Learn: ECON 309 Middy 1

GDP Equation

Y = C + I + G + NX

Net Exports

Exports - Imports

Net Primary Income

GNP - GDP

Value Added

Value of output - value of intermediate goods

GDP

Value of final goods =

Nominal GDPₜ

Σ (Pᵢₜ × Qᵢₜ). current-year prices × current-year quantities, summed over goods i

Real GDPₜ

Σ (Pᵢ,base × Qᵢₜ). base-year prices × current-year quantities

GDP Deflator

100 × (Nominal GDP ÷ Real GDP)

Inflation rate

(Deflatorₜ − Deflatorₜ₋₁) ÷ Deflatorₜ₋₁ × 100. Also works with CPI in place of the deflator

%Δ(X × Y)

%ΔX + %ΔY. "Trick #1" for percentage changes

%Δ(X ÷ Y)

%ΔX − %ΔY". Trick #2" — e.g. inflation ≈ %ΔNGDP − %ΔRGDP

CPI (month t)

100 × (Cost of basket in month t ÷ Cost of basket in base period)

Labor force

L = E + U. Employed + Unemployed

Unemployment rate

(U ÷ L) × 100%

Labor-force participation rate

(L ÷ POP) × 100%

Inventory investment

ending inventories − beginning inventories. can be negative

the production function

Y = F(K, L)

fixed factor supplies determine fixed output

K = K̄, L = L̄ → Ȳ = F(K̄, L̄)

Returns to scale

scale inputs by z: K₂ = zK₁, L₂ = zL₁. Compare Y₂ = F(K₂,L₂) to zY. constant: Y₂ = zY₁; increasing: Y₂ > zY₁; decreasing: Y₂ < zY₁

Marginal Product of Labor

F(K, L+1) − F(K, L)

Real Wage

W/P; Real rental rate = R/P

Profit-maximizing labor

MPL = W/P. firm's labor demand curve

Profit-maximizing capital

MPK = R/P. firm's capital demand curve

Euler's theorem

Ȳ = MPL·L̄ + MPK·K̄. national income splits exactly into labor income + capital income if constant returns to scale

Cobb-Douglas

Y = A Kᵅ L¹⁻ᵅ. A = technology, α = capital's share

Capital income

MPK×K = αY

Labor income

MPL×L = (1−α)Y

Cobb-Douglas MPK

αAKᵅ⁻¹L¹⁻ᵅ = αY/K

Cobb-Douglas MPL

(1−α)AKᵅL⁻ᵅ = (1−α)Y/L

Disposable income

Y-T

Consumption function

C = C(Y − T)

change in C per $1 of extra disposable income

ΔC ÷ Δ(Y − T)

Investment function

I = I(r). depends negatively on the real interest rate

Aggregate demand

C(Ȳ − T̄) + I(r) + Ḡ

Aggregate supply

Ȳ = F(K̄, L̄)

Goods-market equilibrium

Ȳ = C(Ȳ − T̄) + I(r) + Ḡ. r adjusts to clear this market

Private Savings

(Y − T) − C

Public Savings

T - G

National Savings(S)

private saving + public saving. (Y−T) − C + T − G = Y − C − G

Budget surplus

T − G (if T > G); deficit = G − T (if G > T); balanced if T = G

Loanable-funds equilibrium

S = I ⇔ Y − C − G = I ⇔ Y = C + I + G. ties the goods market and loanable-funds market together

sum rule for changes

Δ(X + Y) = ΔX + ΔY

product rule for changes

Δ(XY) = (ΔX)(Y) + (X)(ΔY

Change in Consumption Spending

ΔC = MPC × (ΔY − ΔT) = MPC·ΔY − MPC·ΔT

vertical loanable-funds supply curve

S̄ = Ȳ − C(Ȳ − T̄) − Ḡ

M0

currency in circulation + reserve balances

M1

M0 + demand deposits + traveler's checks + other checkable deposits

M2

M1 + money market mutual fund balances + savings deposits (small time deposits)

velocity

V=T/M

income version, using nominal GDP as a proxy for T

V = (P×Y)/M, i.e. M×V = P×Y

Quantity equation

M × V = P × Y. an identity

Money demand (quantity theory)

(M/P)ᵈ = kY, where k = 1/V

Quantity equation in growth rates

ΔM/M + ΔV/V = ΔP/P + ΔY/Y

Quantity theory of inflation

π = ΔM/M − ΔY/Y. since the theory assumes ΔV/V = 0

real interest rate (realized)

r = i − π

Fisher equation

i = r + π

Ex ante real rate

i − Eπ. expected at the time of the loan

Ex post real rate

i − π. actually realized

General money demand

(M/P)ᵈ = L(i, Y) = L(r + Eπ, Y). depends negatively on i, positively on Y

Money-market equilibrium

M/P = L(r + Eπ, Y)

solves for the nominal rate given r and expected inflation

i = r + Eπ