2nd Year Macroeconomics Chapter 7 & 11

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

Malthusian Production Function

Y = zF(L, N)

Population and Per-Capita Consumption Growth Relationship

N’/N = g(C/N)

Malthusian Per Worker Production Function

y = zf(l)

Output Per Worker

Y/N

Land Per Worker

L/N

Consumption Per Worker

C/N

Malthusian Equilibrium Condition

zf(l) = c

Consumption-Savings Behavior

C = (1 − s)Y

Per Worker Production Function

 y = zf(k)

Investment to Savings Relationship

I = sY

Steady-State Quantity of Capital Per Worker

k’ = [szf(k)]/(1 + n) + [(1 - d)k]/(1 + n)

Solow Growth Distribution Of Income

Y_i = MP_KK_i + MP_NN_i

Capital Share Of National Income

CAPS = kMP_K / zf(k)

Cobb-Douglas Production Function

Y = szF(K, N) = zK^𝛼N(^1-𝛼)

Solow Residual Formula

z = Y / 𝑘^𝛼𝑁^(1−𝛼)