs turns the product into a sum.

a question asks why the three approaches agree. Every lira spent on a final good is a lira of someone's income and a lira of recorded output.

$C$

consumption

$I$

investment, including inventories

$G$

government purchases, excluding transfers

$NX$

X - M, net exports

you add up GDP from spending components, or check what counts where.

$NFP$

net factor payments from abroad: income residents earn abroad minus income foreigners earn here

a question separates output produced in the country (GDP) from income earned by the country's residents (GNP).

$Y$

GDP

$TR$

transfers received from the government

$INT$

interest on government debt

$T$

taxes

you need the income households and firms actually have to spend or save.

$P_t, Q_t$

current prices and quantities

$P_{base}$

base-year prices

you need the price level of everything produced domestically. Current basket (Paasche).

$Q_{base}$

the fixed base-year consumer basket

you need the cost of living for consumers. Fixed basket (Laspeyres).

$E$

employed

$U$

unemployed and looking

$E + U$

labour force

a question gives counts of people. The unemployment denominator is the labour force, not the population.

$\Delta u$

change in the unemployment rate, in percentage points

you translate a change in unemployment into GDP growth, or the reverse.

$z$

common scaling factor, z > 1

a question gives a production function and asks what kind of returns it has. Substitute zK and zL and factor out z.

$W/P$

real wage

$R/P$

real rental price of capital

$MPL$

marginal product of labour

$MPK$

marginal product of capital

you need a wage or rental price from a production function.

$A$

total factor productivity

$\alpha$

capital's share of income

$1-\alpha$

labour's share of income

a question gives Y, K or L and asks for a factor price or an income share.

$Y - T - C$

private saving

$T - G$

public saving (budget surplus)

you need the supply of loanable funds. Compute C first, then subtract.

$r$

real interest rate, the variable that adjusts

you are asked for the equilibrium interest rate. Solve the saving side for a number, then solve I(r) for r.

$S$

national saving

$I$

domestic investment

$S - I$

net capital outflow

$NX$

trade balance

any question links saving, investment and the trade balance. If S is less than I, the country borrows from abroad and runs a trade (current account) deficit.

$\varepsilon$

real exchange rate

$e$

nominal exchange rate, foreign currency per unit of domestic currency

$P$

domestic price level

$P^*$

foreign price level

you compare the price of domestic goods with foreign goods in a common currency.

$\pi$

domestic inflation

$\pi^*$

foreign inflation

a question asks what happens to the lira when Turkish inflation exceeds foreign inflation.

$A$

productivity (technology and management)

$K$

capital

$N$

labour

you work in the ABC chapters. It is the same function as Mankiw's F(K, L), with productivity written in front.

$w$

real wage W/P

$MPN$

marginal product of labour

you derive the labour demand curve. Because MPN falls as N rises, the demand curve slopes down.

$\bar{N}$

equilibrium (full-employment) level of employment

$\bar{Y}$

full-employment or potential output

a question asks how a shock changes potential output. It moves if A, K or the labour market equilibrium changes.

$LF$

labour force = E + U

$E$

employed

$U$

unemployed

a question gives numbers of people and asks for any of the three rates.

$\bar{u}$

natural rate of unemployment, the rate at full employment

$u$

actual rate

a question asks how far the economy is from full employment in unemployment terms.

$C^d$

desired consumption

$G$

government purchases

you need the effect of fiscal policy or income changes on national saving.

$r$

real interest rate

$d$

depreciation rate

$p_K$

real price of a unit of capital

you need the cost side of the investment decision. r p_K is the interest cost (or forgone interest); d p_K is the wear and tear.

$MPK^f$

expected future marginal product of capital

you find how much capital the firm wants. If MPK^f is above uc, add capital; if below, reduce it.

$K^*$

desired capital stock

$K_t$

current capital stock

$d$

depreciation rate

a question gives the desired and current capital stock and asks for this period's investment, assuming firms reach K* in one period.

$V$

stock-market value of the firm

$p_K K$

replacement cost of its capital

a question links the stock market to investment. q above 1 means the market values capital above its cost: invest more. q below 1: do not invest.

$S^d$

desired national saving

$I^d$

desired investment

you find the equilibrium real interest rate in the ABC model.

$Y_t$

output in period t

you compute the growth rate between two periods.

you need a quick doubling time. 7% growth doubles income in about 10 years; 2% takes about 35. The rule of 69 or 72 are the same idea with different rounding.

$\Delta A/A$

productivity growth

$a_K$

elasticity of output with respect to capital, about 0.3

$a_N$

elasticity of output with respect to labour, about 0.7

a question gives output, capital and labour growth and asks for productivity growth. Productivity is the residual: what capital and labour cannot explain.

$y$

output per worker, Y/L

$k$

capital per worker, K/L

$\alpha$

capital's share of income, about 1/3

you need output per worker from capital per worker. Every Solow exam problem starts here.

$\Delta k$

change in capital per worker per period

$s$

saving rate, share of income saved

$\delta$

depreciation rate

you want to know whether capital per worker is rising or falling at a given k.

$k^*$

steady-state capital per worker

$y^*$

steady-state output per worker

a question gives s, delta and alpha and asks for the long-run level. With alpha = 1/2 it simplifies to the square root of k* equal to s/delta.

$c$

consumption per worker in the steady state

$(n + d)k$

steady-state gross investment per worker

you compare steady states by consumption. This is the slides' version; set n = 0 to get Mankiw's f(k) - delta k.

$MPK$

marginal product of capital

$k^*_{gold}$

capital stock that maximises steady-state consumption

$s_{gold}$

saving rate that gets there (Cobb-Douglas)

a question asks whether an economy saves too much or too little. Set n = 0 until population growth is introduced.

$n$

growth rate of the labour force

$(\delta + n)k$

break-even investment

the problem mentions population or labour force growth. Replace delta with delta + n everywhere.

$A$

constant marginal product of capital

a question asks why growth can continue forever from capital accumulation. With no diminishing returns, saving more raises the growth rate permanently.

$M$

money supply

$V$

velocity of money

$P$

price level

$Y$

real output

you need a simple AD curve. With M and V fixed, P and Y are inversely related: a hyperbola.

$FX$

foreign-currency deposits

a question asks which aggregate includes which assets. Each one adds less liquid assets to the one before.

$(M/P)^d$

demand for real money balances

$i$

nominal interest rate, the opportunity cost of holding money (negative effect)

$Y$

real income (positive effect)

$E\pi$

expected inflation

you need to say how money demand responds. L is used because money is the most liquid asset.

$M$

money

$V$

velocity

$P$

GDP deflator

$Y$

real GDP

$P \times Y$

nominal GDP

any quantity-theory question. As written it is an identity: it defines V.

$k$

how much money people hold per unit of income

you need money demand under the quantity theory. When k is large, money changes hands rarely and V is small.

$\pi$

inflation rate

$\%\Delta V$

0 by assumption

a question gives money growth and output growth and asks for long-run inflation.

$i$

nominal interest rate

$r$

real interest rate

$\pi$

inflation

you convert between nominal and real interest rates.

$a$

autonomous consumption, spending at zero income

$b$

MPC, marginal propensity to consume, 0 < b < 1

you need consumption at a given income, or the slope of the consumption line.

$MPS$

marginal propensity to save

a question gives the MPC and needs the MPS, or asks for saving at a given income.

$Y$

aggregate output

$AE$

planned aggregate expenditure

you find equilibrium output. It is a condition, not an identity: it holds only in equilibrium.

$MPS$

1 - MPC

a question changes an exogenous spending item (I, G, autonomous C) and asks for the change in output. The steeper the AE line (the higher the MPC), the bigger the multiplier.

$S + T$

leakages from the spending stream

$I + G$

injections

you check equilibrium with government, or solve without writing out C.

G changes and taxes are fixed.

net taxes change and G is fixed. It is negative and smaller in size than the spending multiplier.

G and T change by the same amount. Output changes by exactly the change in G.

$b$

MPC

$t$

marginal tax rate

$T_0$

autonomous (lump-sum) taxes

taxes are T0 + tY. The multiplier becomes 1/(1 - b + bt), smaller than 1/(1 - b): taxes absorb part of every rise in income. Lecture 10 works through this model in detail.

$MPM$

marginal propensity to import

the economy trades. Part of each extra lira of spending goes on foreign goods, so the multiplier is smaller than in a closed economy.

$a$

autonomous consumption

$b$

MPC

a question asks how the share of income consumed changes with income. With a > 0, APC falls as Y rises.

$\alpha$

marginal propensity to consume out of wealth

$\beta$

marginal propensity to consume out of income

a question gives wealth, income and years and asks for consumption, or asks why APC can fall across households but stay constant over time.

$Y^P$

permanent income, the average income people expect to persist

$Y^T$

transitory income, temporary deviations from it

$\alpha$

fraction of permanent income consumed

a question separates a temporary income change (a bonus, a one-off tax rebate) from a permanent one (a promotion).

$I_n$

net investment function, increasing in the profit rate

$P_K/P$

real price of capital

$\delta K$

replacement investment

a question asks what shifts investment. Anything that raises MPK or lowers the real cost of capital raises investment.

a quick reminder from Lecture 8. The models below generalise both.

$C_0$

autonomous consumption

$b$

MPC, 0 < b < 1

$T_0$

autonomous (lump-sum) taxes

$t$

marginal tax rate, 0 < t < 1

$I_0, G_0$

exogenous investment and government spending

taxes rise with income. This is the lecture's Example 1 setup.

every three-sector numerical question. Plug in, then differentiate for multipliers.

G changes. Positive because 0 < b < 1.

lump-sum taxes change. Negative, and smaller in size than the G multiplier.

the marginal tax rate changes. Because a parameter inside the multiplier changes, this only approximates the effect of a finite change.

G and autonomous taxes rise together but taxes also depend on income. The effect is positive but smaller than 1.

$X_0$

exports

$Z$

imports

$Z_0$

autonomous imports

$z$

marginal propensity to import (MPM)

the problem has trade. The slides write imports as M or Z; the algebra is the same.

every four-sector numerical question.