2nd Year Macroeconomics Final (minus Chapter 7)

Total GDP Product Approach

Σ(Total Value Final Goods - Total Value Intermediate Goods)

Total GDP Expenditure Approach

C + I + G + NX

Total GDP Income Approach

WI + ATP + II + Tpa

CPI

(Base Year Quantities @ New $) / (Base Year Quantities @ Base $)

Implicit Price Deflator

(Nominal GDP / Real GDP) * 100

Nominal Interest Rate

Real Interest Rate + Inflation

Private Disposable Income (Yd)

Y + NFP + INT - T + TR

Private Sector Saving (S^P) [1]

Y^d - C

Private Sector Saving (S^P) [2]

Y + NFP + TR + INT - T - C

Government Saving (-Government Deficit) (S^g)

T - TR - INT - G

National Saving (S) [1]

S^p + S^g

National Saving (S) [2]

Y + NFP - C - G

National Saving (S) [3]

I + NX + NFP

National Saving (S) [4]

I + CA

Unemployment Rate

# Unemployed / Labour Force

Participation Rate

Labour Force / Working Age Population

Employment Population Ratio

Employment / Working Age Population

Labour Force Equation

Employed + Unemployed

Consumer Time Constraint

L + N^S = H

Conusmer's Budget Constraint [1]

C = wN^S + 𝜋 − T

Conusmer's Budget Constraint [2]

 C = w(h - l) + 𝜋 − T

Current Work-leisure Optimal Consumption Bundle

MRS_l,C = w

Labour Supply Curve

N^S(w) = h – l(w)

Perfect Complements Goods Market Ratio

C = al

Current Production Function

Y = zF(K, N^D)

Labour Market Profit Maximization Condition

MP^N = w

Labour Market Profit Formula

Π = zF(K, N^d) - wN^d

Income-Expenditure Identity

Y = C + G

PPF (no distortion)

C = zF(K, Nd) - G

Competitive Equilibrium (no distortion)

𝑀𝑅S_l,C = 𝑀𝑅𝑇_l,C = 𝑀𝑃^N = w

Pareto Optimum (no distortion)

𝑀𝑅S_l,C = 𝑀𝑅𝑇_l,C = 𝑀𝑃^N = w

PPF (distortion)

C = z(h – l) - G

Conusmer's Budget Constraint (distortion)

C = z(1 - t)(h - l)

Profit Formula (distortion)

 Π = (z - w)N^d

Labour Demand Curve Distortion Assumption

w = z

Competitive Equilibrium (distortion)

𝑀𝑅S_l,C = -w

Pareto Optimum (distortion)

𝑀𝑅S_l,C = 𝑀𝑅𝑇_l,C

Government Revenue

REV = tz[h – l(t)]

Tax Rate Formula

t = G/Y

Consumer Current Period Budget Constraint

c = y - t - s

Consumer Future-Period Budget Constraint

c’ = y’ - t’ + (1 + r)s

Consumer Lifetime Budget Constraint

c + c’/(1 + r) = y - t + (y’ - t’)/(1 + r)

Consumer “PV” Lifetime Budget Constraint

c + c’/(1 + r) = y + y’/(1 + r) - t - t’/(1 + r)

Wealth Formula (1)

c + c’/(1 + r)

Wealth Formula (2)

y - t + (y’ + t’)/(1 + r)

Simplified Consumer Lifetime Budget Constraint (Slope-Int Form)

c’ = -(1 + r)c + (1 + r)we

Credit Market Optimal Consumption Bundle

MRS_l,C = 1 + r

Perfect Complements Credit Market Ratio

c’ = ac

Perfect Complements Simplified Consumer Lifetime Budget Constraint (Slope-Int Form)

c’ = [(a)(we)(1 + r)] / (1 + r + a)

Government Current Period Budget Constraint

G = T + B

Government Future Period Budget Constraint

G’ = (1 + r)B = T’

Government’s “PV” Lifetime Budget Constraint

G + G’/(1 + r) = T + T’/(1 + r)

Credit Market Equilibrium Condition

S^P = B

Credit Market Current Shared Tax Burden

T = Nt

Credit Market Future Shared Tax Burden

T’ = Nt’

Credit Market Interest Rate Differences

Private Borrow Rate > Private Lender Rate = Public Borrow/Lend Rate

Good Borrowers (Never Default)

a

Bad Borrowers (Always Default)

1 - a

Bank Loan Profit Average

π = aL(1+r₂) - L(1+r₁) = L[a(1+r₂) – (1+r₁)]

Loan Rate Formula (zero profits)

r₂ = (1 + r₁)/a - 1

Default Premium

r₂ - r₁ = x

Collateralized Consumer Lifetime Budget Constraint

c + c’/(1 + r) = y - t + (y’ - t’ + pH) / (1 + r) = we

Collateral Constraint (1)

-s(1 + r) =< pH

Collateral Constraint (2)

c =< y - t + (pH)/(1 + r)

Population Growth

N’ = (1 + n)N

Pay-as-you-go Benefits Constraint

n > r

Government Balance Budget

Nb = N’t

Pay-as-you-go Tax to Benefits Relationship

t = b/(1 + n)

Real Consumer Current Budget Constraint

C + S^P = w(h - l) + π - T

Real Consumer Future Budget Constraint

C’ = w’(h - l’) + π’ - T’ + (1 + r)S^P

Real Consumer Lifetime Budget Constraint

C + C’/(1 + r) = w(h - l) + π - T + (w’(h - l’) + π’ - T’) / (1 + r)

Future Work-leisure Optimal Consumption Bundle

MRS_l’,C’ = w’

Future Production Function

Y’ = z’F(K’, N^D’)

Firm Capital Stock Equation

K’ = (1 - d)K + I

Firm Current Profits

π = Y - wN - I

Firm Future Profits

π’ = Y’ - w’N’ + (1 - d)K’

Firm “PV” Lifetime Profits

V = π + π’/(1 + r)

Marginal Cost Of Investment [MC(I)]

MC(I) = 1

Marginal Benefit Of Investment [MB(I)]

MB(I) = [MPk’ + (1 - d)] / (1 + r)

Firm Optimal Investment Rule [1]

MB(I) = MC(I)

Firm Optimal Investment Rule [2]

MP’_K - d = r

Asymmetric Firm Optimal Investment Rule

MP’_K - d - x = r

Marginal Propensity to Consume (MPC) [1]

MPC = length(BD) / length(AB)

Marginal Propensity to Consume (MPC) [2]

MPC = [(Y₂^D - Y₁^D) - (1 - MPC)(G₂ - G₁)] / (Y₂^D - Y₁^D)

Demand Multiplier

(Y₂^D - Y₁^D) / (G₂ - G₁) = 1